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A liquid is an almost incompressible fluid. A fluid is defined as “a substance that flows under an applied shear stress”. Gases, plasma and (to a lesser extent) some plastic solids can also be considered to be fluids. We can think of liquids in general terms as fluids that are not gases or plasmas, and that can flow into, and adopt the shape of, a container.
We can also consider liquids to be a slightly mobile state of matter in that sense that they are more mobile than solids, but not as mobile as gases. The molecules in a liquid have more kinetic energy than solids, but less kinetic energy than gases. The force of attraction between the molecules in a liquid is thus able to keep the molecules together to some extent.
A substance becomes a liquid (as opposed to a solid) when its temperature reaches the melting point of the substance, providing the pressure does not exceed that of the triple point of the substance. The triple point is the temperature and pressure at which all three forms of a substance (gas, liquid and solid) can co-exist in thermodynamic equilibrium.
Liquids are affected by gravity, which means they will always flow from a higher elevation to a lower elevation unless acted upon by some force other than gravity. For example, a river always flows downhill from its source (typically located at some point well above sea level), either to the sea itself or into another river as a tributary. If poured into a container, the liquid will fill the container to some level, and will adopt the shape of the container. Unlike a gas, however, a liquid maintains an (almost) constant volume regardless of pressure.
In a solid, the elementary particles making up the substance (atoms, ions or molecules) are held in place by interatomic or intermolecular forces of attraction. They do not have enough energy to break free of these bonds, and can only vibrate around their fixed positions. In a liquid, the particles have acquired enough kinetic energy to overcome these bonds to the extent that they are able to move around each other.
The particles in a liquid are still relatively close together, which is why a liquid is (usually) very difficult to compress. However, for any particular substance, its elementary particles are not so close together in the liquid state as they are in the solid state (one notable exception to this rule is water, which is denser as a liquid than as a solid). This means that a substance in the liquid state usually has a greater volume - because of its lower density - than it does as a solid.
The ability of elementary particles in a liquid to move around one another means that they do not maintain a rigid shape. This is why a liquid can adopt the shape of its container, and why it can be displaced by an object immersed in it. Each elementary particle has many immediate neighbours, but there is no long-range order of the kind found in crystalline solids. Even so, the particles cannot completely overcome the chemical bonds holding them together. This means that a liquid will have a definite volume at a constant temperature and pressure.
A liquid will adopt the shape of its container
Although there are obvious differences between liquids and solids, they share the distinction of being classed as condensed matter, which is the term used to describe all forms of matter in which the elementary particles adhere to each other. To put this into perspective, most of the matter in the universe (as far as we can ascertain) takes the form of gas or plasma.
Most of the liquids we encounter in our daily lives are either chemical compounds, solutions, or mixtures. In fact, the only elemental substances that are liquids at room temperature (or slightly above room temperature) are mercury, francium, cesium, gallium, rubidium (all metals) and bromine (a halogen). Water (H2 O), in its purest form, is a chemical compound in which each molecule consists of two hydrogen atoms and one oxygen atom.
Seawater is actually a solution, consisting for the most part of various salts dissolved in water. Other liquids are typically mixtures of two or more different liquids and/or solids, like the antifreeze mixture in a car - usually a mixture of an alcohol-based antifreeze agent and water (when one liquid can completely dissolve in another liquid, the two liquids are said to be miscible). Actually, the terms solution and mixture are often used interchangeably, but there are subtle - and in some cases not so subtle - differences.
The liquid state is actually the least common state of matter in the known universe, because a substance can only exist as a liquid at relatively high pressures and within a fairly narrow range of temperatures. If you were somehow able to suddenly put a quantity of liquid water into space, for example, it would rapidly boil because of the lack of pressure and then freeze due to the incredibly low temperatures, resulting in a cloud of tiny frozen water crystals.
Liquid quantities are usually expressed in terms of their volume. The SI unit for volume is the cubic metre (m3), although liquid quantities are more often expressed in terms of smaller units, typically litres (a litre has a volume of one thousandth of a cubic metre - 0.001 m3) or millilitres (a millilitre has a volume of one thousandth of a litre - 0.001 l).
Note that the volume of a liquid does not depend on the container in which it is placed. If the container’s volume is less than that of the liquid poured into it, the liquid will spill out of the container. Conversely, if the container’s volume is less than that of the liquid poured into it, there will be space left in the container. Once in the container, and assuming that the container is either closed off or left undisturbed, the liquid will remain there. Its volume will not change unless either the temperature of the liquid changes or some of the liquid is lost through evaporation (we’ll look at what evaporation is in due course).
Liquids of various kinds are used in countless applications. They can be used as lubricants, solvents, cleaning agents, paints, dyes, and inks. The fact that a liquid cannot easily be compressed means that it can be used to transfer mechanical power, making it ideal for use in all kinds of hydraulic systems, and in automotive transmission and vehicle braking systems.
Water, the most abundant liquid on Earth, is used in the cooling systems of everything from computers and motor vehicles to nuclear reactors and rocket launch systems. It flows in the radiators that heat our homes, schools, and places of work, and is used as a heat exchange agent in ventilation and air conditioning systems.
The power of flowing water in rivers and streams has been harnessed by humans for centuries to turn waterwheels that supply water for irrigation systems, or provide mechanical power for machining and milling. Today, it is used to generate electricity in hydro-electric power plants. It is also worth remembering that without water, life on our planet - or at least life as we know it - would not exist!
As we have mentioned, a substance in the liquid state is able to flow and adopt the shape of its container. Some liquids, however, demonstrate these characteristics more readily than others. Water, for example, appears to flow effortlessly, and will immediately adopt the shape of any vessel into which it is poured. Treacle, on the other hand, will flow only very slowly, and when poured into a container it can take a significant amount of time for all of the treacle to reach a uniform depth within the container. You have no doubt also noticed that treacle is considerably more “sticky” than water.
The interactions between different liquids also vary. Some liquids combine easily - alcohol and water, for example. Oil and water, on the other hand, do not mix at all under normal circumstances. The chemical properties of liquids vary considerably, too. Some liquids react vigorously with certain chemicals, some liquids are commonly used as solvents, and some liquids are highly flammable. In short, different liquids can display a huge variety of physical and chemical characteristics.
The characteristics of a particular liquid, and the ways in which it interacts with other substances, are largely determined by the kind of intermolecular forces at work within the liquid. We will be looking at the different types of intermolecular bonding in due course. Meanwhile, here are some of the physical characteristics that can be used by scientists to identify a particular liquid:
We will be exploring some of these physical characteristics in more detail in due course.
The chemical properties of various liquids are also highly diverse. The kind of things chemists are interested in will include the pH (acidity or basicity) of a liquid, the flammability and heat of combustion of the liquid, the electrical conductivity of the liquid, and how it reacts with other substances, especially water.
Technically, all solutions are mixtures, but not all mixtures are solutions. A solution is said to be a homogenous mixture in which two or more substances are mixed in such a way that the resulting liquid behaves as if it were a single substance. The solution is said to be composed of a single phase in that it is chemically and physically uniform throughout. Soda water, for example, is a solution in which carbon dioxide is dissolved in water. The dissolved gas is not visible to the naked eye, and will not cause beams of light to scatter. A solution is also stable. Its components will not separate if the solution is left to stand, and cannot be made to do so through mechanical means, or by filtration.
We usually refer to the component forming the largest fraction of the solution as the solvent, while the component (or components) forming the smaller fraction is the solute. The distinction becomes somewhat ambiguous when the solvent and the solute are present in equal quantities as is the case, for example, with a solution consisting of 50% water and 50% ethanol. We can nevertheless make a distinction by choosing to designate the solvent as the substance most commonly used as such - in this case, water.
Most of the solvents used in the field of chemistry are molecular liquids of one kind or another that can generally be classified as either polar or non-polar, depending on whether or not the molecules have a permanent electric dipole moment (separation of positive and negative electrical charge).
The ease with which a solute can be dissolved in a solvent is referred to as its solubility. The solubility of a given solute will vary, depending on the solvent used. Almost all gases, liquids and solids can be dissolved in a liquid solvent, and virtually all types of liquid can behave as solvents - even molten metals! The choice of solvent used, however, will depend on the chemical properties of the substance (or substances) to be dissolved - not all substances will dissolve in all solvents. A generally accepted rule of thumb is that “like dissolves like”, in the sense that non-polar solutes tend to dissolve more readily in non-polar solvents, while polar solutes dissolve more readily in polar solvents.
In order for a substance to be used as a solvent, it must be able to form chemical bonds with the substance it is intended to dissolve (the solute). These bonds are not as strong as the bonds, known as primary bonds, that hold the atoms together in an elemental substance or chemical compound, and are thus known as secondary bonds.
In non-polar solvents, the average distribution of the electrons throughout each solvent molecule over time is symmetric. At any given instant, however, the distribution of electrons is asymmetric, resulting in the formation of a temporary dipole due to a charge imbalance in the molecule. This charge imbalance can induce a temporary dipole of opposite charge in a nearby (and similarly non-polar) atom or molecule, enabling a momentary dipole-dipole bond to be formed between the two entities. The forces responsible for creating bonds of this type are known as London dispersion forces or just dispersion forces.
In polar solvents, the positive dipole of each solvent molecule will attract the negative dipole of a neighbouring molecule (or a negative ion), while the negative dipole of the solvent molecule will attract the positive dipole of a neighbouring molecule (or a positive ion). The forces involved in bonds of this kind are commonly called dipole-dipole interactions, although if they occur between ions and molecules, it would be more accurate to refer to them as ion-dipole interactions.
