1. Tardigrade
  2. Question
  3. Chemistry
  4. In the Arrhenius equation for a certain reaction the value of A and Ea (activation energy) are 4 × 1013 sec-1 and 98.6 kJ mol-1 respectively. If the reaction is of first order, the temperature at which its half-life period is 10 minutes is

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Q. In the Arrhenius equation for a certain reaction the value of $A$ and $E_a$ (activation energy) are $4 \times 10^{13} sec^{-1}$ and $98.6 kJ mol^{-1}$ respectively. If the reaction is of first order, the temperature at which its half-life period is 10 minutes is

Chemical Kinetics

Solution:

Calculation of $K$
We know that $k=\frac{0.693}{t12}=\frac{0.693}{10\times60}\left(t_{1/2}=10\times60 sec\right)=1.1558\times10^{-3}$
log $k=log A-\frac{E_{a}}{2.303 RT}$
log $1.155\times10^{-3}=log4\times10^{13}-\frac{98.6}{2.303\times8.314\times10^{-3}\times T}$
On usual calculation, $T = 311.3 5 K$