What is the half-life of a first order reaction if the time required to decrease the concentration of the reactant from $1.0 \ M$ to $0.25 \ M$ is $10 \ hours$ (in $hours$)?

The ratio of the time taken to complete $60\%$ and $20\%$ of a first-order reaction $[A \rightarrow \text{product}]$ is : $(\log 2 = 0.3)$

The following results are obtained in one pseudo first order reaction:

Time $(s)$	$0$	$30$	$60$	$90$
Concentration $(mol \ L^{-1})$	$0.551$	$0.312$	$0.173$	$0.085$

$(a)$ Calculate the average rate of reaction between $30$ and $60$ seconds.
$(b)$ Calculate the rate constant $(k)$ of this first order reaction.

For a first-order reaction $A \to B$,what will be the slope of the graph of $t$ versus $\log(a - x)$?

For the thermal decomposition of $N_2O_{5(g)}$ at constant volume,the following table can be formed for the reaction mentioned below:
$2N_2O_{5(g)} \rightarrow 2N_2O_{4(g)} + O_{2(g)}$

$S.NO$	$Time/s$	Total pressure $(atm)$
$1.$	$0$	$0.6$
$2.$	$100$	$X$

$X = . . . . . . \times 10^{-3} \ atm$ [nearest integer]
Given: Rate constant for the reaction is $4.606 \times 10^{-2} \ s^{-1}$.

The units of rate constant for a first-order reaction are: