The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 $\times$ 10$-$3 s$-$1 and the activation energy Ea = 11.488 kJ mol$-$1, the rate constant at 200 K is ____________ $\times$ 10$-$5 s$-$1. (Round off to the Nearest Integer). (Given : R = 8.314 J mol$-$1 K$-$1)
Answer (integer)
10
Solution
$$\log {{{k_2}} \over {{k_1}}} = {{{E_a}} \over {2.303R}}\left[ {{1 \over {{T_1}}} - {1 \over {{T_2}}}} \right]$$<br><br>k<sub>1</sub> (at 200 K) = ?<br><br>k<sub>2</sub> (at 300 K) = $1 \times {10^{ - 3}}{s^{ - 1}}$<br><br>$$\log {{1 \times {{10}^{ - 3}}} \over {{k_1}}} = {{11.488 \times {{10}^3}} \over {2.303 \times 8.314}}\left[ {{1 \over {600}}} \right] = 1$$<br><br>$\Rightarrow$ ${{1 \times {{10}^{ - 3}}} \over {{k_1}}} = 10$<br><br>$\Rightarrow$ ${k_1} = 10 \times {10^{ - 5}}{s^{ - 1}}$
About this question
Subject: Chemistry · Chapter: Chemical Kinetics · Topic: Rate of Reaction
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