The Liquid State

Liquids are considered to be relatively incompressible. Unlike gas molecules, liquid molecules are tightly packed. Liquids have a fixed volume, whereas gases do not. Liquids do not have a definite shape. The properties of liquids can be attributed to the presence of various types of intermolecular forces. 

Intermolecular forces are weak attractive forces that contribute to many of the physical properties exhibited by liquids. From the MCAT point of view, you have to be familiar with the main three types of attractive forces  

The dispersion forces in molecules with iarge atoms are quite significant and are often actuaiiy more important than dipoie-dipoie forces. 

A molecule In the Interior of a liquid is attracted by the molecules surrounding it, whereas a molecule at the surface of a liquid Is attracted only by molecules below It and on each side. Remember that the molecules In a liquid are In constant motion. 

For a given voiume, a sphere has a smaiier surface area than any other shape. 

Surface tension the resistance of a liquid to an increase in its surface area. 

These same ideas also apply to nonpolar molecules such as H2, CH4, CCI4, and CO2 [see Fig. 10.5(b)]. Since none of these molecules has a permanent dipole moment, their principal means of attracting each other is through London dispersion forces. 

Liquids and liquid solutions are vital to our lives. Of course, water is the most important liquid. Besides being essential to life, it provides a medium for food preparation, for transportation, for cooling in many types of machines and industrial processes, for recreation, for cleaning, and for a myriad of other uses. 

Liquids exhibit many characteristics that help us understand their natures. We have already mentioned their low compressibility, lack of rigidity, and high density compared with gases. Many of the properties of liquids give us direct information about the forces that exist among the particles. For example, when a liquid is poured onto a solid surface, it tends to bead as droplets, a phenomenon that depends on the intermolecular forces. Although molecules in the interior of the liquid are completely surrounded by other molecules, those at the liquid s surface are subject to attractions only from the side and from 

Instantaneous dipole on atom A induces a dipole on atom B 

Note from Table 16.2 that the freezing point rises going down the group. The principal cause for this trend is that as the mass (and the atomic number) increases, the number of electrons increases, so there is an increased chance of the occurrence of momentary dipoles. We say that large atoms with many electrons exhibit a higher polarizability than small atoms. Thus the importance of London dispersion forces greatly increases as atomic size increases. 

To increase a liquid s surface area, molecules must move from the interior of the liquid to the surface. This requires energy, since some intermolecular forces must be overcome. The resistance of a liquid to an increase in its surface area is called the surface tension of the liquid. As we would expect, liquids with relatively large intermolecular forces, such as those with polar molecules, tend to have relatively high surface tensions. 

Capillary action is the spontaneous rising of a liquid through a narrow tube, against the force of gravity. It is caused by competition between the intermolecular forces in the liquid 

We shall briefly describe several properties of the liquid state. These properties vary markedly among various hquids, depending on the nature and strength of the attractive forces among the particles (atoms, molecules, ions) making up the liquid. 

Unless otheiwise noted, all content on this page is Cengage Learning. 

Copyright 2013 Ceng eLeamii All RigMs Reserved. not be copied, seamed, or di Hcated, in rtiole or in part Due to electronic i%hts, some third party content may be si ipressed from the eBook arxkor eChapter(s). 

Editorial review has deemed that my suppressed content does not m erially affect the overall leanimg experimee. Cengi e Learning reserves the i%ht to remove additional coiteid at any time if subsequent rights restrictions require it. 

Specific heat. The specific heat of liquids does not invariably rise with the temperature. The variation with the temperature is generally greater in the hquid than in the sohd state, but it occasionally happens that the specific heat of a substance rises at one temperature and falls at another. The best example of this is water, which is abnormal in many ways, and occupies a unique position amongst liquids. According to the measure- 

According to this table, the mean specific heat has a minimum at 37-5, and the true specific heat has a minimum at 25°. The specific heat of mercury decreases steadily, as the temperature rises, according to the linear equation  

The specific heat of most other liquids, like that of solids, rises with the temperature. 

