The slope of a graph $\log [A]_t$ versus '$t$' for a first-order reaction is $-2.5 \times 10^{-3} \,s^{-1}$. Find the rate constant of the reaction.

$A$ substance $A$ decomposes by a first order reaction starting initially with $[A]_0 = 2.00 \, M$ and after $200 \, \min$,$[A]_t = 0.15 \, M$. For this reaction,what is the value of the rate constant $k$?

For a homogeneous gaseous reaction $A_{(g)} \to 3B_{(g)}$,if the pressure after time $t$ is $P_t$ and after completion of the reaction the pressure is $P_\infty$,select the correct relation for the rate constant $K$.

The inactivation rate of a viral preparation is proportional to the amount of virus. In the first minute after preparation,$10 \%$ of the virus is inactivated. The rate constant for viral inactivation is $..... \times 10^{-3} \ min^{-1}$. (Nearest integer)
[Use : $\ln 10 = 2.303; \log_{10} 3 = 0.477; \text{property of logarithm} : \log x^y = y \log x$]

If $60\%$ of a first order reaction was completed in $60 \ min$,$50\%$ of the same reaction would be completed in approximately $.......... \ min.$
$(\log \, 4 = 0.60, \, \log \, 5 = 0.69)$

The decomposition of $N_2O_5$ is a first order reaction represented by $N_2O_5 \to N_2O_4 + \frac{1}{2} O_2$. After $15 \ min$,the volume of $O_2$ produced is $9 \ mL$ and at the end of the reaction,it is $35 \ mL$. The rate constant is equal to: