Equimolar concentrations of H2 and I2 are heated to equilibrium

Discussion Forum : Chemical Equilibrium

Question -

Equimolar concentrations of $H_{2} a n d I_{2}$ are heated to equilibrium in a 2litre flask. At equilibrium, the forward and backward rate constants are found to be equal. What percentage of initial concentration of $H_{2}$ has reacted at equilibrium?

Options:

A .

33.33 %

B .

75 %

C .

50 %

D .

15 %

Answer: Option C
:
C

Solution:Correct option is c).
$\begin{matrix} H_{2} (g) + & l_{2} (g) ⇋ & 2 H I (g) I n i t i a l m o l e s & 1 & 1 & 0 A t e q u i l i b r i u m & 1 - x & 1 - x & 2 x M o l a r c o n c e n t r a t i o n (m o l / L) & (1 - x) / 2 & (1 - x) / 2 & 2 x / 2 = x \end{matrix}$
$K = x^{2} / \frac{(1 - x) \times (1 - x)}{2 \times 2} = 4 x^{2} / (1 - x)^{2} \approx 4 x^{2}$
$K = K_{f} / K_{b} = 1$
$4 x^{2} = 1 x = \frac{1}{2}, i . e ., 50 %$

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