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Characteristics of Equilibrium Constant

The equilibri...

Question

The equilibrium constant, $K_{c}$ for the reaction
$H_{2} (g) + I_{2} (g) ⇌ 2 H I (g)$
is $56.8$ at $800 K$ . When the mixture was analysed, it was found to contain $0.316 m o l / L$ $H I$ at $800 K$ . What are the concentrations of $H_{2}$ and $I_{2}$ at equilibrium? (Assume that initial concentrations of $H_{2}$ and $I_{2}$ were the same)

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Solution

The equilibrium concentration of HI is 0.316 mol/L HI
Let x M be the equilibrium concentrations of hydrogen and iodine each.
The equilibrium constant $K_{c} = \frac{[H I]^{2}}{[H_{2}] [I_{2}]}$
$56.8 = \frac{[0.316]^{2}}{x \times x}$
$0.00176 = x^{2}$
$[H_{2}] = [I_{2}] = x = 0.0419 m o l L^{- 1}$

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