For the reaction

Question:

For the reaction

$\mathrm{Fe}_{2} \mathrm{~N}(\mathrm{~s})+\frac{3}{2} \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Fe}(\mathrm{s})+\mathrm{NH}_{3}(\mathrm{~g})$

  1. $K_{\mathrm{c}}=K_{\mathrm{p}}(\mathrm{RT})$

  2. $K_{\mathrm{c}}=K_{\mathrm{p}}(\mathrm{RT})^{\frac{-1}{2^{\prime}}}$

  3. $K_{\mathrm{c}}=K_{\mathrm{p}}(\mathrm{RT})^{\frac{1}{2}}$

  4. $K_{\mathrm{c}}=K_{\mathrm{p}}(\mathrm{RT})^{\frac{3}{2}}$


Correct Option: , 3

Solution:

$K_{\mathrm{p}}=K_{\mathrm{C}}(\mathrm{RT})^{\Delta \mathrm{n}_{\mathrm{g}}}=K_{\mathrm{C}}(\mathrm{RT})^{1-3 / 2}=K_{\mathrm{C}}(\mathrm{RT})^{-1 / 2}$

$\Rightarrow K_{\mathrm{C}}=K_{\mathrm{p}}(\mathrm{RT})^{1 / 2}$

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