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  3. Chemistry
  4. The activation energy of a reaction at a given temperature is found to be 2.303 RT J mol-1 . The ratio of rate constant to the Arrhenius factor is

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Q. The activation energy of a reaction at a given temperature is found to be $2.303 \,RT \,J mol^{-1}$ . The ratio of rate constant to the Arrhenius factor is

KCETKCET 2011Chemical Kinetics

Solution:

$k=A e^{-E_{a} / R T} $

$\frac{k}{A} = e^{-E_{a} / R T}$

$\ln \left(\frac{k}{A}\right) =\frac{-E_{a}}{R T} $

$2.303 \log \left(\frac{k}{A}\right) =\frac{-E_{a}}{R T}$

$\log \left(\frac{k}{A}\right) =\frac{-E_{a}}{2.303 R T}$

$\log \left(\frac{k}{A}\right) =\frac{-2.303 R T}{2.303 R T}$

$\log \left(\frac{k}{A}\right) =-1 $

$\therefore \frac{k}{A} =0.1$