$A$ first order reaction takes $40 \ min$ for $20 \%$ decomposition. Calculate its rate constant.

$75\%$ of a first order reaction was completed in $32$ minutes. When was $50\%$ of the reaction completed? ......... $\min$

Consider the following first-order gas-phase reaction: $A_{(g)} \to B_{(g)} + C_{(g)}$. At time $t$,the total pressure is $p_t \ atm$. Derive the integrated rate equation for this reaction.

$t_{87.5}$ is the time required for the reaction to undergo $87.5 \%$ completion and $t_{50}$ is the time required for the reaction to undergo $50 \%$ completion. The relation between $t_{87.5}$ and $t_{50}$ for a first order reaction is $t_{87.5} = x \times t_{50}$. The value of $x$ is $......$. (Nearest integer)

If compound $A$ reacts with $B$ following first order kinetics with rate constant $2.011 \times 10^{-3} \ s^{-1}$. The time taken by $A$ (in seconds) to reduce from $7 \ g$ to $2 \ g$ will be $.........$ (Nearest Integer) $[\log 5=0.698, \log 7=0.845, \log 2=0.301]$

$N_{2}O_{5(g)} \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$
In the above first order reaction,the initial concentration of $N_{2}O_{5}$ is $2.40 \times 10^{-2} \ mol \ L^{-1}$ at $318 \ K$. The concentration of $N_{2}O_{5}$ after $1 \ hour$ was $1.60 \times 10^{-2} \ mol \ L^{-1}$. The rate constant of the reaction at $318 \ K$ is $..... \times 10^{-3} \ min^{-1}$. (Nearest integer)
[Given: $\log 3 = 0.477, \log 5 = 0.699$]