At high temperature, the following equilibrium exists in a mixture of carbon, oxygen and their compound:
$C (s) + O_{2} (g) ⇌ C O_{2} (g) {K e q}_{1} = 10^{- 2}$
$2 C (s) + O_{2} (g) ⇌ 2 C O (g) {K e q}_{2} = 10^{- 3}$
$C (s) + C O_{2} (g) ⇌ 2 C O (g) {K e q}_{3} = X$
$2 C O (s) + O_{2} (g) ⇌ 2 C O_{2} (g) {K e q}_{4} = Y$
What is the value of $\frac{X}{Y}$ ?

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Solution

$2 C (s) + O_{2} (g) ⇌ 2 C O (g); {K e q}_{2} = 10^{- 3} . . . (i)$
$C O_{2} (g) ⇌ C (s) + O_{2} (g) {K e q}_{7} = 10^{2} . . . (i i)$
Adding (i) and (ii), we get
$C (s) + C O_{2} (g) ⇌ 2 C O (g); {K e q}_{3} = 10^{- 1} = X . . . (i i i)$
Again, $2 C O (g) ⇌ 2 C (s) + O_{2} (g) {K e q}_{5} = 10^{3} . . . (i v)$
$2 C (s) + 2 O_{2} (g) ⇌ 2 C O_{2} (g) {K e q}_{6} = 10^{- 4} . . . (v)$
Adding $(i v)$ and $(v)$ we get,
$2 C O (s) + O_{2} (g) ⇌ 2 C O_{2} (g) {K e q}_{4} = 10^{- 1} = Y$
Hence, $\frac{X}{Y} = 1$ .

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