Another factor in the efficacy of a given polar solvent is whether or not it can form hydrogen bonds. This type of bond occurs when a hydrogen atom that is covalently bonded to a highly electronegative atom such as oxygen (the proton donor) is attracted to another highly electronegative atom (the proton acceptor). In a water molecule, each hydrogen atom’s electron is strongly attracted by the electronegative oxygen atom, and as a result spends most of its time around the oxygen atom’s nucleus. Consequently, the hydrogen atom has a net positive charge. Furthermore, because the hydrogen atom is very small compared to the oxygen atom, its charge density is relatively high.
A hydrogen bond between two water (H2 O) molecules
The forces of attraction that create the secondary bonds between solvents and solutes - dispersion forces, dipole-dipole interactions, and ion-dipole interactions - are collectively known as Van der Waals forces. These forces are much weaker than the covalent, ionic or metallic primary bonds that hold the formula units of elemental substances or chemical compounds together. The strongest type of dipole-dipole bond is the hydrogen bond. Perhaps not surprisingly water, which is by far the most commonly used solvent, is comprised of highly polar molecules held together primarily by hydrogen bonds.
The concentration of a solution is also an important consideration since it will have a bearing on how the solution behaves in a given situation. Concentration is a measure of how much solute is dissolved in a given quantity of a solvent. We tend to use the term concentrated to describe a solution that has a relatively large amount of solute dissolved in it, whereas a solution with only a very small amount of solute is often described as dilute. These terms, however, are imprecise, and do not provide quantitative information about the solution. There are in fact a number of ways in which we can express the concentration of a solution:
The way in which the concentration of a solution is expressed will depend on who is measuring it. Percentage by volume or mass is often used in medicine, for example, to express the concentration of a drug in solution. If you have ever used Benadryl (an antihistamine medication) to relieve the symptoms of an allergy of some kind, you may have noticed that the concentration of diphenhydramine (the active ingredient) is stated on the bottle as 12.5 mg / 5 ml. This means that 5 ml of the medicine contains 12.5 mg of diphenhydramine.
If the concentration of a particular solute in a solution is expected to be very small - too small, perhaps, to be expressed as a percentage in terms of its volume or weight, we might use parts per million (ppm) or parts per billion (ppb). This could be the case, for example, if we wished to express the amount of a contaminant, such as lead or mercury, found in a sample of seawater, or in a sample of water taken from a lake or river.
That leaves molarity. Chemists will often formulate solutions containing two or more different chemical substances in order to observe a reaction, or to create a specific compound. They need to know that the correct amount of each substance has been used so that all of the reactants will participate in the reaction.
Consider the compound silver chloride (AgCl), which is used (for example) in the production of stained glass, and as an anti-microbial agent. This chemical compound can be created quite simply in a laboratory by mixing an aqueous solution of potassium chloride (NaCl) with an aqueous solution of silver nitrate (AgNO3 ). The reaction that will take place is as follows:
KCl(aq) + AgNO3 (aq) → KNO3 (aq) + AgCl(s)↓
In order for the reaction to proceed efficiently, we need one elementary entity of potassium chloride to combine with one elementary entity of silver nitrate. The term elementary entity refers to the smallest amount of a substance (i.e. a chemical element or compound) that can exist independently. For a given substance, the elementary entity could be a single atom, a molecule, or a formula unit (as is the case for both of the compounds involved here). If you study the formula, you can see that once the reaction has taken place, we are left with an aqueous solution of potassium nitrate (KNO3 ) and a precipitate of insoluble silver chloride (AgCl).
But how does the chemist know how much of each of these two compounds to put into solution to ensure that the same number of elementary entities of each are present? That is where molarity comes in. Essentially, for any elementary substance or chemical compound, a mole of substance (mol) is defined as NA elementary entities, where NA is the Avogadro constant (NA = 6.022 140 76 × 10 23 mol −1). Chemists can determine the exact weight of one mole of a substance by consulting the relevant tables. Once this is known it is relatively easy to calculate how much of each substance should be used in order to achieve a given chemical reaction.
Before we leave the subject of concentration, it should be pointed out that there are (usually) limits on how much of a given solute will dissolve in a specific quantity of a given solvent, and that these limits can vary with temperature and pressure. For example, at standard temperature and pressure, one litre of water will dissolve a maximum of 359 grams of sodium chloride. Once this limit has been reached, the solution is said to be saturated. If you add more sodium chloride to a beaker containing an already saturated sodium chloride solution, you will observe that the additional sodium chloride will not dissolve, and will instead settle to the bottom of the beaker.
If the solute is a gas, then once the solution reaches the saturation point, attempting to add more gas will usually result in the excess gas simply bubbling off from the surface of the liquid. The solubility of a gas typically increases with pressure, which is why, when you open a can or a bottle containing a carbonated drink and pour some into a glass, bubbles will start to form in the glass and rise to the surface. Because the pressure on the liquid has now been reduced, the carbonated drink can no longer hold so much dissolved carbon dioxide.
Note that some solutions never become saturated because the components can be mixed in any proportion. A good example, and one we have already mentioned, is a mixture of water and ethanol. If there is more water than ethanol, then the water is the solvent and the ethanol is the solute. If there is more ethanol than water, the opposite is true. Either way, the solution will never become saturated.
Other kinds of mixture are said to be heterogeneous because the composition of the mixture is not uniform throughout. Blood is an example of a heterogeneous mixture, because it is composed of red and white blood cells, plasma, thrombocytes (or platelets - small, colourless cell fragments that form clots and inhibit bleeding), various proteins, and other substances.
Heterogenous mixtures can be further classified as colloids, suspensions or emulsions. A colloid (or colloidal dispersion) is a mixture in which insoluble microscopic particles of a substance, either a solid or another liquid, are evenly distributed throughout a liquid. Examples of colloids include milk, butter, and gelatine.
A suspension is a mixture in which somewhat larger particles of a solid are distributed throughout a liquid. Over time, if the suspension is left undisturbed, a process of sedimentation will occur, in which gravity causes the dispersed particles to settle to the bottom of the mixture. If the suspension is contained within a glass receptacle such as a test tube or beaker, the sediment will be clearly visible at the bottom of the receptacle.
The sedimentation process can be speeded up using a centrifuge. If you donate blood, for example, the blood is typically sent to a laboratory where the red blood cells, platelets and plasma, each of which has different medical uses, can be separated out in a centrifuge.
An emulsion is a mixture of two or more liquids that do not normally mix (for example, oil and water), typically created by prolonged and vigorous shaking of the mixture. Liquids that do not usually mix are said to be immiscible. Technically, an emulsion is also a colloidal dispersion because microscopic particles of one liquid are distributed throughout another liquid. The distinction between the two is that the insoluble particles in a colloid can be either solids or liquids, whereas those in an emulsion must be liquids.
Homogenous and heterogeneous mixtures can be collectively referred to as complex liquids because they all consist of two or more substances. They are neither elemental substances nor chemical compounds. Indeed, any complex liquid you can think of can vary considerably in its composition. Samples of seawater taken from different locations, for example, will exhibit subtle, and sometimes not so subtle, differences in both the concentration and type of the salts and other substances they contain. Even two different batches of the same colloid or suspension produced under laboratory conditions are not guaranteed to be 100% identical.
Complex liquids tend not to have fixed melting or boiling points. They may freeze at a certain temperature, and become a liquid again when they are heated without undergoing physical changes (although this will not always be the case). When sufficiently heated, a complex liquid will also boil, but it will not transition to a gas because it will decompose chemically. If we apply sufficient heat to a sodium chloride solution, for example, the water will boil away and the sodium and chlorine ions will recombine to form solid sodium chloride crystals.
At a given pressure, the temperature at which a complex liquid boils will depend on its composition. Saltwater has a higher boiling point than pure water, for example. The exact temperature at which it boils will depend on the concentration of salt - higher concentrations tend to have a higher boiling point. Melting points are actually lower for saltwater solutions, which is why we use salt on icy roads and pavements to encourage the ice to melt.
For some substances, the distinction between the liquid and solid states can become blurred. For example, it has often been claimed that glass is actually a liquid rather than a solid, despite the fact that it feels solid to the touch. As evidence for this claim, we are invited to examine the windows in medieval buildings such as churches. Some of these buildings still have their original glass windows, close examination of which shows that the panes are thicker at the bottom than at the top, suggesting that some of the glass has “flowed” downwards under the influence of gravity.
Despite the apparent ability to “flow” downwards over time, glass is not a true liquid
Photo by Krisztina Papp
If glass is indeed a liquid, the reasoning goes, then the fact that it is hard leads to the erroneous conclusion that it must be a supercooled liquid. In fact, glass is neither a liquid nor a true solid, but an amorphous solid, which is essentially somewhere between the two states of matter. The word amorphous means that glass does not have the long-range order characteristic of most solids.
The most common form of glass used today is made using a mixture of silica sand (SiO2 ), sodium oxide (Na2 O), and calcium oxide (CaO). Once mixed in the correct proportion, the materials are heated to around 1500° Celsius to create molten glass. The glass is rapidly cooled, but does not immediately solidify when its temperature drops below the melting point of glass. At this point, it is indeed a supercooled liquid. In order for the glass to become an amorphous solid, it must be cooled further until the movement of its molecules has almost ceased. The molecules are not in an ordered state, but given enough time they will eventually rearrange themselves and adopt a more stable formation.
