(a) (i) The initial concentration of $\text{N}_2\text{O}_5$ in the first order reaction : $$\text{N}_2\text{O}_5\text{ (g)} \rightarrow 2\text{NO}_2\text{ (g)} + \frac{1}{2}\text{O}_2\text{ (g)}$$ was $1\cdot2 \times 10^{-2}\text{ mol L}^{-1}$. The concentration of $\text{N}_2\text{O}_5$ after $60$ minutes was $0\cdot2 \times 10^{-2}\text{ mol L}^{-1}$. Calculate the rate constant of the reaction at $318\text{ K}$. [${\log 6 = 0\cdot778}$]