15 moles of $\mathrm{H}_2$ and 5.2 moles of $\mathrm{I}_2$ are mixed and allowed to attain equilibrium at…

15 moles of $\mathrm{H}_2$ and 5.2 moles of $\mathrm{I}_2$ are mixed and allowed to attain equilibrium at 773 K . At equilibrium, the number of moles of HI is found to be 10 . The equilibrium constant for the dissociation of HI is
  1. $2 \times 10^{-2}$
  2. 50
  3. $2 \times 10^{-1}$
  4. 5.0

Solution

\begin{array}{llll} & \mathrm{H}_2+\mathrm{I}_2 \rightleftharpoons & 2 HI \\Initial & 15 & 5.2 & 0 \\At equilibrium & 15-\mathrm{x} & 5.2-\mathrm{x} & 2 x\end{array} Let ' V ' is volume in liter Given, $2 \mathrm{x}=10$ $x=5$ Concentration of $\mathrm{H}_2$ at equilibrium $=15-5$ $\begin{aligned} & {\left[\mathrm{H}_2\right]=10 / \mathrm{V}} \\ & {\left[\mathrm{I}_2\right]=\frac{0.2}{\mathrm{~V}}} \\ & {[\mathrm{HI}]=\left[\frac{10}{\mathrm{v}}\right]} \end{aligned}$
$\begin{aligned} & K_c=\frac{\left[\frac{10}{V}\right]^2}{\left[\frac{10}{V}\right] \times\left[\frac{0.2}{V}\right]} \\ & K_c=\frac{10 \times 10}{10 \times 0.2}=50 \end{aligned}$
$\mathrm{K}_{\mathrm{c}}^{\prime}$ for the dissociation of HI is $=\frac{\mathrm{I}}{\mathrm{K}_{\mathrm{c}}}$ $\begin{aligned} & =\frac{1}{50}=0.2 \times 10^{-1} \\ & =2 \times 10^{-2} \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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