પ્રથમ ક્રમ પ્રક્રિયાનો વેગ પ્રક્રિયાની શરૂઆત થયા પછી \(10\) minutes પર \(0.04 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~S}^{-1}\) છે અને 20 minutes પર \(0.03 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) છે. પ્રક્રિયાનો અર્ધ આયુષ્ય _______ મિનિટ છે. (આપેલ : \(\log 2=0.3010, \log 3=0.4771)\)

A \(24\)
B \(30\)
C \(35\)
D \(40\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(24\)

Step-by-step Solution

Detailed explanation

\(0.04=\mathrm{k}[\mathrm{A}]_0 \mathrm{e}^{-\mathrm{k} \times 10 \times 60}\) \(...(1)\) \(0.03=\mathrm{k}[\mathrm{A}]_0 \mathrm{e}^{-\mathrm{k} \times 20 \times 60}\) \(...(2)\) \((1) /(2)\) \(\frac{4}{3}=\mathrm{e}^{600 \mathrm{k}(2-1)}\)…

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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પદાર્થ	\(H _{2}\)	\(C\)(ગ્રેફાઈટ)	\(C _{2} H _{6}( g )\)
\(\frac{\Delta_{ C } H ^{\Theta}}{ kJmol ^{-1}}\)	\(-286.0\)	\(-394.0\)	\(-1560.0\)