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

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.

$20 \%$ of a first order reaction was found to be completed at $10:00 \ am$. At $11:30 \ am$ on the same day,$20 \%$ of the reaction was found to be remaining. The half-life period in minutes of the reaction 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.

The half-life values for two different first-order reactions $A$ and $B$ are $75 \ min$ and $2.5 \ h$ respectively. What is the ratio of their rate constants $\frac{k_A}{k_B}$?

Find the rate constant of a first-order reaction in $sec^{-1}$ having a half-life of $2.5 \ hours$.