The half-life of a first-order reaction is $10 \ min$. If the initial concentration is $0.08 \ mol \ L^{-1}$ and the concentration at some instant is $0.01 \ mol \ L^{-1}$,then $t =$ ........... $\min$.

For the first order reaction $2 N_2O_{5(g)} \rightarrow 4 NO_{2(g)} + O_{2(g)}$,which of the following statements are correct?
$A.$ The concentration of the reactant decreases exponentially with time.
$B.$ The half-life of the reaction decreases with increasing temperature.
$C.$ The half-life of the reaction depends on the initial concentration of the reactant.
$D.$ The reaction proceeds to $99.6 \%$ completion in eight half-life durations.

Hydrolysis of sugar is a first order reaction. Write the reaction.

For the first order reaction,half life is $14 \, sec$. The time required for the initial concentration to reduce to $\frac{1}{8}$ of its value is .......... $sec$.

If $k$ is the rate constant and $t$ is the time,then the degree of dissociation for a substance undergoing decay with first-order kinetics is:

For a certain first order reaction,$32 \%$ of the reactant is left after $570 \ s$. The rate constant of this reaction is ........... $\times 10^{-3} \ s^{-1}$. (Round off to the Nearest Integer).
$[$Given: $\log_{10} 2 = 0.301, \ln 10 = 2.303]$