The rate constant of a reaction quadruples when the temperature changes from 300 K to 320 K . Calculate the activation energy for this reaction. $\left[\log 2=0.30, \log 4=0.60,2.303 \mathrm{R}=19.15 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

(a) For the reaction

$$2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \text { at } 318 \mathrm{~K}$$

Calculate the rate of reaction if rate of disappearance of $$\mathrm{N}_2 \mathrm{O}_{5(\mathrm{~g})}$$ is $$1.4 \times 10^{-3} \mathrm{~m} \mathrm{~s}^{-1}$$.

(b) For a first order reaction derive the relationship $$\mathbf{t}_{99 \%}=\mathbf{2} \mathbf{t}_{90 \%}$$