Question

A 1st order reaction is 50% complete in 30 minute at ${27}^{o}C$ and in 10 minute at ${47}^{o}C$. The sum of rate constants for reaction at ${27}^{o}C$ and ${47}^{o}C$ is:

• A. $9.24\times {10}^{-2}mi{n}^{-1}$
• B. $12.24\times {10}^{-2}mi{n}^{-1}$
• C. $8.24\times {10}^{-2}mi{n}^{-1}$
• D. None of these

Answer 1

Answer: (A)

$9.24\times {10}^{-2}mi{n}^{-1}$

For a $1^{st}$ order reaction constant, $K=\frac{0.693}{t_{1/2}}$
At ${27}^{o}C:K_1=\left(0.693/30\right)=2.31\times {10}^{-2}mi{n}^{-1}$
At ${47}^{o}C:K_2=\left(0.693/10\right)=6.93\times {10}^{-2}mi{n}^{-1}$

Hence, the correct option is (A).