For a first-order reaction, $20 \%$ of the initial concentration remains after $10 \text{ min}$. What is the rate constant of the reaction (in $\text{ min}^{-1}$)? (Given: $\log_{10}(5) = 0.6989$)

The reaction,$N_2O_5 \longrightarrow 2NO_2 + \frac{1}{2} O_2$ is of first order for $N_2O_5$ with rate constant $6.2 \times 10^{-4} \ s^{-1}$. What is the value of rate of reaction when $[N_2O_5] = 1.25 \ mol \ L^{-1}$?

For the gaseous reaction $A(g) \longrightarrow B(g) + C(g) + D(g)$,starting with an initial pressure of $400 \ atm$. If the total pressure after $2 \ hr$ is $800 \ atm$,the value of the rate constant is: (consider the reaction to be $1^{st}$ order): (in $hr^{-1}$)

The rate constant for a first order reaction is $7.0 \times 10^{-4} \ s^{-1}$. If initial concentration of the reactant is $0.080 \ M$,what is the half-life of the reaction?

What is the rate constant of a first-order reaction if the time required to decrease the concentration of the reactant from $1.6 \ M$ to $0.4 \ M$ is $12 \ hours$?

Find the rate constant of a first-order reaction in $sec^{-1}$ having a half-life of $2.5 \ hours$.