The relative equilibrium concentrations of two chemical species (a and b. that directly interconvert were measured to be [a]: [b] = 240: 1 at 37 °c. what is the change in standard gibbs free energy that accompanies the reaction a → b?

ΔG° = 14.1 kJ/mol

For the reaction A → B, K = [B]/[A].

If [A] = 240 and [B] = 1, then

K = 1/240 = 4.167 x 10^(-3)

The relationship between ΔG° and K is:

ΔG° = -RTlnK

where

R = the gas constant = 8.314 J·K^(-1)mol^(-1)

T = the Kelvin temperature

In this problem, T = (37 + 273.15) K = 310.15 K

∴ #ΔG° = -8.314 J·K^(-1)mol^(-1) × 310.15 K × ln(4.167× 10^(-3)

= -2579 × [-5.481 J·mol^(-1)] = 14 100 J·mol^(-1) = 14.1 kJ/mol

Note: We should expect ΔG° to be positive because K < 1.