Entropy of liquids

Fig. 2.16 The molar entropy for nitrogen adsorbed ongraphitizedcarbon (Graphon) at — 189-3°C, as a function of the amount adsorbed s, = molar entropy of adsorbed nitrogen s, = molar entropy of liquid nitrogen. (Courtesy Hill, Emmett and Joyner.)...

Conventional Partial Molal Entropy of (H30)+ and (OH)-. Let us now consider the partial molal entropy for the (1I30)+ ion and the (OH)- ion. If we wish to add an (HsO)+ ion to water, this may be done in two steps we first add an H2O molecule to the liquid, and then add a proton to this molecule. The entropy of liquid water at 25°C is 16.75 cal/deg/mole. This value may be obtained (1) from the low temperature calorimetric data of Giauque and Stout,1 combined with the zero point entropy predicted by Pauling, or (2) from the spectroscopic entropy of steam loss the entropy of vaporization. 2 Values obtained by the two methods agree within 0.01 cal/deg. 

Figure 4.12 Entropy of liquid helium near absolute zero.

An example of the role of the surroundings in determining the spontaneous direction of a process is the freezing of water. We can see from Table 7.2 that, at 0°C, the molar entropy of liquid water is 22.0 J-K 1-mo -1 higher than that of ice... 

Explain why the standard molar entropy of liquid benzene is less than that of liquid cyclohexane. 

In 1950, Pomeranchuck (1913-1966) predicted that for 3He on the melting curve below about 0.3 K, the entropy of liquid is smaller than that of solid. It was only after 15 years that Anufriev [2], after Pomeranchuck s suggestion, succeeded in reducing the temperature from 50 to 18mK in an experiment based on this 3He property. Four years later, the Pomeranchuck method produced a temperature of 2mK [3],... 

For temperatures above 0.32 K, the entropy of liquid is higher than that of the solid as happens in all other materials (see Section 7.2.1) below 0.32 K, the situation is reversed. We remind that this property allows to cool the liquid by isoentropic compression (see Section 7.1). 

Figure 5.3 Entropy of liquid and crystalline aluminium in stable, metastable and unstable temperature regions [12]. The temperatures where the entropy of liquid and crystalline aluminium are equal are denoted Tf and 7 jm crySt, respectively.

Computing Free Volume, Structural Order, and Entropy of Liquids and Glasses... 

Fig. 15. The enthalpy of liquid water calculated from the Weres-Rice model (from Ref. 64>) Fig. 16. The entropy of liquid water calculated from the Weres-Rice model (from Ref. 84>) Fig. 17. The specific heat of liquid water calculated from the Weres-Rice model (from Ref. 64>)...

Figure 11.6. Entropy of liquid He under its equilibrium vapor pressure. Data below 1.90 K from H. C. Kramers, J. D. Wasscber, and C. J. Gorter, Physica 18, 329 (1952). Data from 1.90 K to 4.00 K from R. W. Hill and O. V. Lounasmaa, Phil. Mag. Ser. 8, 2, 143 (1957).

The surface entropy of liquids is given by (-d y/dT). This means that the entropy is positive at higher temperatures. The rate of decrease of surface tension with temperature is found to be different for different liquids (Appendix A), which supports the foregoing description of liquids. This observation explains the molecular description of surface tension. 

We can see from Table 7.2 that at 0°C the molar entropy of liquid water is 22.0 J-K -mol 1 higher than that of ice at the same temperature. This difference makes sense, because the molecules in liquid water are more disordered than in ice. It follows that when water freezes at 0°C, its entropy decreases by 22.0 J-K -mol-1. Entropy changes do not vary much with temperature so just below 0°C, we can expect almost the same decrease. Yet we know from everyday experience that water freezes spontaneously below 0°C. Clearly, the surroundings must be playing a deciding role if we can show that their entropy increases by more than 22.0 J-K -mol 1 when water freezes, then the total entropy change will be positive and freezing will be spontaneous. 

