Question

The rate coefficient $(k)$ for a particular reactions is $1.3 \times 10^{-4}\, M^{-1}\, s^{-1}$ at $100^{\circ}C$, and $1.3 \times 10^{-3}\,M^{-1}s^{-1}$ at $150^{\circ}C$ What is the energy of activation $(E_{a})$ (in $kJ$) for this reaction ? ($R =$ molar gas constant $= 8.314 \,JK^{-1}\,mol^{-1})$

• A. 16
• B. 60
• C. 99
• D. 132

Answer 1

Answer: (B)

60

Answer 2

According to Arrhenius equation $log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303\,R}\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right)$ $log \frac{1.3\times10^{-3}}{1.3\times10^{-4}}=\frac{E_{a}}{2.303\times8.314} \left[\frac{1}{373}-\frac{1}{423}\right]$ $1==\frac{E_{a}}{2.303\times8.314}\left[\frac{1}{373}-\frac{1}{423}\right]$ $E_{a}=60\,kJ/ mole$