Question

The rate constant of a reaction is $1.5 \times 10^{7} \,s ^{-1}$ at $50^{\circ} C$ and $4.5 \times 10^{7} \,s ^{-1}$ at $100^{\circ} C$. What is the value of activation energy?

• A. $2.2 \times 10^{3} \,J \,mol ^{-1}$
• B. $2300 \,J \, mol ^{-1}$
• C. $2.2 \times 10^{4} \,J \, mol ^{-1}$
• D. $220 \,J \, mol ^{-1}$

Answer 1

Answer: (C)

$\log \frac{4.5 \times 10^{7}}{1.5 \times 10^{7}}=\frac{E_{a}}{2.303 \times 8.314}\left[\frac{373-323}{373 \times 323}\right]$
$T _{1}=50+273=323$
$T _{2}=100+273=373$
$\log 3=\frac{E_{a}}{2.303 \times 8.314}\left[\frac{50}{373 \times 323}\right]$
$\frac{0.4770 \times 2.303 \times 8.314 \times 373 \times 323}{50}=E_{a}$
$E_{a}=22007\, J \,mol ^{-1} \approx 2.2 \times 10^{4}$