Question

9.2 A mixture of H, and CH4 establishes a "carbon activity", defined as the ratio of the carbon partial pressure generated by the reaction C(g) + 2H2(g) = CH (g) to the vapor pressure of solid carbon (graphite). The standard free energy change for the above reaction is AG (g). For the reaction with solid carbon, C(s) + 2H2(g) = CH4(g), the standard free energy change is AG (S). For graphite sublimation, C(S) = C(g) the free energy change is AG"(sub). (a) What is the relationship between AG°(g), AG'(s), and AG°(sub)? (b) At 1000 K and 1 atm total pressure, what hydrogen pressure gives a carbon activity of unity? At this temperature, AG'S) - 19.2 kJ/mole. (c) What happens if the H2 pressure is lower than the value in part (b)?

Answer 1

a) According to Hess law, $\Delta$ G(s)=$\Delta$G(g)+$\Delta$G(sub) as $\Delta$ G is a state function.

b)-lnK = $\Delta$ G/RT, Now lnK=-(19.2*1000)/(8.314*1000)

                                   or lnK=-2.303

                                    or K=0.1    Now K=P(CH₄)/(P(H₂))^2

                             Now x/4x²=0.1 hence x=2.5 atm. Sine total pressure is 1 atm $\Delta$ G(s) must be negative.