The reaction C(s)+2H2(g)⇌CH4(g)

Question

The reaction

C(s)+2H2(g)⇌CH4(g)

has 𝐾p=0.263 at 1000. K. Calculate the total pressure at equilibrium when 5.984 g of H2 and 23.77 g of C(s) are placed in a 8.70 L flask and heated to 1000. K.

Answer 1

C(s) + 2H₂(g) <==> CH₄(g) ... balanced equation

Kp = (CH₄) / (H₂)² where ( ) is the partial pressure of each gas. Note C is not included as it is a solid.

So, we will need to first find the initial pressure of H2 at the start of the reaction, and use an ICE table to find pressures at equilibrium.

PV = nRT

P = pressure = ?

V = volume = 8.70 L

n = moles H₂ = 5.984 g H2 x 1 mol / 2.0159 g = 2.9684 moles H₂ (limiting reactant)

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 1000K

Solving for P, we have...

P = nRT/V = (2.9684)(0.0821)(1000) / 8.70

P = 28.01 atm

C(s) + 2H₂(g) <==> CH₄(g)

..........28.01...............0........Initial

.........-2x..................+x........Change

.........28.01-2x...........x.........Equilibrium

0.263 = x / (28.01 - 2x)²

x = 10.7 (be sure to check the math. Would expect this to be less since Kp is less than 1)

Total pressure @ equilibrium = P_H2 + P_CH4

P_H2 = 28.01 - 21.4 = 6.61 atm

P_CH4 = 10.7 atm

Total P = 17.3 atm