Liquid helium presents an interesting case leading to further understanding of the third law. When liquid 4He, the abundant isotope of helium, is cooled at pressures of < 25 bar, a second-order transition takes place at approximately 2 K to form liquid Hell. On further cooling Hell remains liquid to the lowest observed temperature at 10 5 K. Hell does become solid at pressures greater than about 25 bar. The slope of the equilibrium line between liquid and solid helium apparently becomes zero at temperatures below approximately 1 K. Thus, dP/dT becomes zero for these temperatures and therefore AS, the difference between the molar entropies of liquid Hell and solid helium, is zero because AV remains finite. We may assume that liquid Hell remains liquid as 0 K is approached at pressures below 25 bar. Then, if the value of the entropy function for sol 4 helium becomes zero at 0 K, so must the value for liquid Hell. Liquid 3He apparently does not have the second-order transition, but like 4He it appears to remain liquid as the temperature is lowered at pressures of less than approximately 30 bar. The slope of the equilibrium line between solid and liquid 3He appears to become zero as the temperature approaches 0 K. If, then, the slope is zero at 0 K, the value of the entropy function of liquid 3He is zero at 0 K if we assume that the entropy of solid 3He is zero at 0 K. Helium is the only known substance that apparently remains liquid as absolute zero is approached under appropriate pressures. Here we have evidence that the third law is applicable to liquid helium and is not restricted to crystalline phases. 

Equations (8) and (15) indicate that the surface entropy of liquids is positive. This is because extending the surface creates an additional environment into which molecules can partition. When, in Eq. (15), n = 1 is employed, the surface energy is independent of temperature (problem 3). In practice, this is found not to hold when approaching the critical temperature, where the surface energy is also found to approach zero. 

A frequent assumption is that pressure has a negligible effect on liquid-phase properties, and that the properties of a compressed liquid are essentially those of the saturated liquid at the same temperature. Estimate the errors when the enthalpy and entropy of liquid ammonia at 270 K. and 1,500 kPa are assumed equal to the enthalpy and entropy of saturated liquid ammonia at 270 K. For saturated liquid ammonia at 270 K, P" = 381 kPa, V1 = 1.551 x 10 3 m3 kg , and p = 2,095 x 10 3 K . 

Thus the effect of a pressure change of almost 1,000 bar on the enthalpy and entropy of liquid water is less than that of a temperature change of only 25°C. 

Calculate the absolute entropy of liquid n-hexanol at 20°C (68°F) and 1 atm (101.3 kPa) from these heat-capacity data ... 

Based on knowledge of heats and temperatures of transformations, entropies of liquid, gaseous and other transformed phases can be determined. Similarly, it is possible with the knowledge of heats of formation and temperatures of equilibrium to determine entropy in many cases. In case of stable compounds, the integration method (Fig. 6.5) is used for entropy determination. 

The entropy of liquid ethanol is 38.4 cal. deg." mole at 25 C. At this temperature the vapor pressure is 59.0 mm. and the heat of vaporization is -f 10.19 kcal. rnole. Assuming the vapor to behave ideally, calculate the entropy of ethanol vapor at 1 atm. pressure at 25 C. 

S. G. Sayegh and J. H. Vera. 1980. Lattice-model expressions for the combinatorial entropy of liquid mixtures A critical discussion. Chem. Eng. J. 19 1. 

The heat capacity of liquid mercury at constant pressure is almost constant at 28 J K 1 mol 1 between its freezing point at 234 K and 298 K. Estimate the entropy of liquid mercury at its freezing point. The entropy of liquid mercury at 298 K is 77.4 J K"1 mol"... 

It is known that the calorimetrically measured entropy is less than the entropy obtained from the spectroscopic data by 0.81 e.u. This is due to the residual entropy. The calculated entropy of liquid is compared with the spectroscopic entropy which may be evaluated from the difference between the spectroscopic entropy of gas and the entropy of vaporization. 

The second approach is to formulate rules for the correlation of the enthalpies and entropies of liquids and gases so that by the use of established correlations of the parameters for the gases, those for the corresponding liquids may be estimated. A recent paper by Patrick [398] has considerably clarified this approach. Assuming ideal thermodynamic behaviour of the solution components, it was concluded that for reactions involving no change in the number of molecules, i.e. transfer reactions of the present type, the ratio of equilibrium constants of the gas and liquid phase reactions is unity. This would appear to be most simply explained if the forward and reverse rate coefficients (fef(liq.), kf(gas), k (liq.) and fer(gas)) were equal, i.e. fef(liq.) = fef(gas) and fer(hq-) = fer(gas), but this remains to be confirmed experimentjdly. 

It is easy now to understand why the entropies of liquids and solids are nearly unchanged by a change in pressure. The volume of condensed materials is altered so little by a change in pressure that the breadth of the spatial distribution remains about the same. The entropy therefore remains at very nearly the same value. 

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