द्रव \('M'\) तथा द्रव \('N'\) एक आदर्श विलयन बनाते हैं। समान ताप पर शुद्ध द्रवों \('M'\) तथा \('N'\) को बाष्प दाब क्रमश: \(450\) तथा \(700\) \(mm\) \(Hg\) है। तब सही कथन है \(X _{ M }= ^{\prime} M ^{\prime}\) का विलयन में मोल प्रभाज \(X _{ N }= ^{\prime} N^{\prime}\) का विलयन में मोल प्रभाज \(Y _{ M }= ^{\prime} M ^{\prime}\) का वाष्म अवस्था में मोल प्रभाज \(Y _{ N }= ^{\prime} N ^{\prime}\) का वाष्प अवस्था में मोल प्रभाज

A \(\frac{{{x_M}}}{{{x_N}}} > \frac{{{y_M}}}{{{y_N}}}\)
B \(\frac{{{x_M}}}{{{x_N}}} = \frac{{{y_M}}}{{{y_N}}}\)
C \(({x_M} - {y_M})\, < {\kern 1pt} \,({x_N} - {y_N})\)
D \(\frac{{{x_M}}}{{{x_N}}} < \frac{{{y_M}}}{{{y_N}}}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{{{x_M}}}{{{x_N}}} > \frac{{{y_M}}}{{{y_N}}}\)

Step-by-step Solution

Detailed explanation

\(P_M^o\, = \,450\) \(P_N^o\, = \,700\) \({P_M}\, = \,{X_M}450\) \({P_N}\, = \,{X_N}700\) \({Y_M}{P_T}\, = \,{P_M}\) \({Y_N}{P_T}\, = \,{P_N}\) \(\frac{{{Y_M}{P_T}}}{{{Y_N}{P_T}}}\, = \,\frac{{{X_M}}}{{{X_N}}}\frac{{450}}{{700}}\)…

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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