Chemical Kinetics Question 314
Question: The time required for 10% completion of a first order reaction at 298 K is equal to that required for its 25% completion at 308 K, If the pre-exponential factor for the reaction is $ 3.56\times 10^{9}{s^{-1}} $ the rate constant at 318 K is:
Options:
A) $ 18.39kcalmo{l^{-1}} $
B) $ 20,kcal,mo{l^{-1}} $
C) $ 16,kcal,mo{l^{-1}} $
D) $ 21.5,kcal,mo{l^{-1}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let the initial concentration [a] = 100 Final concentration at $ 298K=100-10=90 $ Final concentration at $ 308K=100-25=75 $
Substituting the values in the 1st order rate reaction $ t=\frac{2.303}{k_{298}}\log \frac{100}{90} $ …. (i) $ t=\frac{2.303}{k_{308}}\log \frac{100}{75} $ ….. (ii)
From (i) and (ii) $ \frac{k_{308}}{k_{208}}=2.73 $
Substituting the value in the following relation $ E_{a}=\frac{2.303R\times T_1\times T_2}{T_2-T_1}\log \frac{k_2}{k_1} $
$ =\frac{2.303\times 8.314\times 298\times 308}{308-298}\log 2.73 $
$ E_{a}=76.62kJ,mo{l^{-1}}=18.39kcalmo{l^{-1}} $