Liquid crystals provide a further example of a state of matter that falls somewhere between that of a conventional liquid and that of a crystalline solid. The molecules of liquid crystals can flow like a liquid, but can also be oriented in a manner typical of crystalline substances. Liquid crystal materials occur throughout nature, both in biological systems and as inorganic compounds. Man-made liquid crystals are used in a number of technological applications, notably in liquid crystal displays (LCDs).
A digital alarm clock with a liquid crystal display
Liquid crystal substances are composed of large, elongated and rod-like molecules that are either strong dipoles in their own right or that can be easily polarised. They are also all anisotropic to some degree. This means that their molecules have a strong tendency to align along a common axis called the director. The properties of an anisotropic material, including its refractive index, will have different values when measured in different directions.
When an external electric field is applied to an anisotropic material, the director tends to align itself with the field, changing the optical properties of the material. In the most basic type of LCD display, each display element consists of a thin layer of a liquid crystalline material that will either allow or block the transmission of light, depending on whether or not a voltage is applied to it.
In the remainder of this article, we will be mainly concentrating on the properties of substances that are true liquids at standard temperature and pressure (we will be looking at amorphous solids in more detail elsewhere).
The electrical conductivity of a liquid is of interest to chemists because when sufficient electric current is passed through a conductive liquid, it can generate a chemical reaction. The type of reaction depends on the composition of the liquid, which will also determine the degree to which the liquid conducts electricity. Some liquids are better conductors of electricity than others. Pure water, for example, is a relatively poor conductor, whereas an aqueous salt solution containing sodium chloride (NaCl) conducts electricity readily because the dissolved NaCl separates into positively and negatively charged ions (Na+ and Cl-), which facilitates the flow of electric current.
A process known as electrolysis is used in the study of chemistry and in manufacturing to separate chemical compounds into their constituent elements. The process was officially discovered in 1800 by the English scientist William Nicholson (1753-1815) and English surgeon Sir Anthony Carlisle (1768-1840), when they split water into hydrogen and oxygen using a voltaic pile.
Engraving showing Carlisle and Nicholson using electrolysis to decompose water into oxygen and hydrogen
Electrolysis requires a direct current power source, an electrolyte typically consisting of an aqueous solution of an ionic chemical compound, and two (preferably non-reactive) electrodes, which are immersed in the electrolyte. Each electrode is connected via a wire to a different terminal of the dc power source. When a current is applied, positively charged ions (cations) are attracted to the negative electrode, and negatively charged ions (anions) are attracted to the positive electrode.
The products of electrolysis will depend on the nature and concentration of the electrolytic solution, and to a lesser extent the potential difference applied across it. For example, electrolysis of a dilute sodium chloride solution will result in chlorine gas being produced at the positive electrode (cathode) and hydrogen gas being formed at the negative electrode (anode). Any sodium atoms produced at the anode will react with the water to form sodium hydroxide. If the electrolysis process continues for a sufficient amount of time, the result will eventually be a sodium hydroxide solution.
Electrolysis of sodium chloride in aqueous solution produces chlorine and hydrogen
Electrolysis is used in industry for a range of applications, including the extraction and refining of metals such as aluminium and copper, the production of chemicals such as sodium hydroxide and chlorine, and for electroplating (the process of coating an object with metal to give a decorative or protective finish). As we have already noted, the electrolysis of water can be used to produce hydrogen and oxygen, although it is not a particularly cost-effective method of doing so.
The intermolecular forces of attraction holding the molecules of a liquid together are called secondary bonds because they are much weaker than the covalent, ionic or metallic bonds (known as primary bonds) that hold the atoms of an individual molecule together. Because these secondary bonds are relatively weak, the molecules in a liquid are not fixed in place. They tend to remain together, but can move around one another, which is why liquids can flow and adapt to the shape of any container into which they are poured.
You may recall that we have already touched upon the subject of secondary bonds in our discussion of solutions. They are collectively known as Van der Waals forces, and can be broadly categorised as dipole-dipole interactions, ion-dipole interactions, dispersion forces, or hydrogen bonds. Note that some texts assert that the hydrogen bond does not conform to the strict definition of a Van der Waals force due to its partially covalent nature. However, it is essentially a very strong dipole-dipole interaction, so we will ignore the distinction for the purposes of this discussion.
Water molecules form hydrogen bonds with one another
We will concern ourselves mainly with molecular liquids here, although it is worth noting that non-molecular liquids also exist. Molten salts, for example, are ionic liquids, and continue to be held together by metallic bonds, even though they no longer have an ordered structure. And, as we have already seen, ionic compounds like sodium chloride (NaCl) form ion-dipole bonds in aqueous solutions. These ion-dipole bonds are significantly stronger than hydrogen bonds because each ion carries a net positive or negative charge.
Water molecules form ion-dipole bonds with Na+ ions (left) and Cl- ions (right)
The nature of the intermolecular forces that hold the molecules of a liquid substance together are responsible for determining the cohesion of that substance - essentially, a measure of how strongly the molecules attract one another. This will have a bearing on the overall characteristics of the liquid, such as its melting and boiling points. Water, for example, has strong intermolecular bonds as we have already seen, and consequently has high cohesion. Motor oil, on the other hand, has weak intermolecular bonds, and thus low cohesion, allowing the molecules to move around each other more freely - one of the reasons it is a good lubricant.
Essentially, all intermolecular forces, whether attractive or repulsive, are electrostatic in nature. They are the result of a positive or negative electrical charge in one molecule interacting with a positive or negative electrical charge in another molecule. The way in which charge is distributed within an individual molecule will therefore play a large part in determining how that molecule interacts with other molecules, and the charge distribution within a molecule depends in turn on the nature of the forces holding the individual atoms together within the molecule.
As previously mentioned, molecular liquids are generally categorised as either polar or non-polar, depending on whether or not the molecules have a permanent electric dipole moment (separation of positive and negative electrical charge).
Hydrogen bonds are by far the strongest type of bond found in molecular liquids, but not all molecular liquids can form hydrogen bonds. As we have seen, hydrogen bonds occur when a hydrogen atom that is covalently bonded to a highly electronegative atom (the proton donor) is attracted to another highly electronegative atom (the proton acceptor). The hydrogen bond is the result of the electromagnetic attraction between the positive charge on the proton donor’s hydrogen atom and the negative charge on the proton acceptor.
The only elements whose atoms are sufficiently electronegative - and sufficiently small - to participate in a hydrogen bond are nitrogen, oxygen, and fluorine. Chlorine, for example, has an electronegativity that falls between that of nitrogen and that of oxygen, but because of its larger size, it cannot form hydrogen bonds because its electron density is too low.
At this point it might be useful to delve a little deeper into the nature of intramolecular bonds. Electronegativity (or electron affinity) is the degree to which an atom of a particular element can attract a shared electron when participating in a chemical bond. Electronegativity is a dimensionless property, and values are usually assigned according to the Pauling Scale. This scale gives fluorine - the most electronegative element - a value of 3.98. All other elements are assigned a value depending on their electronegativity relative to fluorine. The version of the periodic table shown below gives the Pauling Scale electronegativity values for each element.
The periodic table, showing the Pauling Scale electronegativity value of each element
In the article “Chemical Bonding” in this section we looked at three different types of intramolecular bond - covalent, ionic and metallic. In this article we are primarily interested in molecular liquids, so the intramolecular bonds we are dealing with are (mostly) covalent in nature. Covalent bonds can be either polar or non-polar. In a purely non-polar covalent bond, the shared electrons reside half way between the bonded atoms. This requires the atoms in question to have the same electronegativity, so purely non-polar covalent bonds only occur in simple molecules involving atoms of the same type - for example hydrogen (H2 ), oxygen (O2 ), or chlorine (Cl2 ) molecules.
A polar covalent bond occurs when one of the bonded atoms has a greater electronegativity, and thus a greater attraction for the shared electrons, than the other bonded atom. The result is that one end of the bond achieves a greater electron density and becomes slightly negative, while the other end, with a lower electron density, becomes slightly positive. The difference in electron density will be proportional to the difference in electronegativity between the two bonded atoms.
The negative and positive charges created by the asymmetric distribution of electrons in polar covalent bonds are referred to as net atomic charges (or partial charges) because they have a non-integer value when measured against elementary charge units. They are usually represented using the Greek lowercase letter 𝛿 (delta), i.e. as either 𝛿− or 𝛿+. Note that although the difference in electronegativity between the bonded atoms creates partial charges at each end of the bond, it does not change the molecule’s overall charge.
As we have previously mentioned, the separation of charge in a single covalent bond - its dipole moment - is created by differences in the electronegativity of its constituent atoms. Determining the overall dipole moment of a molecule is a somewhat more complex, and will require an examination of several factors.
The first consideration is something called the Lewis structure of the molecule. We look in more detail at how the Lewis structure of a particular molecule is derived elsewhere, but the basic idea is to find the total number of valence electrons available, deduct the number of valence electrons involved in intramolecular bonds, and work out how the remaining valence electrons are distributed among the outermost atoms.
The second consideration is the molecule’s geometry. Whereas a large difference in electronegativity within a molecule can result in the formation of more polar compounds, symmetry can balance out net polarities and cause electrostatic forces working in opposite directions to cancel each other out.
