What is the value of the equilibrium constant, Kc, at this constant temperature?

Question

When 1.50 mol of CO₂ and an excess of solid carbon are heated in a 20.0 L container to a high constant temperature, the equilibrium concentration of CO is 0.0776 M.

C_(s) + CO_2(g)  ⇆ 2 CO_(g)

What is the value of the equilibrium constant, K_c, at this constant temperature?

Answer 1

C(s) + CO2(g) <==> 2CO(g)

First, simply write the equilibrium expression (note that solids are not included)

Kc = [CO]² / [CO₂]

Next, find the concentrations from the information given and plug them into the expression:

[CO] = 0.0776 M (at equilibrium)

[CO₂] = 1.50 mol / 20.0 L = 0.0750 M (initial concentration)

Now, find [CO₂] at equilibrium...

C + CO₂ <===> 2 CO

.....0.075.................0......I

.....-x......................+2x...C

....0.075-x.............2x......E

Since 2x = 0.0776,

x = 0.0388

[CO₂] @ equilibrium = 0.075 - 0.0388 = 0.0362 M

Now plug in the equilibrium values into the equilibrium expression and solve for K

Kc = [CO]² / [CO₂] = (0.0776)² / 0.0362)

Kc = 0.166