The value of

Question:

The value of $\mathrm{Kc}$ is 64 at $800 \mathrm{~K}$ for the reaction $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})$. The value of $K_{\mathrm{c}}$ for the following reaction is :

  1. $1 / 64$

  2. 8

  3. $1 / 4$

  4. $1 / 8$


Correct Option:

Solution:

$\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}) ; K_{c}$

$2 \mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) ; \quad \frac{1}{K_{c}}$

For

$\mathrm{NH}_{3}(\mathrm{~g}) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(\mathrm{~g})+\frac{3}{2} \mathrm{H}_{2}(\mathrm{~g}) ; \quad \frac{1}{K_{c}^{1 / 2}}$

$\frac{1}{K_{c}^{1 / 2}}=\frac{1}{(64)^{1 / 2}}=\frac{1}{8}$

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