**Relating the Equilibrium Constants K_p and K_c**

Hydrogen is produced industrially by the steam–hydrocarbon re-forming process. The reaction that takes place in the first step of this process is

\mathrm{H}_2 \mathrm{O}(g)+\mathrm{CH}_4(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_2(g)(a) If K_c = 3.8 × 10^{-3} at 1000 K, what is the value of K_p at the same temperature?

(b) If K_p = 6.1 × 10^4 at 1125 °C, what is the value of K_c at 1125 °C?

**STRATEGY **

To calculate K_p from K_c, or vice versa, use the equation K_p = K_c(RT)^{Δn} , where R must be in units of (L . atm)/(K . mol), T is the temperature in kelvin, and Δn is the number of moles of gaseous products minus the number of moles of gaseous reactants.

Step-by-Step

Learn more on how do we answer questions.

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

K_{\mathrm{p}}=K_{\mathrm{c}}(R T)^{\Delta n}=K_{\mathrm{c}}(R T)^2=\left(3.8 \times 10^{-3}\right)[(0.08206)(1000)]^2=26(b) Solving the equation K_p = K_c(RT)^2 for K_c gives

K_{\mathrm{c}}=\frac{K_{\mathrm{p}}}{(R T)^2}=\frac{6.1 \times 10^4}{[(0.08206)(1398)]^2}=4.6Note that the temperature in these equations is the absolute temperature; 1125 °C corresponds to 1125 + 273 = 1398 K.

Question: 13.6

K_{\mathrm{p}}=\frac{\left(P_{\mathrm{CS}_2...

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}{\...