At 1500°c the equilibrium constant for the reaction co(g) + 2h2(g) ch3oh(g) has the value kp = 1.4 × 10–7. calculate ? g° for this reaction at 1500°c.

To determine the standard gibbs free energy, we need an equation that would relate chemical equilibrium and the free energy. We derive this expression from the relationship:

ΔG = ΔG° + RT ln Q

When the system is at equilibrium G = 0 which means the system had reached the minimum free energy. At this state, the reaction quotient is equal to the equilibrium constant. So, the reaction reduce to

0 = ΔG° + RT ln Kp

ΔG°  = - RT ln Kp

We use this equation as follows:
ΔG°  = - RT ln Kp
ΔG°  = - 8.314 (1500 + 273.15) ln (1.4x10^-7)
ΔG°  = 232652.2047 J / mol

The standard Gibbs Free Energy at 1500 degrees Celsius is 232652.2047 J / mol.