Question

The rate of the elementary reaction $H_2\left(g\right)+I_2\left(g\right)\rightleftharpoons 2HI\left(g\right)$ at ${25}^{\circ }C$ is given by:
Rate = $1.7\times {10}^{-18}\left[H_2\right]\left[I_2\right]$. The rate of decomposition of gaseous $HI$ to $H_2\left(g\right)$ and $I_2\left(g\right)$ at 25C is rate = $2.4\times {10}^{-21}{\left[HI\right]}^2$. Equilibrium constant for ${1/2H}_2\left(g\right)+1/2I_2\left(g\right)\rightleftharpoons HI\left(g\right)$ is:

• A. 708
• B. 354
• C. 0.0014
• D. 26.6

Answer 1

Answer: (D)

26.6

$H_2+I_2\rightleftharpoons 2HI$

rate $=1.7\times {10}^{-18}\left[H_2\right]\left[I_2\right]$

rate of decomposition of $HI$ is $2.4\times {10}^{-21}{\left[HI\right]}^2$

let, the equilibrium constant for the reaction

$\frac{1}{2}{H}_2\left(g\right)+\frac{1}{2}{I}_2\left(g\right)\rightleftharpoons HI\left(g\right)$ be $K$

$K=\frac{\left[HI\right]}{{\left[H_2\right]}^{1/2}{\left[I_2\right]}^{1/2}}$

$K=\sqrt{\frac{1.7\times {10}^{-18}}{2.4\times {10}^{-21}}}$

$=\sqrt{0.708\times {10}^3}$

$=\sqrt{708}$

$K=26.6$

$\Rightarrow$ the equilibrium constant is $26.6$