Initial concentration of reactant in a first order reaction is $0.08 \text{ mol dm}^{-3}$. What concentration would remain after $40 \text{ minutes}$? (Given $\frac{[A]_0}{[A]_t} = 5.00$)

For the first-order gaseous reaction $A \rightarrow 2B + C$ at $373 \, K$,starting with pure $A$,the total pressure of the system after $10 \, min$ is $176 \, mm \, Hg$ and after a long time,it is $270 \, mm \, Hg$. Based on this information,calculate: $(1)$ Initial pressure of $A$,$(2)$ Pressure of $A$ after $10 \, min$,and $(3)$ Rate constant.

Rate of first order reaction $A \rightarrow \text{product}$ is $0.01 \ mol \ dm^{-3} \ s^{-1}$. Calculate the rate constant if the concentration of the reactant is $0.2 \ M$. (in $s^{-1}$)

Isomerisation of gaseous cyclobutene to butadiene is a first order reaction. At $T \ K$,the rate constant of the reaction is $3.3 \times 10^{-4} \ s^{-1}$. What is the time required (in $min$) to complete $90 \%$ of this reaction at the same temperature? $(\log 2 = 0.3)$

The rate constant of a first order reaction whose half-life is $480 \ s$,is

$[A] \rightarrow [B]$. If the formation of compound $[B]$ follows first-order kinetics and after $70 \ min$ the concentration of $[A]$ was found to be half of its initial concentration,then the rate constant of the reaction is $x \times 10^{-6} \ s^{-1}$. The value of $x$ is $......$ (Nearest Integer).