Equilibrium Table Question

Question

The reaction

C(s)+2H2(g)⇌CH4(g)

has 𝐾p=0.263 at 1000 K. 

What is the total pressure when 5.441 g of H2 and 8.674 g of C(s) are placed in a 9.81 L flask and heated to 1000 K?

𝑃total=

Answer 1

5.441 g H₂ x 1 mol H₂ / 2 g = 2.72 mols H₂

8.674 g C(s) x 1 mol C / 12 g = 0.723 mols C

C(s) + 2H₂(g) ⇌ CH₄(g)

0.723....2.72.......0.............Initial

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

0.723-x..2.72-2x...x..........Equilibrium

Kp = (CH₄) / (H₂)²

0.263 = x / (2.72-2x)²

0.263 = x / 4x² - 10,88x + 7.40

0 = 0.05x² - 2.86x + 1.95

x = 0.690 mols CH₄(g)

mols H₂(g) @ equilibrium = 2.72 - 2x0.690 = 1.34 mols H₂(g)

Total mols gas = 0.690 + 1.34 = 2.03 mols

PV = nRT

P = nRT/V = (2.03)(0.0821)(1000) / 9.81

P = 17.0 atm

(be sure to check the math)