As we have seen, the attraction between the positive dipole of one molecule and the negative dipole of another can create a dipole-dipole intermolecular bond. A good example of this type of bond - one that does not involve hydrogen bonds - can be found in dichloromethane (CH2 Cl2 ), a colorless and volatile liquid that is used as a solvent in a number of chemical processes, and as a propellant in aerosol sprays. A dichloromethane molecule consists of a single carbon atom covalently bonded to two hydrogen atoms and two chlorine atoms, as shown in the illustration below.
A dichloromethane (CH2Cl2) molecule
As you can see, the dichloromethane molecule contains two chlorine atoms, two hydrogen atoms and a single carbon atom. The absence of nitrogen, oxygen or fluorine in the molecule precludes the possibility of it forming hydrogen bonds with other molecules. However, since the electronegativity of the chlorine atoms (3.16 on the Pauling scale) is much higher than that of either the carbon atom (2.55) or the hydrogen atoms (2.20), the C-CL bonds are highly polar, and electron density within the molecule is thus significantly higher around the chlorine atoms.
If the chlorine atoms were located on opposite sides of the carbon atom, the opposing dipole moments of the two C-Cl bonds would essentially cancel each other out, producing a non-polar molecule. However, the AXE formula for CH2 Cl2 is AX4 E0 , giving the molecule a tetrahedral geometry that makes it impossible for the chlorine atoms to lie on opposite sides of the central carbon atom (if you are not familiar with AXE formulae, we have covered the subject in the article "VSEPR and Molecular Geometry" in this section).
Because the CH2 Cl2 molecule is asymmetric, its electron charge density is not evenly distributed. The molecule has a significant permanent dipole moment due to the partial positive charge on the hydrogen atoms and the partial negative charge on the chlorine atoms. The CH2 Cl2 molecule is therefore a polar molecule, and can form dipole-dipole bonds with other polar molecules.
It is important to note here that, although we have talked about the different kinds of attractive forces that can contribute to intermolecular bonding, it would be misleading to say that the bond between two molecules can be attributed to only one type of bond. Often, whilst a particular bonding mechanism predominates, other forces of attraction are also making a contribution.
London dispersion forces, for example, can form between any molecules that find themselves in close proximity to one another because, even if the electrons in those molecules are evenly distributed over time, momentary charge imbalances are inevitable due to the constant movement of electrons. This enables the formation of temporary dipole-dipole bonds between molecules. The strength of the bonds created due to dispersion forces is also dependent on the size of the molecule in which they occur - larger molecules can have larger temporary dipoles, resulting in stronger bonds being formed.
Many of the liquids we are familiar with (water, for example) can also exist in a solid or gaseous state. However, we tend to refer to substances as being solids, liquids or gases depending on the state in which they are found to exist under standard laboratory conditions, which are usually defined as an atmospheric pressure of one atmosphere (1 atm, 1.01325 bar or 14.69594878 PSI) and a standard temperature of twenty-five degrees Celsius (25 °C).
Suppose we have a liquid, at standard atmospheric pressure, to which we apply a heat source. As the temperature of the liquid increases, the average kinetic energy of the liquid’s elementary particles (atoms or molecules) will also increase, and they will move around more. This causes the average distance between the particles, and thus the volume of the liquid, to increase.
When a liquid reaches a high enough temperature - its boiling point - its elementary particles will acquire enough kinetic energy to overcome the bonds holding them together and the liquid becomes a gas. The exact temperature at which this occurs will depend on the atmospheric pressure.
The lower the atmospheric pressure, the lower the temperature at which a liquid will boil. At the top of Mount Everest, which has an elevation of 29,032 feet (8,848 metres), the average atmospheric pressure is only about one third of the atmospheric pressure at sea level. As a consequence, water will boil there at just seventy-one degrees Celsius (71 °C).
Water boils at around 71° Celsius at the summit of Mount Everest
If we cool a liquid down, its elementary particles will lose some of their kinetic energy (the kinetic energy of an object or particle is the energy it has due to its motion). As the temperature of the liquid falls, the average kinetic energy of the liquid’s elementary particles (atoms or molecules) will also fall, and they will move around less. This causes the average distance between the particles, and thus the volume of the liquid, to decrease.
When the substance is cool enough, i.e. at a temperature below the melting point of the substance, the particles will not have sufficient energy to overcome the intermolecular forces acting on them, and will become locked into position in a rigid crystalline structure. The liquid will freeze and become a solid. Like the boiling point, the melting point of a substance depends on atmospheric pressure. Lower pressures mean lower melting points.
Note that the definition of standard conditions for temperature and pressure (STP) depends on the standard used. The most frequently used standards are those defined by the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST).
NIST still defines “standard atmospheric pressure” as one atmosphere (1.01325 bar), but as of 1982 IUPAC uses 1.0 bar. IUPAC defines “standard temperature” as 273.15 K (0 °C or 32 °F), while NIST defines it as 293.15 K (20 °C or 68 °F). It is quite important to be aware of these differences, because text books and other publications sometimes give the melting and boiling points of various substances with reference to “standard temperature and pressure” without actually specifying which standard (if any) is being applied.
Interestingly, only two elemental substances (mercury and bromine) are liquids at standard temperature and pressure - whichever standard is being used. By far the most abundant liquid on Earth is water - a compound of hydrogen and oxygen, and a fundamental requirement for life. Water is a liquid at a standard pressure of one atmosphere and at temperatures of between 0 °C and 100 °C.
The energy absorbed or released by a substance when it transitions from one state to another before there is any change in its temperature is called latent heat. The latent heat associated with the transition of a substance from the liquid to the solid state is called the heat of fusion. This heat energy is lost to the environment when the liquid freezes. The particles are now unable to move around one another and are fixed in place, but will continue to vibrate at the same frequency as long as the temperature remains at the freezing point of the liquid.
The latent heat associated with the transition of a substance from the liquid to the gaseous state is called the heat of vaporisation. This heat energy enables the particles to overcome the forces binding them to one another, and allows them to move freely.
Before we proceed, we should probably discuss the concept of vapour pressure. Vapour pressure, also sometimes referred to as equilibrium vapour pressure, is the pressure exerted by a vapour in thermodynamic equilibrium with one or both of its condensed (solid or liquid) phases, at a given temperature, in a closed system.
At any given temperature, the liquid will partly vaporise into the space above it. The vapour pressure of the liquid is the pressure exerted by the vapour present above the liquid surface, and is a measure of the tendency of the liquid to transition into a vapour. As the temperature of the liquid increases, the kinetic energy of the liquid’s molecules will also increase, enabling more of them to enter the vapour phase, and increasing the vapour pressure.
The temperature at which the vapour pressure at the surface of a liquid becomes equal to the pressure exerted by its surroundings is called the boiling point of the liquid. Once this point is reached, the addition of more heat will result in the transformation of the liquid into its vapour without raising the temperature further. Vapour bubbles will start to form within the liquid and rise to the surface.
The normal boiling point of a liquid is the temperature at which its vapour pressure is equal to the standard atmospheric pressure (i.e. Earth’s average atmospheric pressure at sea level, expressed as 1 atmosphere, 760 Torr, or 101.325 kPa). As we have seen, at higher elevations, where atmospheric pressure is lower, a liquid will boil at a lower temperature.
We have already seen that the temperature at which a liquid will boil depends on pressure. In fact, for any pure substance, a given combination of temperature and pressure will determine the phase of the substance. We can draw a pressure-temperature phase diagram - essentially a graph of temperature versus pressure - for any given substance that shows where the boundary lies between a solid and a gas (the sublimation curve), between a solid and a liquid (the fusion curve), and between a liquid and a gas (the vaporisation curve). The illustration below is a generic phase diagram.
A generic phase diagram
As the diagram shows, both the solid phase and the gas phase of a substance can exist simultaneously and in thermodynamic equilibrium at any point on the sublimation curve. Similarly, both the solid phase and the liquid phase can co-exist at any point on the fusion curve, and the liquid and gas phases can co-exist along the vaporisation curve.
There is one point on the graph that represents a specific temperature and pressure at which a substance can exist in all three states of matter, simultaneously and in thermodynamic equilibrium. This point is called the triple point of the substance - a term first proposed by the British engineer and physicist James Thompson (1822-1892) - and it occurs at the junction of the sublimation curve, fusion curve and vaporisation curve. At this point, the melting point and the boiling point of the substance are the same. The triple point pressure is the lowest pressure at which a substance can exist as a liquid. Below that pressure, sublimation will occur (the substance will convert directly to the gas phase).
The triple point of water - by far the most abundant liquid on Earth - has a temperature of 273.16 K (0.01 °C) and a partial vapour pressure of 611.657 pascals (0.00603659 atm). At this combination of temperature and pressure, ice, liquid water and water vapour can co-exist in stable thermal equilibrium. Any pure substance, in fact, can exist in all three phases simultaneously (solid, liquid and vapour) at its triple point. Note, however, that a relatively small deviation in temperature or pressure can result in all of the substance entering the solid, liquid or vapour phase.
For most substances, the triple point is also the lowest temperature at which the substance can exist as a liquid. The notable exception is water, since the melting point of pure water ice decreases with pressure (this anomalous behaviour is represented by the dashed green line in the phase diagram above). If the temperature is held just below the triple point, increasing the pressure will transform water vapour to a solid, and then to a liquid. This happens because water ice is less dense than liquid water.
Whereas the triple point of a substance occurs at the lower end of the vaporisation curve, the top end of the vaporisation curve is delineated by something we call the critical point of the substance, and is the point at which both the critical temperature and the critical pressure of the substance have been reached.
