जब लैक्टोबैसिलस एसिडोफिलस, की आबादी दुगुनी होती है तो दूध का एक प्रतिदर्श \(300 \,K\) पर \(60\) मिनट के बाद तथा \(400 \,K\) पर \(40\) मिनट के बाद विपाटित होता है। इस प्रक्रम के लिए सक्रियण ऊर्जा ( \(kJ / mol\) में) लगभग है ............ (दिया गया है, \(R =8.3 \,J mol ^{-1} K ^{-1}, \ln \left(\frac{2}{3}\right)=0.4\), \(\left.e ^{-3}=4.0\right)\)

A \(2.88\)
B \(2.52\)
C \(1.96\)
D \(3.98\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(3.98\)

Step-by-step Solution

Detailed explanation

\(\ln \left(\frac{t_{1}}{t_{2}}\right)=\frac{-\operatorname{Ea}}{R}\left[\frac{1}{T_{2}}-\frac{1}{T_{1}}\right]\) \(\ln \left(\frac{60}{40}\right)=\frac{-\operatorname{Ea}}{8.3}\left[\frac{1}{400}-\frac{1}{300}\right]\) \(\mathrm{E}=0.4 \times 1200 \times 8.3\)…

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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