For a first order reaction with rate constant $k$,the slope of the plot of $\log(\text{reactant concentration})$ against time is

Calculate the rate constant of a first order reaction if the half-life of the reaction is $40 \ minute$.

Calculate the time required for a reactant to decrease in concentration from $100 \%$ to $20 \%$,if the rate constant of the first-order reaction is $0.02303 \ hour^{-1}$. (in $hour$)

The reaction $N_{2}O_{5} \longrightarrow 2NO_{2} + \frac{1}{2}O_{2}$ is first order in $N_{2}O_{5}$ having rate constant $6.2 \times 10^{-4} \ s^{-1}$. What is the value of rate of reaction when concentration of $N_{2}O_{5}$ is $1.25 \ mol \ L^{-1}$?

Reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ is a first order reaction. It was started with pure $A$.

$t/min$	Pressure of system at time $t/mm \ Hg$
$10$	$160$
$\infty$	$240$

Which of the following option is incorrect?

The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$