The existence of a critical point was first observed by the French physicist Charles Cagniard de la Tour (1777-1859) during a series of experiments carried out in 1822 and 1823 to determine the effects of heat and pressure on various liquids. He found that, for each substance, there was a specific temperature above which the substance would not condense from the vapour phase to a liquid, no matter how much pressure was applied to it.
The existence of this critical temperature was confirmed in 1869 by the Irish chemist Thomas Andrews (1813-1885) who carried out a number of experiments involving phase transitions between gases and liquids. In one such experiment, he found that he could condense CO2 gas into a liquid by raising the pressure on the gas so long as its temperature did not exceed 31° C. Once this temperature was exceeded, the gas would not condense to form a liquid, regardless of how much pressure was applied.
We now know that every chemically pure substance has a critical temperature (Tc ) above which it can only exist as a gas and cannot condense into a liquid, regardless of the pressure acting on it. The critical pressure (Pc ) of a substance is the vapour pressure of the substance at the critical temperature. The vapour pressure of the substance never gets higher than this critical pressure, regardless of the temperature of the substance.
When both the critical pressure and the critical temperature of a substance are exceeded, the densities of the liquid and gas phases become equal. As a result, the distinction between them essentially disappears, resulting in what is known as the supercritical fluid phase. In this state, there is no way to distinguish between the liquid and gas phases, and the heat of vaporisation - the latent heat associated with the transition of a substance from the liquid to the gaseous state - becomes zero.
The concept of critical temperature and pressure can be illustrated by examining the behaviour of two gases commonly sold commercially in purpose-built steel cylinders - oxygen and propane.
Oxygen has a critical temperature of −118.6 °C and a critical pressure of 49.83962 atmospheres, so at room temperature it is well above its critical temperature but well below its critical pressure, and is comfortably within the gas phase. The cylinder will contain a uniform fluid rather than a mix of liquid and vapour. As the oxygen is used up the pressure gradually falls to one atmosphere, at which point no more oxygen will escape.
Propane has a critical temperature of 97 °C and a critical pressure of 41.8 atmospheres, so at room temperature it is well below its critical temperature. The propane in a gas cylinder is therefore a mix of liquid and vapour, and the pressure of the propane gas will be the vapour pressure of propane (9.53 atmospheres). As long as there is some liquid propane in the tank, the pressure will remain at 9.53 atmospheres. Only when all of the liquid has evaporated will the pressure begin to fall, by which time the cylinder is almost empty.
We mentioned earlier that the volume of a liquid in a container will not change unless the temperature of the liquid changes or some of the liquid is lost through evaporation - but what is evaporation? We know that if a liquid is heated to a sufficiently high temperature (its boiling point) it will transition from a liquid to a gas. Evaporation is what happens when a gas (or more accurately, a vapour) forms from a liquid at temperatures below the boiling point of the liquid.
We talked earlier about the average kinetic energy of the particles in a liquid. If this value decreases to a sufficient degree, the liquid will freeze and become a solid. Conversely, if the value becomes great enough, the liquid will boil and become a gas. Note however that individual particles within the liquid can be moving at different speeds, and thus possess different kinetic energies. Also, because the direction of movement of these particles is effectively random, the distribution of particles within the liquid is largely independent of the kinetic energy they possess.
Evaporation is possible because, at any given time, some of the elementary elements of which the liquid is composed (atoms or molecules) will have enough energy to leave the liquid phase. If these particles happen to be at the surface of the liquid, they will escape to form a vapour. We use the term vapour rather than gas because the temperatures involved are often significantly below the boiling point of the liquid. The particles escaping the liquid are therefore said to be in the vapour phase rather than in the more stable gas phase.
The rate at which evaporation occurs depends on the temperature and surface area of the liquid. At higher temperatures, a greater proportion of the particles in the liquid will have the energy needed to enable them to escape. Although the volume of a liquid is not a factor in determining the rate of evaporation, a given volume of the liquid with a large surface area will evaporate more rapidly than the same volume of liquid with a small surface area, simply because a large surface area provides more opportunities for particles with sufficient energy to escape the liquid.
You may have noticed that a freshly mopped floor will dry relatively quickly at room temperature - usually in a matter of minutes. This is because a relatively small volume of water is distributed over a comparatively large area. You may have wondered why much larger bodies of water do not dry up as a result of evaporation. Although there are various scenarios where this can happen, mostly related to localised and extreme environmental conditions, rest assured that our lakes and oceans are not going to disappear in the foreseeable future.
Having said that, evaporation will occur at the surface of any body of water. In fact, even snow and ice will evaporate eventually, albeit at a much slower rate. In the case of Earth’s oceans, most of the water vapour generated as a result of evaporation will mix with the surrounding air to form a layer of moist air above the surface of the ocean. Since the density of the water vapour is considerably lower than that of dry air, the density of the moist air will also be lower than that of dry air. The moist air will thus rise through the troposphere (the lowest layer of Earth’s atmosphere, extending from sea level up to approximately 10,000 metres), and will be replaced by dry air.
In order for evaporation to occur, a certain amount of energy is required to break the bonds holding the water molecules together. This energy is taken from the environment, creating a cooling effect. Condensation is essentially the opposite of evaporation. It is the process by which water vapour is turned back into liquid water, and occurs when the water vapour is sufficiently cooled and bonds are formed once more between the water molecules. During the process, the water will lose some heat to the environment.
As mentioned earlier, the energy absorbed or released by a substance when it transitions from one state to another before there is any change in its temperature is called latent heat. The latent heat associated with evaporation and condensation is called the heat of vaporisation, expressed in joules or calories per mole or unit mass of the substance that is undergoing a phase change.
As we have seen, water vapour will rise through the troposphere. Because the temperature at the higher altitudes is much lower than it is at sea level, the water vapour will condense into tiny droplets of water as heat energy is lost to the environment, and becomes visible as clouds. The water droplets are initially small, and light enough to remain airborne, typically for several days, but they will eventually combine to form heavier droplets. Once the water droplets are too heavy to remain airborne, they will fall to the ground as precipitation - i.e., as rain, snow or hailstones depending on the temperature of the surrounding air.
To give you some perspective, approximately 90% of the moisture in Earth’s atmosphere is due to the evaporation of water from oceans, lakes and rivers. Oceans make by far the largest contribution, which is not surprising because they cover more than 70% of the Earth’s surface. Most of this moisture is returned to the oceans as precipitation, although some 10% of all precipitation occurs over land. At any given time, the amount of water entering the Earth’s atmosphere as water vapour due to evaporation is roughly the same as the amount of water leaving the atmosphere as precipitation.
Water vapour is in the air all around us, thanks to evaporation. The term we use to express the amount of water vapour in the air at any given time is humidity. The term relative humidity is often used to describe the amount of water vapour in the air at a given temperature as a percentage of the maximum amount of water vapour the air could hold at that temperature. Air that has a humidity of 100% is said to be saturated. At room temperature (circa 20° C), saturated air would hold approximately seventeen grams of moisture per cubic metre (17 g/m3).
Even though we can’t usually see the water vapour in the air around us, we can see what happens when it condenses. If you’ve ever enjoyed a canned beverage straight from the refrigerator on a hot day, you have probably noticed drops of water forming on the outside of the can. This is caused by water vapour in the air coming into contact with the cold surface of the can, causing it to condense. The more humid the surrounding air is (and the colder the can), the more noticeable the effect will be.
Evaporation and condensation will occur wherever there is an interface between a liquid and a gas, such as that which occurs at the surface of oceans, lakes and rivers. Evaporation and condensation will also occur within a closed system, albeit on a much smaller scale. Because the vapour phase is not stable, an exchange of particles is taking place constantly at the interface between a liquid and a gas. Fast liquid molecules at the surface of the liquid escape into the gas as vapour, whilst at the same time, slower gas molecules condense into the liquid surface.
A point will eventually be reached at which the number of particles entering the vapour phase is balanced by the number of particles re-entering the liquid phase, and the overall amount of vapour in the system remains constant. Once this point is reached, the system is said to be in a state of dynamic equilibrium. The partial pressure of the vapour at equilibrium (see above) is called the vapour pressure of the liquid.
The exchange of particles within a closed system will attain dynamic equilibrium
Why is it that some objects float when placed in water and others will sink? If you throw a stone into the sea (making sure, of course, that there is nobody swimming in the immediate vicinity), it will sink. If you throw an inflatable swimming ring into the sea, it will float. The credit for discovering the answer to the question of why some things float and some don’t is generally given to the Greek mathematician Archimedes of Syracuse (circa 287-212 BCE).
According to an account written by the Roman architect and engineer Vitruvius, about whom relatively little is known apart from his writings on the subject of architecture, Archimedes was taking a bath when he discovered the principle of buoyancy, which is today commonly referred to as Archimedes’ Principle. This principle states that if an object is fully or partially submerged, there will be an upward force exerted on the object that opposes the force exerted on it by gravity. This force is equal to the weight of the liquid displaced by the object. Immediately on making his discovery (according to Vitruvius), Archimedes leapt out of the bath and ran naked through the streets of Syracuse shouting "Eureka!", which means something like “I have it!”.
16th Century carving showing Archimedes in his bath
In a gravitational field, a liquid will exert pressure on the sides of its container. It will also exert pressure on any object fully or partially immersed in it. This pressure is exerted in all directions, and it increases with depth. If we assume that the liquid is at rest and the gravitational field is uniform then the pressure p at a given depth d in metres is given by:
p = ρgd
where ρ (the Greek lower case letter rho) is the density of the liquid (assumed to be a constant), and g is the acceleration due to gravity. Note that for this formula the pressure at the free surface of the liquid is assumed to be zero. Note also that the formula ignores the effects of surface tension (see below), which in most cases will be negligible.
