Question

A box has two compartments of equal size. One side there are 6 moles of hydrogen gas and the other has 2 moles of nitrogen gas. The box is kept at 20C and the barrier between the two compartments is removed. Assume ideal gas behavior and calculate Gibbs energy when allowing the gases to mix.

Answer 1

Given:

Moles of Hydrogen = n₁ = 6

Moles of Nitrogen = n₂ = 2

Total moles = N = 6 +2 = 8

Temperature = T =20⁰C = 273.15 + 20 = 293.15 K

Now,

Gibb's Energy change of mixing can be calculated as

p_i denotes the initial pressure

After mixing, the partial pressures of the gases are P_A and P_B , where the
total pressure is P_f=P_A + P_B The total Gibbs energy is then

.....................................................(1)

From Ideal gas law, as initial volume of both gases is equal

consider the pressure of N₂ = P

As Gas behaves ideally, the partial pressure of constituents will fall become half of that was initially

put all respective values in eq.(1)

.............................ans.

As ?_mixG < 0 at constant temperature and pressure, this means that the mixing of two ideal gases is a spontaneous process.