Question

Consider the reaction:
2 NO₂(g) → N₂O₄(g)

Calculate ΔG (in kJ/mol) at 298°K if the equilibrium partial pressures of NO₂ and N₂O₄ are 1.337 atm and 0.657 atm, respectively.

Answer 1

The equation for Gibbs free energy is

                                                               ΔG=ΔG^o+RTlnK

where K is the equilibrium constant

For a gas phase reaction of the type

aA(g) + bB(g) ⇌ cC(g) + dD(g),

K_P=P^c_CP^d_D/ P^a_AP^b_B (equilibrium constant in terms of Partial pressure)

Here

2 NO₂(g) → N₂O₄(g)

K_P = P_N2O4 / P²_NO2

K_p = 0.657 / 1.337²

K_p = 0.3675

At equilibrium constant ΔG= 0

ΔG^o = -RTlnK

ΔG^o = -8.314 J·K⁻¹mol⁻¹ × 298 K × ln(0.3675)

ΔG^o = −2480.12 J mol⁻¹

ΔG^o = −2.4801 J mol⁻¹