From the above we can see that the pressure in a liquid will be greater at the bottom of a container than at the top. It follows that the pressure exerted on the bottom of an object immersed in a liquid will be greater than the pressure exerted on the top of the object. This pressure difference creates a net upward force - the buoyant force. The magnitude of the buoyant force is proportional to the difference in pressure, and is equal to the weight of the liquid displaced by the object, as surmised by Archimedes.
buoyancy force = weight of displaced fluid
If the buoyant force acting on an object is equal to the gravitational force exerted on the object, it will float. It follows that if the average density of an object is greater than that of the liquid in which it is immersed, and assuming that the only forces acting on the object are gravity and the buoyant force, the object will sink. If the object is less dense on average than the liquid, it will float.
The reason that ships weighing hundreds of thousands of metric tonnes can stay afloat is that they are designed to displace a large volume of water whilst being only partially submerged. The buoyancy force is equal to the weight of the displaced water, which is in turn equal to the weight of the ship. This weight is known as the ship’s displacement tonnage, or simply displacement.
A ship’s displacement tonnage represents the amount of water it displaces
Image: Chris Wells
A ship’s displacement tonnage can vary considerably depending on what the ship is carrying, and will determine the vertical distance between the waterline and the bottom of the hull. This distance is known as the draft of the ship. The more heavily the ship is loaded, the greater its draft will be. Many ships have a reference mark known as a Plimsoll line painted on both sides of the hull to indicate the maximum depth to which the vessel may safely be submerged.
Looking at the image above, it may have occurred to you that most of the ship’s hull, superstructure and cargo are above the waterline. This might lead you to question the stability of the vessel, especially when it encounters heavy seas. However, the design of the ship takes into account the need for stability. In simple terms, the aim is to make sure that the vessel is bottom-heavy as opposed to top-heavy, preventing it from capsizing.
There are two critical factors to consider in this respect. The first is the ship’s centre of gravity, which is effectively the same as its centre of mass in the Earth’s gravitational field. The second is the ship’s centre of buoyancy, which is the centre of gravity of the water displaced by the ship. A vessel will be stable so long as its centre of gravity is always below the centre of buoyancy. This is usually achieved using one or more ballast tanks located at the bottom of the hull, which can be filled with water in order to lower the vessel’s centre of gravity.
Consider an object that is completely immersed in a liquid. A submarine is a good example, because it spends most of its time underwater. If the buoyant force acting on the submarine is smaller than the force exerted on the submarine by gravity (i.e. the weight of the submarine), it will sink. If the buoyant force is greater than the weight of the submarine, it will rise. If the two forces are equal, they effectively cancel each other out and the submarine will remain at the same depth unless acted upon by some other force. In this situation, the submarine has the same overall density as the surrounding liquid.
Conceptual drawing of a Virginia-class attack submarine
Image: U.S. D.O.D. graphic by Ron Stern
When a submarine is moving in the forward direction, it can use its control surfaces (usually referred to as diving planes or hydroplanes) to make minor adjustments to its depth. More radical changes in depth are achieved by pumping water into or out of the submarine’s buoyancy tanks. In order to dive, water is pumped into the tanks. Since the submarine’s volume does not change, its density effectively becomes greater than that of the surrounding water and it sinks. In order to ascend, water is pumped out of the tanks. The submarine’s density is now less than that of the surrounding water and it rises.
Viscosity, usually denoted in formulae using the Greek letter µ, can be defined as the resistance of a liquid to the tendency to flow. We can perhaps think of it as the thickness of the liquid. Note, however, that viscosity is not the same thing as density. We can think of viscosity as the internal friction of the liquid - essentially, the friction between two adjacent layers of a liquid when those layers move relative to one another. Density, on the other hand, is a measure of the mass per unit volume of the liquid (density = mass/volume), and is not directly related to viscosity.
It is of course true that both the density and the viscosity of a liquid will vary with temperature, and that at higher temperatures the value of both of these properties will be reduced. However, whereas density tends to vary with temperature in a linear fashion, the variance in viscosity is far more dramatic. Viscosity depends in part on the strength of the intermolecular forces of attraction at work within the liquid - the stronger these forces are, the greater the viscosity will be. As the temperature increases, the molecules within the liquid will gain kinetic energy, weakening the intermolecular bonds.
You could probably think of a number of examples of liquids with that have a high viscosity at room temperature. Treacle, for example, has a very high viscosity. It is very “thick”, and flows very slowly. Water, on the other hand, has a much lower viscosity. It pours easily, unlike treacle, and offers relatively little resistance to the movement of a submerged object. That is why you can wade through water, or swim in it, without having to expend a huge amount of effort. Imagine trying to wade through or swim in treacle!
A comparison of water and engine oil serves to highlight the fact that viscosity and density have no direct relationship. Water has a higher density than engine oil, but at room temperature it has a much lower viscosity. It may occur to you to wonder why motor oil is more viscous than water, given that the molecules in motor oil are non-polar and held together primarily by weak Van der Waals forces (London dispersion forces), whereas water molecules form strong hydrogen bonds with each other.
The answer lies in the relative size of the molecules. A water molecule is small, consisting of a single oxygen atom and two hydrogen atoms. Motor oil, on the other hand, consists primarily of large hydrocarbon molecules, each of which typically contains between 18 and 34 carbon atoms. Thus, despite the fact that the intermolecular forces in water are stronger than those in motor oil, the much greater size of the molecules in motor oil makes it more difficult for those molecules to move past each other, resulting the motor oil having a significantly greater viscosity.
The viscosity of a liquid essentially depends on three factors - temperature, molecular size, and the strength of the intermolecular bonds. If we compare the viscosity of two substances at the same temperature, the difference between them will depend on both molecular size and the relative strengths of their intermolecular bonding. Let's take the example of water (H2 O) versus pentane (C5 H12 ).
Pentane is an acrylic saturated hydrocarbon (usually referred to as an alkane) - a simple organic compound consisting of carbon atoms, single-bonded to each other and to some number of hydrogen atoms, in a tree-like structure. In the case of pentane, five carbon atoms are chained together in this fashion. The three inner carbon atoms are each bonded to two hydrogen atoms, whilst the first and last carbon atoms in the chain are each bonded to three hydrogen atoms.
Pentane (C5 H12 ) is an alkane consisting of five carbon atoms and twelve hydrogen atoms
A pentane molecule is approximately four times as heavy and five times as big as a water molecule, so on the basis of size we could reasonably expect it to have a higher viscosity. Remember, however, that only nitrogen, oxygen, and fluorine can participate in hydrogen bonds. Water molecules are highly polar, and the intermolecular forces that hold them together consist primarily of hydrogen bonds.
Alkanes such as pentane, on the other hand, are non-polar because the carbon and hydrogen atoms have similar electronegativity values, so charge density in a pentane molecule is relatively evenly distributed throughout the molecule. The intermolecular forces holding pentane molecules together thus consist primarily of London dispersion forces, which are far weaker than the hydrogen bonds holding water molecules together.
Basic methods of determining the viscosity of a liquid include measuring the rate at which a metal ball falls through the liquid, or the rate at which the liquid flows through a narrow-bore tube. The unit of measurement for viscosity is the Pascal-second (Nm-2s), known as the poiseuille, or just poise, in the centimetre-gram–second (CGS) system of units.
The poiseuille is named after the French physicist Jean Léonard Marie Poiseuille (1797-1869) who formulated the equation, originally known as Poiseuille's law but now more often referred to as the Hagen-Poiseuille equation, to describe the laminar (non-turbulent) flow of a liquid through a pipe of uniform section.
In 1844, Poiseuille was able to demonstrate that the volume V of a fluid flowing through a small diameter glass capillary tube per unit time t is proportional to the radius r of the tube, the pressure p required to push the fluid through the tube at a uniform rate, the length l of the tube, and the viscosity η of the fluid - a relationship described by the following equation:
| V | = | πr4p |
| t | 8ηl |
If we rearrange this equation somewhat to get η on the left-hand side, we can derive the Hagen-Poiseuille equation as follows:
| η = | πpr4t |
| 8Vl |
An instrument used to measure viscosity is called a viscometer, and there are many different kinds of viscometer available. The relatively simple instrument shown in the illustration below is an Ostwald viscometer (also known as a U-tube viscometer or capillary viscometer) after its inventor, the German chemist Wilhelm Ostwald (1853-1932). It is used to find the viscosity of a liquid with a known density by measuring the time taken for a known volume of the liquid to flow, under the influence of gravity, from the upper reservoir (the bulb occupying the section of tubing between points A and B in the illustration) to the lower reservoir (the bulb below point C), through a narrow capillary tube.
The Ostwald viscometer is calibrated using a substance whose viscosity is already known, such as chemically pure water. Let's suppose we have a liquid - we'll call it liquid x - with a known density, whose viscosity we wish to measure using an Ostwald viscometer. We have calibrated the instrument using a fixed volume of (pure) water, so we know the time taken for the water to flow from the upper to the lower reservoir. We also know both the density and the viscosity of the water.
