Physical Chemistry , 1st ed.

The 2s are from the stoichiometry of the balanced chemical reaction. We get

rxnS326.68 J/K

(Is this reasonable, knowing what you should know about entropy?) In com-

bining rxnHand rxnS, we need to make the units compatible. We convert

rxnSinto kilojoule-containing units:

rxnS0.32668 kJ/K

Using equation 4.13, we calculate rxnG:

GHTS

G571.66 kJ (298.15 K)(0.32668 kJ/K)

Notice that the K temperature units cancel in the second term. Both terms

have the same units of kJ, and we get

G474.26 kJ

using equation 4.13. Using the idea of products-minus-reactants, we use the

fGvalues from the table to get

rxnG2(237.13) (2 0 0) kJ

rxnG474.26 kJ

This shows that eitherway of evaluating Gis appropriate.

4.4 Natural Variable Equations and Partial Derivatives

Now that we have defined all independent energy quantities in terms ofp,V,

T, and S, we summarize them in terms of their natural variables:

dUT dSp dV (4.14)

dHT dS V dp (4.15)

dAS dTp dV (4.16)

dGSdT V dp (4.17)

These equations are important because when the behaviors of these energies

on their natural variables are known,all thermodynamic properties of the sys-

tem can be determined.

For example, consider the internal energy,U. Its natural variables are Sand

V; that is, the internal energy is a function ofSand V:

UU(S,V)

As discussed in the last chapter, the overall change in U,dU, can be separated

into a component that varies with Sand a component that varies with V.The

variation ofUwith respect to Sonly (that is,Vis kept constant) is represented

as ( U/ S)V, the partial derivative ofUwith respect to Sat constant V. This is

simply the slope of the graph ofUplotted against the entropy,S. Similarly, the

variation ofUas Vchanges but Sremains constant is represented by ( U/ V)S,

the partial derivative ofUwith respect to V at constant S. This is the slope of

the graph ofUplotted versus V. The overall change in U,dU, is therefore

dU

U

S

VdS (^) 

U

V



S

dV

96 CHAPTER 4 Free Energy and Chemical Potential