1. Tardigrade
  2. Question
  3. Chemistry
  4. The rate coefficient (k) for a particular reactions is 1.3 × 10-4 M-1 s-1 at 100°C, and 1.3 × 10-3 M-1s-1 at 150°C What is the energy of activation (Ea) (in kJ) for this reaction ? (R = molar gas constant = 8.314 JK-1 mol-1)

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Q. 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 $= 8.314 \,JK^{-1}\,mol^{-1})$

JEE MainJEE Main 2014Chemical Kinetics

Solution:

According to Arrhenius equation

$log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303\,R}\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right)$

$log \frac{1.3\times10^{-3}}{1.3\times10^{-4}}=\frac{E_{a}}{2.303\times8.314} \left[\frac{1}{373}-\frac{1}{423}\right]$

$1==\frac{E_{a}}{2.303\times8.314}\left[\frac{1}{373}-\frac{1}{423}\right]$

$E_{a}=60\,kJ/ mole$