Consider a general reaction

a) The ΔG° of the reaction is - 4.140 kJ mol. Calculate the equilibrium constant for the reaction. (Assume a temperature of 25°C.)

b) What is ΔG at body temperature (37.0°C) if the concentration of A is 1.6 M and the concentration of B is 0.45 M?

a) K = 5.3175

b) ΔG = 3.2694

Explanation:

a) ΔG° = - RT Ln K

∴ T = 25°C ≅ 298 K

∴ R = 8.314 E-3 KJ/K. mol

∴ ΔG° = - 4.140 KJ/mol

⇒ Ln K = - (ΔG°) / RT

⇒ Ln K = - (-4.140 KJ/mol) / ((8.314 E-3 KJ/K. mol) (298 K))

⇒ Ln K = 1.671

⇒ K = 5.3175

b) A → B

∴ T = 37°C = 310 K

∴ [A] = 1.6 M

∴ [B] = 0.45 M

∴ K = [B] / [A]

⇒ K = (0.45 M) / (1.6 M)

⇒ K = 0.28125

⇒ Ln K = - 1.2685

∴ ΔG = - RT Ln K

⇒ ΔG = - (8.314 E-3 KJ/K. mol) (310 K) ( - 1.2685)

⇒ ΔG = 3.2694