Question

For the reaction

${\mathrm{Fe}}_2\mathrm{N}\left(\mathrm{s}\right)+$$\frac{3}{2}{H}_2\left(g\right)$$\rightleftharpoons 2\mathrm{Fe}\left(\mathrm{s}\right)+{\mathrm{NH}}_3\left(\mathrm{g}\right)$

• A. $K_c=K_p{\left(RT\right)}^{1/2}$
• B. $K_c=K_p{\left(RT\right)}^{-1/2}$
• C. $K_c=K_p{\left(RT\right)}^{3/2}$
• D. $K_c=K_p\left(RT\right)$

Answer 1

The correct option is A

$K_c=K_p{\left(RT\right)}^{1/2}$

Explanation for the correct option:

Step 1:

${\mathrm{Fe}}_2\mathrm{N}\left(\mathrm{s}\right)+$$\frac{3}{2}{H}_2\left(g\right)$$\rightleftharpoons 2\mathrm{Fe}\left(\mathrm{s}\right)+{\mathrm{NH}}_3\left(\mathrm{g}\right)$

Step 2:

$∆\mathrm{ng}=\left(1-3/2\right)=-1/2$

Step 3:

$$\begin{gathered} \mathrm{K}=\mathrm{K}{\left(\mathrm{RT}\right)}^{∆\mathrm{ng}}{\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{c}}{\left(\mathrm{RT}\right)}^{-1/2} \\ {\mathrm{K}}_{\mathrm{c}}={\mathrm{K}}_{\mathrm{p}}{\left(\mathrm{RT}\right)}^{1/2} \end{gathered}$$

Hence for the given reaction $K_c=K_p{\left(RT\right)}^{1/2}$ the correct option is A

Explanation for the incorrect option:

The above explanation clearly indicates that the $K_c=K_p{\left(RT\right)}^{1/2}$ and option B is incorrect.

The above explanation clearly indicates that the $K_c=K_p{\left(RT\right)}^{1/2}$ and option C is incorrect.

The above explanation clearly indicates that the $K_c=K_p{\left(RT\right)}^{1/2}$ and option D is incorrect.