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 (integer)
225
Solution
$$
\begin{aligned}
&k=A \mathrm{e}^{\frac{-E_{a}}{R T}} \\\\
&\ln k=\ln A-\frac{E_{a}}{R T} \\\\
&\Rightarrow \log \left(2 \times 10^{-6}\right)=\log \left(4 \times 10^{13}\right)-\frac{8.3 \times 10^{3}}{8.3 \times T \times 2.3} \\\\
&\Rightarrow \log (2)-6=2 \times \log (2)+13-\frac{8.3 \times 10^{3}}{8.3 \times T \times 2.3} \\\\
&\Rightarrow-19.3=-\frac{10^{3}}{T \times 2.3} \Rightarrow T=225 \times 10^{-1} \mathrm{~K}
\end{aligned}
$$
About this question
Subject: Chemistry · Chapter: Chemical Kinetics · Topic: Rate of Reaction
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