The viscometer measures the time taken for the same fixed volume of liquid x to flow from the upper to the lower reservoir. Once this time is known, it is possible to calculate the viscosity of liquid x using the following equation:
| η1 = η2 | p1t1 |
| p2t2 |
where
η1 is the viscosity of liquid x
η2 is the viscosity of water
ρ1 is the density of liquid x
ρ2 is the density of water
t1 is the time required for liquid x to flow from the upper to the lower reservoir
t2 is the time required for water to flow from the upper to the lower reservoir
A viscometer like the one described above can be used to find the viscosity of an incompressible Newtonian fluid exhibiting laminar flow. A Newtonian fluid is one in which the viscosity remains constant regardless of flow speed or shear rate (the rate at which the flow speed changes from one layer of the fluid to the next). The term laminar flow essentially means that the fluid flows smoothly; there is no turbulence. Viscosities in non-Newtonian liquids can vary with shear rate, and measuring them requires a somewhat more sophisticated type of viscometer called a rheometer.
Adhesion is a measure of the degree to which two different substances are attracted to each other, as opposed to cohesion, which is a measure of the strength of the intermolecular forces at work within a single substance. The concept of adhesion can be used to explain how a liquid interacts with the walls of its container.
For example, both glass and water molecules are polar, so the intermolecular bonds between water and any glass receptacle in which it resides are strong, resulting in high adhesion. In fact, because glass molecules are even more polar than water molecules, the water molecules are more strongly attracted to the glass molecules than to other water molecules. The result of this high adhesion is that the water tends to "stick" to the surface of a glass container.
The effect is demonstrated by water in a glass test tube. The surface of the water will curve upwards at the interface between the water and the sides of the test tube, creating a concave meniscus (from the Greek word mēniskos, meaning “crescent” - a curve in the upper surface of a liquid).
The meniscus adopts this shape because the forces of adhesion between the water and the glass of the test tube are significantly greater than the cohesive forces within the water itself. Water molecules close to the walls of the test tube are strongly attracted to the glass molecules, and tend to climb up the walls of the test tube. Because the force of cohesion between water molecules is also quite strong, these molecules tend to drag other water molecules with them.
The opposite effect can be seen when the cohesive forces within a liquid are stronger than the forces of adhesion acting between the liquid and its container. If we observe mercury in a glass test tube, the meniscus formed is convex - the surface of the mercury curves downwards at the interface between the mercury and the sides of the test tube. This happens because the cohesive forces within the mercury are significantly stronger than the forces of adhesion acting between the mercury and the glass, and tend to pull mercury molecules away from the sides of the test tube.
In a situation where the forces of cohesion and adhesion balance out, the meniscus will be virtually flat (this occurs, for example, when water is poured into containers made of certain types of plastic material).
Water and mercury behave very differently in a glass test tube
If the forces of adhesion between a liquid and some solid material it comes into contact with are significantly stronger than the forces of cohesion within the liquid itself, the liquid is said to wet the solid. You can observe this by filling a glass with water and then tipping the water out again. Even if you hold the glass upside down for several seconds, not all of the water will come out of the glass under the influence of gravity. Some of the water "sticks" to the inside of the glass.
If the forces of cohesion within a liquid are significantly stronger than the forces of adhesion between the liquid and a solid material it comes into contact with, the liquid will not wet the solid. This is the case, for example, when water comes into contact with plastic materials such as polythene. The same effect can be seen when water is in contact with waxed paper, or the waxy layer covering the leaves of some plants. The water tends to form droplets on these surfaces due to surface tension (see below), but does not wet them.
As we have already mentioned, Mercury has greater cohesion than water - the only common liquid (at room temperature) for which this is true. This is because the atoms in liquid mercury are held together by weak covalent bonds, whereas water molecules are predominantly held together by hydrogen bonds. Because the atoms in mercury are all of the same type, the covalent bonds in mercury are non-polar. The force of adhesion between mercury and the walls of a glass container is thus far weaker than the force of cohesion within the mercury itself. As a consequence, mercury does not wet a glass surface.
We have already explored the roles that two opposing forces - cohesion and adhesion - play in the formation of a meniscus where the surface of a liquid is in contact with the walls of its container. There is however another force at work - usually referred to as surface tension - that also plays a part in determining the shape of the meniscus. Surface tension is a property of a liquid's interface with another medium when the liquid is at rest.
When we talk about surface tension, we generally focus specifically on the interface between the upper surface of the liquid and the medium above it - typically air. Surface tension is a measure of the strength of the bonds formed between liquid molecules at the surface of the liquid. The stronger those bonds are, the greater the ability of the surface to resist an external force. We can see surface tension in action when we observe pond skaters on the surface of a pond. The pond skater's weight is distributed over six elongated hydrophobic (water-repellent) legs.
A pond skater at rest on the surface of a pond
The pond skater has evolved to take advantage of the surface tension of water by spreading the weight borne by each leg over the surface of the water in a linear fashion. If you look carefully at the picture, you can see that wherever the pond skater's legs are in contact with the surface of the water, it is deformed due to the weight of the pond skater. Surface tension is a force that acts tangentially to the surface of the water, so this distortion will give it a vertical component that acts in the opposite direction to the weight of the pond skater.
Below the surface of a pond, water molecules form bonds with the other water molecules that surround them. The forces of cohesion holding the water molecules together are the same in every direction. The net force of attraction acting on any single water molecule is therefore zero. Water molecules at the surface of the pond, on the other hand, have fewer neighbouring water molecules with which to bond. They form bonds only with their neighbours on the surface and the molecules below them. The principle is illustrated by the graphic below.
Molecules at the surface have fewer neighbours
One way of explaining surface tension, therefore, is in terms of force. The force of cohesion acting between the water molecules at the surface of a pond is significantly stronger than the cohesive forces acting between the water molecules beneath the surface. This increased cohesion makes it harder for an object to penetrate the surface of the pond, because in order to do so it must break the bonds holding the surface molecules together.
Surface tension is represented using the symbol γ (the lowercase Greek letter gamma), and is measured in terms of force per unit length - its SI unit is Newton per metre (N/m), although it is usually expressed in millinewton per meter (mN/m). The general formula for surface tension γ (in terms of force) is:
| γ = | F |
| L |
where
F is the total surface tension force acting over a given length in Newtons
L is the length along which the force acts in metres
Surface tension is often demonstrated in schools and colleges by getting a (non-wettable) object such as a steel needle or a paper clip to "float" on the surface of the water in a glass receptacle. One commonly used method is to place the object - let's say a needle - on a small piece of blotting paper, which is then placed carefully on the surface of the water. The blotting paper will very quickly absorb water and sink to the bottom of the receptacle, leaving the needle "floating" on the surface.
A steel needle "floating" on the surface of water in a bowl
Image: Chris Wells
Because the needle is made of steel it is actually denser than water, so we would expect it to sink to the bottom with the blotting paper, since its weight is greater than the water it would displace. As with the pond skater's specially adapted legs, however, the length of the needle distributes its weight linearly over the surface of the water. The upward force exerted by the vertical component of the surface tension, where the needle is in contact with the surface of the water, will cancel out the downward force exerted by the needle due to its weight.
The surface tension of a liquid is temperature dependent. It weakens as temperature increases because, as the molecules become more energetic, the bonds between them are easier to break. At room temperature (25°), and assuming a surface interface with air, water has the strongest surface tension (72 mN/m) of any common liquid except mercury (485.5 mN/m) because the intermolecular bonds between water molecules are predominantly hydrogen bonds.
We know that a liquid tends to adopt the shape of its container, which leads us to the question of why very small amounts of water on a flat, non-polar waxy surface tend to form almost spherical beads rather than spread out to form a thin continuous layer across the surface, as it does with a flat polar surface like a sheet of glass.
Again, this can be explained in terms of force. We already know that the attraction of water molecules for each other is greater than their attraction for non-polar surfaces, but water forming into an almost spherical shape appears to defy gravity. Remember, however, that the water molecules inside a water droplet are surrounded by other water molecules, and feel the same force of attraction in all directions.
The molecules at the surface are attracted by the molecules inside the droplet, and by neighbouring molecules on the surface, but experience little attraction from the surrounding air molecules (the atmosphere is mainly composed of non-polar O2 and N2 molecules) or the non-polar waxy surface. The surface molecules thus experience a net inward force of attraction that increases their potential energy.
Since physical systems tend to move towards configurations that minimise their potential energy, the water droplet tries to adopt the shape with the smallest surface area for a given volume (a sphere) by pulling as many molecules away from the surface as possible. In the absence of external forces, a water droplet will adopt a spherical shape, although a falling raindrop will undergo distortion due to the resistance of the air, and larger water droplets falling on the waxy surface of a leaf will adopt a more dome-like shape, as the illustration below demonstrates.
in 1804, the English polymath Thomas Young (1773-1829) published a paper entitled "An Essay on the Cohesion of Fluids", in which he describes the principles governing the interface between two fluids. Specifically, he explores the relationship between contact angle and the forces exerted on a water droplet deposited on a solid surface due to surface tension, from which he was able to derive a purely qualitative theory of capillary action (a topic we will discuss in due course).
Thomas Young's essay was, in fact, devoid of any formal definitions or equations, but his essay describes his theory clearly and in sufficient detail to allow us to derive the following equation from the text thereof:
γSV = γLS + γLV cos(θ)
where
γSV is the surface energy of the solid-vapour interface
γLS is the surface energy of the liquid-solid interface
γLV is the surface energy of the liquid-vapour interface
θ is the contact angle between the liquid and solid phases
The following illustration should serve to clarify the relationship between these elements.
