For a first order reaction $t_{1/2}$ is $1200 \ s$. The specific rate constant in $s^{-1}$ is

$A$ first order reaction takes $40 \ min$ for $20 \%$ decomposition. Calculate its rate constant.

The rate constant of a first order reaction whose half-life is $480 \ s$,is

Consider a general first order reaction $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. If the initial pressure is $200 \ mm$ and after $20 \ minutes$ it is $250 \ mm$,then the half-life period of the reaction (in minutes) is. $(\log 2 = 0.30, \log 3 = 0.48, \log 4 = 0.60)$

The integrated rate law equation for a first-order gas-phase reaction $A(g) \rightarrow B(g) + C(g)$ is given by (where $P_i$ is the initial pressure and $P_t$ is the total pressure at time $t$):

Which is the correct relation between rate constant and half-life of a first-order reaction?