The rate constant and half-life of a first-order reaction are related to each other as -

$R \rightarrow P$ is a first order reaction. For this reaction,a graph of $\ln [R]$ (on $y$-axis) and time (on $x$-axis) gives a straight line with a negative slope. The intercept on the $y$-axis is equal to ($k =$ rate constant):

The time taken for $10 \%$ completion of a first order reaction is $20 \ min$. Then, for $19 \%$ completion, the reaction will take (in $min$)

$N_2O_{(g)} \to N_{2(g)} + \frac{1}{2}O_{2(g)}$
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 which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

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