Determining the Equilibrium Constant K_p

Methane (CH_4) reacts with hydrogen sulfide to yield H_2 and carbon disulfide, a solvent used in manufacturing rayon and cellophane:

\mathrm{CH}_4(g)+2 \mathrm{H}_2 \mathrm{~S}(g) \rightleftharpoons \mathrm{CS}_2(g)+4 \mathrm{H}_2(g)What is the value of K_p at 1000 K if the partial pressures in an equilibrium mixture at 1000 K are 0.20 atm of CH_4, 0.25 atm of H_2S, 0.52 atm of CS_2, and 0.10 atm of H_2?

**STRATEGY **

Write the equilibrium equation by setting K_p equal to the equilibrium-constant expression using partial pressures. Put the partial pressures of products in the numerator and the partial pressures of reactants in the denominator, with the pressure of each substance raised to the power of its coefficient in the balanced chemical equation. Then substitute the partial pressures into the equilibrium equation and solve for K_p.

Step-by-Step

Learn more on how do we answer questions.

K_{\mathrm{p}}=\frac{\left(P_{\mathrm{CS}_2}\right)\left(P_{\mathrm{H}_2}\right)^{4 \ \leftarrow Coefficient \ of \ H_2}}{\left(P_{\mathrm{CH}_4}\right)\left(P_{\mathrm{H}_2 \mathrm{~S}}\right)^{2 \ \leftarrow \ Coefficient of H_2S}} \\ K_{\mathrm{p}}=\frac{\left(P_{\mathrm{CS}_2}\right)\left(P_{\mathrm{H}_2}\right)^4}{\left(P_{\mathrm{CH}_4}\right)\left(P_{\mathrm{H}_2 \mathrm{~S}}\right)^2}=\frac{(0.52)(0.10)^4}{(0.20)(0.25)^2}=4.2 \times 10^{-3}

Note that the partial pressures must be in units of atmospheres (not mm Hg) because the standard-state partial pressure for gases is 1 atm

Question: 13.16

Two A and five A_2 molecules are pr...

Question: 13.15

Because the oxidation of ammonia is exothermic, we...

Question: 13.14

(a) Because the forward reaction converts 1 mol of...

Question: 13.13

(a) Because Fe_2O_3 is a pure solid...

Question: 13.12

Step 1 The balanced equation is \mathrm{FeO...

Question: 13.11

Step 1 The balanced equation is \mathrm{H}_...

Question: 13.10

Step 1 The balanced equation is given: \mat...

Question: 13.9

The initial concentration of N_2 is...

Question: 13.8

(a) K_{\mathrm{c}}=\frac{[\mathrm{CO}]^2}{\...

Question: 13.7

(a) For this reaction, Δn = (1 + 3) - (1 + 1) = 2....