Half-life of a first order reaction is $20 \ s$ and initial concentration of reactant is $0.2 \ M$. The concentration of reactant left after $80 \ s$ is (in $M$)

For a first order reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ at constant volume and $300 \ K$,the total pressure at the beginning $(t=0)$ and at time $t$ are $P_0$ and $P_t$,respectively. Initially,only $A$ is present with concentration $[A]_0$,and $t_{1/3}$ is the time required for the partial pressure of $A$ to reach $1/3^{rd}$ of its initial value. The correct option$(s)$ is (are) (Assume that all these gases behave as ideal gases)

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

Following data was obtained for the first order decomposition of $SO_2Cl_{2(g)}$ at constant volume:
$SO_2Cl_{2(g)} \to SO_{2(g)} + Cl_{2(g)}$

$S. No.$	$Time$ $(s)$	$Total$ $pressure$ $(atm)$
$1$	$0$	$0.5$
$2$	$100$	$0.6$

Calculate the rate constant.

For which order reaction is a straight line parallel to the $x-$axis obtained by plotting a graph between half-life $(t_{1/2})$ and initial concentration '$a$'?

In a first order reaction,$87.5 \%$ of the reactant is converted into the product in $15 \ minutes$. The rate constant for the reaction is given by: