For a first order reaction $A \rightarrow \text{Products}$,initial concentration of $A$ is $0.1 \, M$,which becomes $0.001 \, M$ after $5 \, \min$. Rate constant for the reaction in $\min^{-1}$ is .... .

Which of the following curves represents a first-order reaction?

The reaction $CH_3COCH_{3(g)} \to C_2H_{4(g)} + H_{2(g)} + CO_{(g)}$ is a first-order reaction. If the initial pressure is $0.40 \ atm$ and the total pressure after $10 \ min$ is $0.50 \ atm$,calculate the rate constant of the reaction. $(\log 3.5 = 0.5441)$

$A$ $20 \%$ first-order reaction is completed in $32 \ \text{min}$. How much time (in $\text{min}$) will it take for $60 \%$ of the reaction to be completed (in $.00$)?

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of $3.33 \ h$ at $25^{\circ} C$. After $9 \ h$,the fraction of sucrose remaining is $f$. The value of $\log _{10} (\frac{1}{f})$ is ..... $\times 10^{-2}$. (Rounded off to the nearest integer) [Assume : $\ln 10 = 2.303, \ln 2 = 0.693$ ]

For a first order reaction $R \longrightarrow P$,the rate constant is $k$. If the initial concentration of $R$ is $[R_0]$,the concentration of $R$ at any time $t$ is given by the expression: