In a first order reaction,the concentration of reactant decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^2 \ s$. The rate constant of the reaction in $s^{-1}$ is:

Among the following statements,the correct statement about the half-life period for a first order reaction is

$N_2O_{(g)} \to N_{2(g)} + \frac{1}{2}O_{2(g)}$
In a closed vessel,the reaction follows first-order kinetics. If starting with pure $N_2O_{(g)}$,the total pressure after time $t$ is $P_t$ and after a very long time is $P_{\infty}$,then which of the following expressions is correct?

For the first order reaction $A \rightarrow B$,the half-life is $30 \ min$. The time taken for $75 \%$ completion of the reaction is $..... \ min$. (Nearest integer)
Given: $\log 2 = 0.3010, \log 3 = 0.4771, \log 5 = 0.6989$

The reaction $CH_3COCH_{3(g)} \to C_2H_{4(g)} + H_{2(g)} + CO_{(g)}$ is a first-order reaction. If the initial pressure is $0.40 \ atm$ and the total pressure after $10 \ min$ is $0.50 \ atm$,calculate the rate constant of the reaction. $(\log 3.5 = 0.5441)$

The rate constant of a first order reaction is $3 \times 10^{-6} \ s^{-1}$. If the initial concentration is $0.10 \ M$,the initial rate of reaction is: