If $k$ is the rate constant and $t$ is the time,then the degree of dissociation for a substance undergoing decay with first-order kinetics is:

The half-life for radioactive decay of $^{14}C$ is $5730$ years. An archaeological artifact containing wood had only $80 \%$ of the $^{14}C$ found in a living tree. Estimate the age of the sample.

For the reaction $2A + B \to \text{product}$,the rate law is given by $\frac{-d[A]}{dt} = k[A]$. At a time $t = \frac{t_{1/2}}{\ln 2}$,what is the concentration of the reactant $A$?

In the reaction $2N_2O_5 \to 4NO_2 + O_2$,the initial pressure is $500 \ atm$ and the rate constant $K$ is $3.38 \times 10^{-5} \ s^{-1}$. After $10 \ minutes$,the final pressure of $N_2O_5$ is ........ $atm$.

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.

The following data is obtained during the first order thermal decomposition of $2A_{(g)} \longrightarrow B_{(g)} + C_{(s)}$ at constant volume and temperature. The rate constant in $min^{-1}$ is:

$S$.No.	Time	Total pressure in Pascal
$1$.	At the end of $10 \ min$	$300$
$2$.	After completion	$200$