Question

consider the reaction:
c(s) + 1/2o₂(g) ⇌ co(g)
write the equilibrium constant for this reaction in terms of the equilibrium constants, k₁ and k₂, for the reactions below:
c(s) + o₂(g) ⇌ co₂(g) k₁
co(g) + 1/2o₂(g) ⇌ co₂(g) k₂
for answers with both a subscript and a superscript, enter the subscript first. for example, enter k²₁ if the first equilibrium constant should be squared.
k =

Explanation:

Step1: Write equilibrium constant expressions

For the reaction \(C(s)+O_{2}(g)
ightleftharpoons CO_{2}(g)\), \(K_{1}=\frac{[CO_{2}]}{[O_{2}]}\) (since \(C(s)\) has a constant concentration and is omitted from the expression).
For the reaction \(CO(g)+\frac{1}{2}O_{2}(g)
ightleftharpoons CO_{2}(g)\), \(K_{2}=\frac{[CO_{2}]}{[CO][O_{2}]^{\frac{1}{2}}}\).
The target reaction is \(C(s)+\frac{1}{2}O_{2}(g)
ightleftharpoons CO(g)\).

Step2: Manipulate the equilibrium constant expressions

If we rewrite the target reaction as \(C(s)+O_{2}(g)- (CO(g)+\frac{1}{2}O_{2}(g))
ightleftharpoons CO_{2}(g)-CO_{2}(g)\) (using the first two reactions).
The equilibrium constant \(K\) for the target reaction. From \(K_{1}=\frac{[CO_{2}]}{[O_{2}]}\) and \(K_{2}=\frac{[CO_{2}]}{[CO][O_{2}]^{\frac{1}{2}}}\), we can express \(K\) as \(K = \frac{K_{1}}{K_{2}}\).
Substitute the expressions: \(K=\frac{\frac{[CO_{2}]}{[O_{2}]}}{\frac{[CO_{2}]}{[CO][O_{2}]^{\frac{1}{2}}}}=\frac{[CO]}{[O_{2}]^{\frac{1}{2}}}\)

Answer:

\(K=\frac{K_{1}}{K_{2}}\)