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. $18.4$