निम्नलिखित अभिक्रिया पर विचार कीजिए : \(N _{2}( g )+3 H _{2}( g )=2 NH _{3}( g )\) उपर्युक्त अभिक्रिया का साम्य स्थिरांक \(K_{p}\) है। यदि विशुद्ध अमोनिया को वियोजित होने दिया जाता है, तो साम्यावस्था पर अमोनिया का आंशिक दाब है : (मान लीजिए साम्यावस्था पर \(P _{ NH _{3}} \ll p _{\text {total }}\) )

A \(\frac{{{3^{3/2}}K_p^{1/2}{P^2}}}{{16}}\)
B \(\frac{{K_p^{1/2}{P^2}}}{16}\)
C \(\frac{{K_p^{1/2}{P^2}}}{4}\)
D \(\frac{{{3^{3/2}}K_p^{1/2}{P^2}}}{4}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{{{3^{3/2}}K_p^{1/2}{P^2}}}{{16}}\)

Step-by-step Solution

Detailed explanation

\(\mathop {{N_2}}\limits_x + \mathop {3{H_2}}\limits_{3x} \leftrightarrow \mathop {2N{H_3}}\limits_{{P_1}} \) \({P_T} = 4x\,{K_P} = \frac{{P_1^2}}{{x \times 27 \times 3}}\) \(x = \left( {\frac{P}{4}} \right)\) \({P_1} = \sqrt {27{X^4}{K_P}} \)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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