Young's equation describes the relationship between surface energies and contact angle
Note that we use the generic term surface energy rather than surface tension here, since the term surface tension is generally assumed to refer exclusively to the surface energy of the liquid-vapour interface and has SI units in Newtons per meter (N/m). Surface energy - physically equivalent to surface tension but usually expressed in SI units of joules per square meter (J/m²) - also exists at the interface between a liquid and a solid (the liquid-solid interface), and at the interface between a solid and a gas (the solid-vapour interface).
The surface energy of a substance - sometimes referred to as the free surface energy because it is energy that can be converted into mechanical work - arises from an imbalance between the intermolecular (or interatomic) forces acting at the surface of a material and those acting within the bulk of the material. The atoms or molecules at the surface are involved in fewer bonds, and thus have more energy.
All physical systems in equilibrium adopt a state in which the system’s free energy achieves its lowest possible value. Young’s equation describes the balance between three interfacial tensions, each of which arises from the interaction of two phases of matter. As we have seen, a liquid will adopt the smallest possible surface area for a given volume in order to minimise surface energy. Solids cannot minimise their surface area, but can be wetted to form an interface with a liquid in order to reduce surface energy.
The contact angle is the angle between the liquid-solid interface and the tangent to the liquid-vapor interface at the point where these two surfaces meet. Its value depends on the relative surface energies of the three phase interfaces involved, and is indicative of how well a liquid wets the surface of the solid with which it is in contact. A small contact angle (less than 90°) indicates that the liquid wets the surface well and tends to spread out over the surface. A large contact angle (greater than 90°) indicates the opposite - the liquid tends to bead up, and form droplets on the surface.
Young’s equation is of limited usefulness when it comes to calculating the wettability of a material, even if the contact angle can be measured and the surface tension of the liquid is known, because there are still two variables (γSV and γLS ) that are difficult to measure, and other factors, such as the texture of the solid surface, will also have an influence on the material’s wettability.
Generally speaking, the free surface energies at both the liquid-vapour interface and the solid-vapour interface will be significantly higher than the free surface energy of a liquid-solid interface because bonds are less likely to from between a gas and either a solid or a liquid than they are to form between a solid and a liquid because the particles in a gas are much farther apart and in constant motion.
Young’s equation implies that, when a solid material is in contact with a liquid, the contact angle, and hence the degree to which the liquid will wet the solid, will depend largely on the relative values of the surface tension of the liquid and the free surface energy of the solid-vapour interface. High surface energy materials like metal and glass tend to be more wettable. Non-polar materials like certain plastics have low surface energy and are far less so.
When water rises up a glass capillary tube (see below), a previously dry section of the inside of the tube is wetted. Some area A of the solid-vapour interface is replaced by an equivalent area of liquid-solid interface. The free surface energy lost from the solid-vapour interface is the energy required to create the new area of liquid-solid interface and raise the level of the water in the capillary. This change in surface energy, ΔE, can be expressed as:
ΔE = (γLS - γSV ) A
The force of adhesion between a liquid and some other medium is responsible for the movement of a liquid through a narrow channel in the absence of, or even in spite of, any other external force acting on the liquid, due to capillary action. If a narrow-bore glass tube is immersed in water, water will be drawn up the tube to a level higher than the surrounding water - a phenomenon known as capillary rise. The illustration shows how water rises up a narrow-bore glass tube due to capillary action.
Water rises up a narrow glass tube due to capillary action
Narrow-bore tubes of this type are called capillary tubes (or just capillaries), from the Latin word capillaris meaning "of or resembling hair" (capillaries are the smallest blood vessels in the body, but the word capillary can be used to describe any narrow-bore tube or tube-like channel). Note that the capillary action becomes more pronounced as the diameter of the capillary tube decreases, as you can see from the illustration above.
When a glass capillary is inserted into water, capillary rise occurs because the attraction between the water molecules and the glass molecules is stronger than the attraction the water molecules have for one another. In other words, the adhesive force is greater than the cohesive force. At the same time, the water molecules that are drawn up the sides of the tube due to adhesive forces will pull other water molecules up the tube with them due to the cohesive forces between water molecules. Water will continue to be drawn up the tube until the weight of the water in the tube cancels out the upward force created by capillary action.
Now let's suppose that instead of water, we insert the glass capillary into mercury. The force of attraction between mercury and glass is weak, but the cohesive forces within the mercury are strong. This time, the level of mercury in the tube will be lower than that of the mercury surrounding the tube. This kind of capillary action is known as capillary depression.
Mercury is forced down a narrow glass tube due to capillary action
To summarise then, when a capillary tube dipped into a liquid at standard temperature and pressure, the result will depend on three main factors - the type of liquid, the material of which the tube is made, and the inner diameter of the tube.
Capillary action occurs both in the natural world and in many of the materials we use every day. Water is absorbed by paper towels, for example, due to capillary action. If you dip one end of a paper towel into a bowl of water, the water will rise up the paper towel for some distance, apparently defying gravity. This is possible thanks to the porous nature of the paper towel, which allows capillary rise to occur within it. The phenomenon is sometimes referred to as "wicking", because it is capillary action that is responsible for melted wax being drawn up the wick of a lighted candle.
Capillary action is also partially responsible for the way in which water containing dissolved nutrients is absorbed by the roots of a plant and conveyed up through the stems of the plant to its leaves and flowers - an important part of the cyclical process known as transpiration, which culminates in water being lost from the aerial parts of the plant (the leaves, stems and flowers) through evaporation. In trees, capillary action is also partially responsible for moving water a considerable distance, from the roots to the highest branches in the tree.
We can think of capillary action as the result of competing adhesive and cohesive forces. We can also think of it as work done in order to minimise the free surface energies of a system. However, let’s now turn our attention now to how capillary action can be explained in terms of the pressure difference - known as the Laplace pressure - across the interface between two fluids.
The year after Thomas Young published his essay describing the forces of cohesion in fluids, the French scholar Pierre-Simon Laplace (1749-1827) discovered the relationship between the radius of the meniscus separating two static fluids - for example, water and air - and capillary action. If the meniscus forms within a tube with a circular cross-section and a sufficiently narrow inner diameter, its shape will be some portion of the surface of a sphere.
The pressure difference across this interface is described by the Young-Laplace equation, so called because it is based on the work of both Young and Laplace, although the equation itself was formally derived in 1830 by the German scientist Johann Carl Friedrich Gauss (1777-1855). For that reason, it is sometimes called the Young-Laplace-Gauss equation. It defines the Laplace pressure ΔP as follows:
| ΔP = γ ( | 1 | + | 1 | ) |
| R1 | R2 |
where:
ΔP is the pressure difference
γ Is the surface tension of the meniscus
R1 and R2 are the two principal radii of curvature
If the curved interface is some portion of a sphere, as is the case for a liquid in a capillary tube with a circular cross section, the interface has a single radius of curvature (R), and the equation becomes:
| ΔP = | 2γ |
| R |
The Young-Laplace equation describes the relationship between the Laplace pressure across the curved interface between two fluids, the surface tension at that interface, and the radius of curvature of the interface. It asserts that the pressure on the concave side of the curved interface is greater than the pressure on the convex side, and that the Laplace pressure increases as the radius of curvature of the interface becomes smaller.
It turns out that the radius of curvature of the meniscus formed at the surface of a liquid in a capillary tube is a function of the contact angle, θ, formed between the liquid and the walls of the capillary which, as we have already seen, depends in turn on the properties of the fluids involved and the material from which the capillary tube is constructed.
The radius of curvature of the meniscus is a function of the contact angle
From the above, we can apply the cosine rule to express the value of R as follows:
| R = | r |
| cos(θ) |
We can now rewrite the Young-Laplace equation to express the Laplace pressure as:
| ΔP = | 2γ cos(θ) |
| r |
When we insert a capillary tube into water, we see the water in the capillary tube rising above the level of the water surrounding the capillary tube. This is because the Laplace pressure (sometimes called the capillary pressure) exerts an upward force on the water inside the tube. The Laplace pressure pushes water up the tube until the downward force exerted due to the weight of the displaced water is equal to the Laplace pressure.
The degree to which a column of water in a capillary tube rises above the level of the water surrounding the tube can be described using Jurin's law, named after the English physician James Jurin (1684-1750) who first derived it in (circa) 1718. The law states that the maximum height of a liquid in a capillary tube due to capillary rise is proportional to the surface tension of the liquid, and inversely proportional to the density of the liquid and the inside diameter of the tube (the other dimensions of the tube are not relevant to the process).
The Laplace pressure exerts an upward force on the concave side of the meniscus due to the surface tension of the water and the curvature of the meniscus, causing it to rise up the tube for some distance. The water continues to rise until the hydrostatic pressure of the displaced water - the downward pressure exerted per unit area by a column of water of a given height due to gravity - is equal to the Laplace pressure. Jurin’s law can be stated as follows:
| h = | 2γ cos(θ) |
| ρgr |
where:
h is the height to which a liquid is raised
γ Is the surface tension of the liquid
ρ is the density of the liquid
r is the radius of the capillary tube
g is the acceleration due to gravity (circa 9.8 m/s2)
θ is the contact angle
We should point out here that if the contact angle is greater than 90°, the liquid in the capillary tube will be subject to capillary depression - the value of h will be negative because the cosine of the contact angle will be negative, and the level of the liquid inside the capillary will be lower than that of the liquid surrounding it. This is the case, for example, if the capillary is made of glass and the liquid involved is mercury, because the contact angle of mercury on glass is typically around 135°.
