પ્રથમક્રમની એક પ્રક્રિયા 27°C તાપમાને 75% પૂર્ણ થવા માટે 20 સેકન્ડ લાગે, તો વેગ અચળાકનું મૂલ્ય કેટલું થશે ?

A 0.693 સેકેન્ડ \(^{-1}\)
B 0.0693 સેકેન્ડ \(^{-1}\)
C 0.693 સેકેન્ડ\(^{-1}\) મોલ \(^{-1}\) લિટર
D 0.0693 સેકેન્ડ\(_{}^{-1}\) મોલ \(_{}^{-1}\)લિટર

Verified Solution

Answer & Solution

Correct Answer

(B) 0.0693 સેકેન્ડ \(^{-1}\)

Step-by-step Solution

Detailed explanation

B
For 1st order reaction;

\(\begin{array}{l}
K t=\ln \left(\frac{A_0}{A_t}\right) \\
K(20)=\ln \left(\frac{A_0}{0.25 A_0}\right) \\
K(20)=\ln (4) \\
K=\frac{2 \ln 2}{20}=\frac{0.693}{10}=0.0693 s^{-1}
\end{array}\)

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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