The following table shows the variation of the specific heat with temperature for a few hquids  

The specific heat of some liquids appears to decrease towards a lower hmit between O and -100°. S 

The first term of the l.h.s. of Equation 21 describes the acceleration produced by the electric force, while the second term describes the friction which the electrons experience due to collisions while drifting through the liquid, depends on temperature. In the stationary state, a constant drift velocity is observed and the acceleration term vanishes. The drift velocity is proportional to the electric field strength, so that 

Since eo/mei= 1.76 x 10 cm V S and = 10 s (the order of the vibrational frequencies of the molecules), Pei =176 cm V s is obtained which is in the range of the highest electron mobilities observed in nonpolar molecular liquids (see Chapter 3). 

With these definitions, the current density becomes 

In the random motion, the distance between two subsequent collisions will be a statistical variable. When the electron collective is in thermal equilibrium with the liquid, we can define a mean free path which is given by 

---

Low temperature. Low-temperature process (below 0°C) can contain large amounts of fluids kept in the liquid state by pressure and/or low temperature. If for any reason it is not possible to keep them under pressure or keep them cold, then the liquids will begin to vaporize. If this happens, impurities in the fluids are liable to... 

Prepared by the sulphonation of benzene in the liquid state or by passing benzene vapour into concentrated sulphuric acid at 150-180"C. 

The effect of pressure is neglected. The limits of this model are easy to understand each component must exist in the liquid state for the Cp/ to be known equally important is that the effect of pressure must be negligible which is the case for < 0.8 and P < 1. 

V, = molar volume of component i Xj, = volume fraction of component i Xj = mole fraction of component i l = conductivity of the component i in the liquid state A, = conductivity of the mixture in the liquid state... 

When the reduced temperature is less than 0.8, it is better to estimate the C starting from the Co, of the fraction in the liquid state by the following... 

Ui = internal molar energy of component i at 25°C and in the liquid state... 

The mass or volume heating value represents the quantity of energy released by a unit mass or volume of fuel during the chemical reaction for complete combustion producing CO2 and H2O. The fuel is taken to be, unless mentioned otherwise, at the liquid state and at a reference temperature, generally 25°C. The air and the combustion products are considered to be at this same temperature. 

In the expression for heating value, it is useful to define the physical state of the motor fuel for conventional motor fuels such as gasoline, diesei fuel, and jet fuels, the liquid state is chosen most often as the reference. Nevertheless, if the material is already in its vapor state before entering the combustion system because of mechanical action like atomization or thermal effects such as preheating by exhaust gases, an increase of usefui energy resufts that is not previously taken into consideration. 

If one imagine.s that the fuel is used in the liquid state in the form of droplets —as in the case of fuel injection— the specific energy of the motor fuel (SE) is expressed in kilojoules per kilogram of air utilized, under predetermined conditions of equivalence ratio (stoichiometry for example). The SE is none other than the NHY /r quotient where r represents the previously defined stoichiometric ratio. 

Fig. XVII-23. (a) Entropy enthalpy, and free energy of adsorption relative to the liquid state of N2 on Graphon at 78.3 K (From Ref. 89.) b) Differential entropies of adsorption of n-hexane on (1) 1700°C heat-treated Spheron 6, (2) 2800°C heat-treated, (3) 3000°C heat-treated, and (4) Sterling MT-1, 3100°C heat-treated. (From Ref 18.)...

As with enthalpies of adsorption, the entropies tend to approach the entropy of condensation as P approaches in further support of the conclusion that the nature of the adsorbate is approaching that of the liquid state. 

Traditionally one categorizes matter by phases such as gases, liquids and solids. Chemistry is usually concerned with matter m the gas and liquid phases, whereas physics is concerned with the solid phase. However, this distinction is not well defined often chemists are concerned with the solid state and reactions between solid-state phases, and physicists often study atoms and molecular systems in the gas phase. The tenn condensed phases usually encompasses both the liquid state and the solid state, but not the gas state. In this section, the emphasis will be placed on the solid state with a brief discussion of liquids. 

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... 

Typical results for a semiconducting liquid are illustrated in figure Al.3.29 where the experunental pair correlation and structure factors for silicon are presented. The radial distribution function shows a sharp first peak followed by oscillations. The structure in the radial distribution fiinction reflects some local ordering. The nature and degree of this order depends on the chemical nature of the liquid state. For example, semiconductor liquids are especially interesting in this sense as they are believed to retain covalent bonding characteristics even in the melt. 

