Entropy molar

Por most normal liquids the constant has a value of approx. 88JmolK" . Associated liquids show marked variations from this value. The Trouton constant is the molar entropy of vaporization. 

G = Gibbs molar free energy S = molar entropy F = Helmholtz free molar energy H = molar enthalpy U = molar internal energy... 

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

The molar entropy and the molar enthalpy, also with constants of integration, can be obtained, either by differentiating equation (A2.1.56) or by integrating equation (A2.T42) or equation (A2.1.50) ... 

Because of the Nemst heat theorem and the third law, standard themrodynamic tables usually do not report entropies of fomiation of compounds instead they report the molar entropy 50 7 for each element and... 

To characterize the state of the adsorbed phase, it is useful to evaluate its molar entropy, s , defined as the mean molar value for all the molecules adsorbed over the complete range of surface coverage up to the given amount adsorbed. The molar integral entropy of adsorption. As, is then defined as... 

Also, the differential molar entropy of adsorption, AJ, is defined as... 

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.)...

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

The heats of formation, the standard molar entropies at 298 K, are given below. 

The molar entropy of solution of a crystal—the AS0 of (168)—may be regarded as the difference between (1) the molar entropy of the crystal, and (2) the partial molal entropy of the solute in a solution of a certain Concentration. The question arises In a solution of what concentration Now we notice that (168) may be written in the form... 

As mentioned in Sec. 90 we may think of this AS0 as being the difference between the molar entropy of solid 1 j2C03 and the partial molal entropies of one (C03) ion and two Lif ions, each in its hypothetical standard aqueous solution. We propose now to compare the AS of the reaction... 

From Table 44 it will be seen that the molar entropy of solid Li2C03 amounts to 21.60 cal/degree. In Sec. 104 it was pointed out that, if the AS0 for the process (192) is added to the entropy of solid Li2C03, the sum will be equal to the partial molal entropies of the COJ" ion and two Li+ ions. For this sum then we obtain... 

Molar entropy of ammonia as a function of temperature. Note the large increases in entropy upon fusion (melting) and vaporization. 

The entropy of a substance, unlike its enthalpy, can be evaluated directly. The details of how this is done are beyond the level of this text, but Figure 17.4 shows the results for one substance, ammonia. From such a plot you can read off the standard molar entropy at 1 atm pressure and any given temperature, most often 25°C. This quantity is given the symbol S° and has the units of joules per mole per kelvin (J/mol-K). From Figure 17.4, it appears that... 

Standard molar entropies of elements, compounds, and aqueous ions are listed in Table 17.1 (p. 456). Notice that—... 

In taking these sums, the standard molar entropies are multiplied by the number of moles specified in the balanced chemical equation. 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Entropy is an extensive property and Sm the molar entropy is often used. 

Self-Test 7.3A Calculate the change in molar entropy of an ideal gas when it is compressed isothermally to one-third its initial volume. 

TABLE 7.2 Standard Molar Entropy of Water at Various Temperatures... 

---