JEE MAIN - Chemistry (2022 - 30th June Morning Shift - No. 18)
For the reaction P $$\to$$ B, the values of frequency factor A and activation energy EA are 4 $$\times$$ 1013 s$$-$$1 and 8.3 kJ mol$$-$$1 respectively. If the reaction is of first order, the temperature at which the rate constant is 2 $$\times$$ 10$$-$$6 s$$-$$1 is _____________ $$\times$$ 10$$-$$1 K.
(Given : ln 10 = 2.3, R = 8.3 J K$$-$$1 mol$$-$$1, log2 = 0.30)
Answer
225
Explanation
$$
\begin{aligned}
&k=A \mathrm{e}^{\frac{-E_{a}}{R T}} \\\\
&\ln k=\ln A-\frac{E_{a}}{R T} \\\\
&\Rightarrow \log \left(2 \times 10^{-6}\right)=\log \left(4 \times 10^{13}\right)-\frac{8.3 \times 10^{3}}{8.3 \times T \times 2.3} \\\\
&\Rightarrow \log (2)-6=2 \times \log (2)+13-\frac{8.3 \times 10^{3}}{8.3 \times T \times 2.3} \\\\
&\Rightarrow-19.3=-\frac{10^{3}}{T \times 2.3} \Rightarrow T=225 \times 10^{-1} \mathrm{~K}
\end{aligned}
$$
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