Percus J K 1982 Non uniform fluids The Liquid State of Matter Fluids, Simple and Complex ed E W Montroll and J L Lebowitz (Amsterdam North-Holland)... 

Haksjold B and Stell G 1982 The equilibrium studies of simple ionic liquids The Liquid State of... 

Stillinger F 1973 Structure in aqueous solutions from the standpoint of scaled particle theory J. Solution Chem. 2 141 Widom B 1967 Intermolecular forces and the nature of the liquid state Sc/e/ ce 375 157 Longuet-Higgins H C and Widom B 1964 A rigid sphere model for the melting of argon Mol. Phys. 8 549... 

Rasaiah J C 1987 Theories of electrolyte solutions The Liquid State and its Electrical Properties (NATO Advanced Science Institute Series Vol 193) ed E E Kunhardt, L G Christophous and L H Luessen (New York Plenum)... 

Baliicani U and Zoppi M 1994 Dynamics of the Liquid State (Oxford Oxford University Press)... 

Yu J and Berg M 1992 Solvent-electronic state interactions measured from the glassy to the liquid state. I. Ultrafast transient and permanent hole burning in glycerol J. Chem. Phys. 96 8741-9... 

In the theory of the liquid state, the hard-sphere model plays an important role. For hard spheres, the pair interaction potential V r) = qo for r < J, where d is the particle diameter, whereas V(r) = 0 for r s d. The stmcture of a simple fluid, such as argon, is very similar to that of a hard-sphere fluid. Hard-sphere atoms do, of course, not exist. Certain model colloids, however, come very close to hard-sphere behaviour. These systems have been studied in much detail and some results will be quoted below. 

Phosphine is a colourless gas at room temperature, boiling point 183K. with an unpleasant odour it is extremely poisonous. Like ammonia, phosphine has an essentially tetrahedral structure with one position occupied by a lone pair of electrons. Phosphorus, however, is a larger atom than nitrogen and the lone pair of electrons on the phosphorus are much less concentrated in space. Thus phosphine has a very much smaller dipole moment than ammonia. Hence phosphine is not associated (like ammonia) in the liquid state (see data in Table 9.2) and it is only sparingly soluble in water. 

It is a well-known fact that substances like water and acetic acid can be cooled below the freezing point in this condition they are said to be supercooled (compare supersaturated solution). Such supercooled substances have vapour pressures which change in a normal manner with temperature the vapour pressure curve is represented by the dotted line ML —a continuation of ML. The curve ML lies above the vapour pressure curve of the solid and it is apparent that the vapour pressure of the supersaturated liquid is greater than that of the solid. The supercooled liquid is in a condition of metastabUity. As soon as crystallisation sets in, the temperature rises to the true freezing or melting point. It will be observed that no dotted continuation of the vapour pressure curve of the solid is shown this would mean a suspended transformation in the change from the solid to the liquid state. Such a change has not been observed nor is it theoretically possible. 

System in which the solid phases consist of the pure components and the components are completely miscible in the liquid phase. We may now conveniently consider the general case of a system in which the two components A and B are completely miscible in the liquid state and the solid phases consist of the pure components. The equilibrium diagram is shown in Fig. 1,12, 1. Here the points A and B are the melting points of the pure components A and B respectively. If the freezing points of a series of liquid mixtures, varying in composition from pure A to pure B, are determined, the two curves represented by AC and BC will be obtained. The curve AC expresses the compositions of solutions which are in equilibrium, at different temperatures, with the solid component A, and, likewise, the curve BC denotes the compositions... 

The theory of sublimation, t.e. the direct conversion from the vapour to the sohd state without the intermediate formation of the liquid state, has been discussed in Section 1,19. The number of compounds which can be purified by sublimation under normal pressure is comparatively small (these include naphthalene, anthracene, benzoic acid, hexachloroethane, camphor, and the quinones). The process does, in general, yield products of high purity, but considerable loss of product may occur. 

---