Chapter 14, Problem 14.4P

Consider the water-gas-shift reaction:

$H_2(g)+C{O}_2(g)\to H_{2}O(g)+CO(g)$

At high temperatures and low to moderate pressures the reacting species form an ideal-gas mixture. By Eq. (10.27):

$G={\displaystyle \underset{i}{\sum }{y}_i{G}_i+RT{\displaystyle \underset{i}{\sum }{y}_{i}In{y}_i}}$

When the Gibbs energies of the elements in their standard states are set equal to zero. $G_i=\Delta G_{f_i}^{°}$ for each species, and then:

At the beginning of Sec. 14.2 we noted that Eq. (123) is a criterion of equilibrium. Applied to the water-gas-shift reaction with the understanding that T and P are con¬stant. this equation becomes:

$d{G}^t=d\left(nG\right)=ndG+Gdn=0n\frac{dG}{d\in }+G\frac{dn}{d\in }$

Once the yi are eliminated in favor of e. Eq. (A) relates G to c. Data for $\Delta G_{f_i}^{°}$ for the compounds of interest are given with Ex. 14.13. For a temperature of 1000 K (the reaction is unaffected by P) and for a feed of 1 mol H₂ and 1 mol CO₂:

1. Determine the equilibrium value of e by application of Eq. (B).
2. Plot G vs. $\in$ , indicating the location of the equilibrium value of $\in$ determined in (a).