In a first order reaction，the concentration of reactant decreases from 400 moles lit $^{-1}$ to 50 moles lit ${ }^{-1}$ in $7 \cdot 5 \times 10^3 \mathrm{~s}$ ．The rate constant of the reaction is（approximately）

An organic compound undergoes first order decomposition．The time taken for its decomposition to $\frac{1}{8}$ th and $\frac{1}{10}$ th of its initial concentration are $t_{1 / 8}$ and $t_{1 / 10}$ respectively．The value of $\left[\frac{t_{1 / 8}}{t_{1 / 10}}\right]$ is ［Given $\log _{10} 2=0 \cdot 3$ ］

For a chemical reaction, half-life period $\left(t_{\frac{1}{2}}\right)$ is 10 minutes. How much reactant will be left after 20 minutes if one starts with 100 moles of reactant and the order of the reaction be (i) zero, (ii) one and (iii) two?

An egg takes 4.0 minutes to boil at sea level where the boiling point of water is $T_1 K$, where as it takes 8.0 minutes to boil on a mountain top where the boiling point of water is $\mathrm{T}_2 \mathrm{~K}$. The activation energy for the reaction that takes place during the boiling of egg is