Question 17.9: Methanol (CH3OH), an important alcohol used in the manufactu......
Methanol (CH_{3}OH), an important alcohol used in the manufacture of adhesives, fibers, and plastics, is synthesized industrially by the reaction
CO(g) + 2 H_{2}(g)\xrightleftharpoons{} CH_{3}OH(g)Use the thermodynamic data in Appendix B to calculate the equilibrium constant for this reaction at 25 °C.
STRATEGY
First calculate ΔG° for the reaction from the tabulated values of ΔG°_{f} for the reactants and products. Then use the equation ΔG° = -RT ln K to find the value of the equilibrium constant.
| IDENTIFY | |
| Known | Unknown |
| Standard free energies of formation (ΔG°_{f}) | Equilibrium constant (K_{p}) |
| T = 25 °C | |
= (1 mol)(-162.3 kJ/mol) – [(1 mol)(-137.2 kJ/mol) + (2 mol)(0 kJ/mol)]
ΔG° = -25.1 kJ
Solving the equation ΔG° = -RT ln K
for ln K gives ln K=\frac{-ΔG°}{RT}=\frac{-(-25.1\times 10^{3} J/mol)}{[8.314 J/(K \cdot mol)](298 K)}=10.1
Therefore, K = K_{p} = antiln 10.1 = e^{10.1} = 2\times 10^{4}
The equilibrium constant obtained by this procedure is K_{p} because the reactants and products are gases and their standard states are defined in terms of pressure. If we want the value of K_{c}, we must calculate it from the relation K_{p}=K_{c}(RT)^{\Delta n} (Section 14.3), where R must be expressed in the proper units [R = 0.082 06 (L · atm)/(K · mol)].