If the half-life $(t_{1/2})$ of a first-order reaction is $20 \ minutes$,what fraction of the reactant remains after $40 \ minutes$?

Consider the following first order gas phase reaction at constant temperature:
$A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$
If the total pressure of the gases is found to be $200 \ torr$ after $23 \ s$ and $300 \ torr$ upon the complete decomposition of $A$ after a very long time,then the rate constant of the given reaction is . . . . . . $\times 10^{-2} \ s^{-1}$ (nearest integer).
[Given: $\log_{10}(2) = 0.301$]

Which of the following relations is correct for the given reaction orders?

$A$ first order reaction is $75\%$ completed in $100 \ min$. How long will it take for its $87.5\%$ completion? (in $\min$)

What is the value of the rate constant for a first-order reaction,if it takes $15 \ min$ for the consumption of $20 \%$ of the reactants?

State whether the following sentences are true $(T)$ or false $(F)$.
$(a)$ The reaction of an ester with water produces an alcohol and an acid.
$(b)$ The concentration of water remains constant during the hydrolysis of an ester.
$(c)$ In the hydrolysis of an ester,$[H_2O]$ remains constant.