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For a chemical reaction, the ratio of rate constant at $500\:K$ to that at $400\:K$ is $2.5$. Given $R=8.314\:J$ mol$^{-1}$ $K^{-1}$, the value of activation energy (in $kJ$/mol) is 

  1. $10.5$
  2. $12.0$
  3. $15.2$
  4. $18.4$
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