Molar standard

The standard molar free energy change upon adsorption of the probe gas is thus given by... 

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

These quantities (which are standard molar quantities) describe the process initial state transition state... 

The standard molar enthalpy of formation of a compound, AH , is equal to the enthalpy change when one mole of the compound is formed at a constant pressure of 1 atm and a fixed temperature, ordinarily 25°C, from the elements in their stable states at that pressure and temperature. From the equations... 

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. 

To find a numerical value for AHi, we need to know ArH° at one temperature, while evaluation of I requires ArG° at one temperature. The usual choice is to obtain ArH° and ArG° at T = 298.15 K from standard molar enthalpies of formation and standard molar Gibbs free energies of formation. Earlier in this chapter we referred to examples of these quantities. It is now time to define AfH° and AfG° explicitly and describe methods for their measurement. 

Standard molar enthalpies of formation, AfH°m, and standard molar Gibbs free energies of formation, Af(7, are useful, since they can be used to calculate ArH° and ArG°. The relationships are... 

P. A. G. O Hare, "Thermochemistry of Uranium Compounds XV. Calorimetric Measurements on UCI4, UOiCl . and UCFF . and the Standard Molar Enthalpy of Formation at 298.15 K of UC14", J. Chem. Thermodyn.. 17. 611-622 (1985). 

The interpretation of AC is that it is the difference in the standard molar heat capacities of the transition state and the reactants. Values of AC for the solvolysis of neutral molecules lie in the range 0 to -400 J mol-1 K l. The need for high-precision determinations of k (and 77) is emphasized by these values. 

In a chemical reaction, old bonds are broken and new ones formed. We can estimate reaction enthalpies if we know the enthalpy changes that accompany the breaking and making of bonds. The strength of a chemical bond is measured by the bond enthalpy, AHR, the difference between the standard molar enthalpies of a molecule, X-Y (for instance, H3C—OH), and its fragments X and Y (such as CH3 and OH) in the gas phase ... 

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

Standard molar entropies increase as the complexity of a substance increases. 

The standard molar entropies of gases are higher than those of comparable... 

To calculate the change in entropy that accompanies a reaction, we need to know the molar entropies of all the substances taking part then we calculate the difference between the entropies of the products and those of the reactants. More specifically, the standard reaction entropy, AS°, is the difference between the standard molar entropies of the products and those of the reactants, taking into account their stoichiometric coefficients ... 

The standard reaction entropy is the difference between the standard molar entropy of the products and that of the reactants weighted by the amounts of each species taking part in the reaction. It is positive (an increase in entropy) if there is a net production of gas in a reaction it is negative (a decrease) if there is a net consumption of gas. 

The standard Gibbs free energy of reaction, AG°, is defined like the Gibbs free energy of reaction but in terms of the standard molar Gibbs energies of the reactants and products ... 

Calculate the standard Gibbs free energy of formation of HI(g) at 25°C from its standard molar entropy and standard enthalpy of formation. 

Calculate the standard reaction entropy from standard molar entropies (Example 7.9). 

Which substance in each of the following pairs would you expect to have the higher standard molar entropy at 298 K Explain your reasoning, (a) Iodine vapor or bromine vapor ... 

Predict which of the hydrocarbons below has the greater standard molar entropy at 25°C. Explain your reasoning. 

Predict which of the organic compounds (a) dimethyl ether, (CH3)20, or (b) diethyl ether (CH3CH2)20, has the greater standard molar entropy at 25°C. Explain your reasoning. 

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

We use a different measure of concentration when writing expressions for the equilibrium constants of reactions that involve species other than gases. Thus, for a species J that forms an ideal solution in a liquid solvent, the partial pressure in the expression for K is replaced by the molarity fjl relative to the standard molarity c° = 1 mol-L 1. Although K should be written in terms of the dimensionless ratio UJ/c°, it is common practice to write K in terms of [J] alone and to interpret each [JJ as the molarity with the units struck out. It has been found empirically, and is justified by thermodynamics, that pure liquids or solids should not appear in K. So, even though CaC03(s) and CaO(s) occur in the equilibrium... 

As we saw in Section 9.2, the activity of a solute J in a dilute solution is approximately equal to the molar concentration relative to the standard molar concentration, [JJ/c°, with c° = 1 mol-L, and so a practical form of this expression is... 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

---