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)
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)
Show Hint
Correct Answer: 225
Solution and Explanation
Step 2: A/k = (4 \(\times\) 1013)/(2 \(\times\) 10\(-6\)) = 2 \(\times\) 1019. log(A/k) = 0.30 + 19 = 19.30, so ln(A/k) = 2.3 \(\times\) 19.30 = 44.39.
Step 3: Ea/R = 8300/8.3 = 1000 K.
Step 4: T = 1000/44.39 = 22.53 K = 225.3 \(\times\) 10\(-1\) K, i.e. 225 (nearest integer).
Answer: 225
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