7.1 Gibbs Energy Changes and the Equilibrium Constant 307
Values of standard-state Gibbs energy changes of formation for a number of substances
are included in Table A.8 of Appendix A, and larger tables are available. This table
also includes values of the function−(G◦m−Hm,298◦)/T, which can also be used to
calculate∆G◦for a reaction, as is done in Example 7.1. This function generally varies
more slowly with temperature than does∆fG◦. If a value of∆G◦is needed for a
temperature that is not included in the table, interpolation of this function usually gives
better accuracy than does interpolation in a table of∆fG◦values.
The Gibbs energy change of a constant-temperature reaction can also be calculated
from∆G∆H−T∆S (7.1-15)where the enthalpy change is calculated from enthalpy changes of formation, using Eq.
(2.7-12), and the entropy change for a reaction is calculated from third-law (“absolute”)
entropies, using Eq. (3.5-7).EXAMPLE 7.1
a.Using tabulated Gibbs energy changes of formation, find the standard-state Gibbs energy
change at 298.15 K for the reaction 2 CO(g)+O 2 (g)2CO 2 (g).
b.Calculate∆G◦for this reaction at 298.15 K from∆H◦and∆S◦.
c.Calculate∆G◦for the same reaction using values of−(G◦m−Hm,298◦ )/Tand values of
∆fH◦.
Solution
a.From values in Table A.8 of Appendix A,∆G◦ 2 ∆fG◦(CO 2 )+(−2)∆fG◦(CO)+(−1)∆fG◦(O 2 )
2(− 394 .389 kJ mol−^1 )−2(− 137 .163 kJ mol−^1 )+ 0
− 514 .452 kJ mol−^1b.From values in Table A.8 of Appendix A,∆H◦ 2 ∆fH◦(CO 2 )+(−2)∆fH◦(CO)+(−1)∆fH◦(O 2 )
2(− 393 .522 kJ mol−^1 )−2(− 110 .527 kJ mol−^1 )− 0
− 565 .990 kJ mol−^1∆S◦ 2 S◦(CO 2 )+(−2)S◦(CO)− 1 S◦(O 2 )
2(213.795JK−^1 mol−^1 )−2(197.653JK−^1 mol−^1 )
+(−1)(205.147JK−^1 mol−^1 )
− 172 .863JK−^1 mol−^1∆G◦∆H◦−T∆S◦
− 565 .990 kJ mol−^1 −(298.15 K)(− 0 .172863 kJ K−^1 mol−^1 )
− 514 .451 kJ mol−^1