गैस प्रावस्था अभिक्रिया \(2 A ( g ) \rightleftharpoons A _{2}( g )\) के लिए \(400 K\) पर \(\Delta G ^{\circ}=+25.2 \,kJ\, mol ^{-1}\) है। इस अभिक्रिया के लिए साम्य स्थिरांक \(K _{ C }\) है...............\(\times 10^{-2}\). (निकटतम पूर्णांक में) [उपयोग कीजिए : \(R =8.3 J mol ^{-1} K ^{-1}, \ln 10=2.3\) \(\left.\log _{10} 2=0.30,1 atm =1 bar \right]\) \([\operatorname{antilog}(-0.3)=0.501]\)

A \(141\)
B \(166\)
C \(206\)
D \(111\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(166\)

Step-by-step Solution

Detailed explanation

Using formula \(\Delta_{ r } G ^{0}=- RT \ln K _{ p }\) \(25200=-2.3 \times 8.3 \times 400 \log \left( K _{ p }\right)\) \(K _{ p }=10^{-3.3}=10^{-3} \times 0.501\) \(=5.01 \times 10^{-4} \,Bar ^{-1}\) \(=5.01 \times 10^{-9}\, Pa ^{-1}\) \(=\frac{ K _{ C }}{8.3 \times 400}\)…

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.

Same subject

सूची \(-I\) को सूची \(-II\) के साथ मिलाऐं।

सूची \(-I\) (अभिकर्मक)	सूची \(-II\) (उत्पाद)
(\(A\)) फीनॉल, \(\mathrm{Zn} / \Delta\)	\((I)\) सेलिसिलैल्डिहाइड
(\(B\)) फीनॉल, \(\mathrm{CHCl}_3, \mathrm{NaOH}, \mathrm{HCl}\)	\((II)\) सैलिसिलिक अम्ल
(\(C\)) फीनॉल, \(\mathrm{CO}_2, \mathrm{NaOH}, \mathrm{HCl}\)	\((III)\) बेन्जीन
(\(D\)) फीनॉल, सांद्र. \(\mathrm{HNO}_3\)	\((IV)\) पिक्रिक अम्ल

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वर्ग	\(0-6\)	\(6-12\)	\(12-18\)	\(18-24\)	\(24-30\)
बारंबारता	\(a\)	\(b\)	\(12\)	\(9\)	\(5\)