Question

The rate of the elementary reaction $H_2\left(g\right)+I_2\left(g\right)\rightleftharpoons 2HI\left(g\right)$ at $25$ 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 $25$ is rate = 2.4$\times {10}^{-21}{\left[HI\right]}^2$. Equilibrium constant for $1/2H_2\left(g\right)+1/2I_2\left(g\right)\rightleftharpoons 2HI\left(g\right)$ is :

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

Answer 1

The correct option is D $26.6$

$\begin{array}{c}{H}_2+I_2⟶2HI\\ {\left(\frac{dx}{dt}\right)}_f=k_f\left[H_2\right]\left[I_2\right]=1.7\times {10}^{-18}\left[H_2\right]\left[I_2\right]\end{array}$

$2HI⟶H_2+I_2$

$\Rightarrow {\left(\frac{dx}{dt}\right)}_b=k_b[HI{]}^2=2.4\times {10}^{-21}[HI{]}^2$

$\begin{array}{cc}\Rightarrow H_2+I_2& \leftrightharpoons 24I\\ K_C=\frac{K_f}{K_b}& =\frac{1.7\times {10}^{-18}}{2.4\times {10}^{-21}}\\ \frac{1}{2}{H}_2+\frac{1}{2}{I}_2& \leftrightharpoons HI,\\ K_C^{\prime }=\sqrt{K_C}& =\sqrt{\frac{1.7}{2.4}\times {10}^3}\\ & =26.6\end{array}$