The reaction $A + B \xrightarrow{k}$ product is first order with respect to $A$ and zero order with respect to $B$. If $a_0$ and $a_t$ are the concentrations of $A$ at $t = 0$ and after time $t \, sec$ respectively,then select the correct relationship -

The value of the velocity constant for a first-order reaction is $3.46 \times 10^{-3} \ min^{-1}$. The time for half-change is ........ $min$.

In a first order reaction,the concentration of the reactant decreases from $0.6 \ M$ to $0.3 \ M$ in $15 \ min$. The time taken for the concentration to change from $0.1 \ M$ to $0.025 \ M$ in minutes is

The reaction $A \to B$ follows first-order kinetics. It takes $1 \ hr$ for $0.60 \ mole$ of $B$ to be formed from $0.80 \ mole$ of $A$. How much time (in $hr$) will it take for $0.675 \ mole$ of $B$ to be formed from $0.90 \ mole$ of $A$?

The decomposition of $O_{3(g)}$ follows first order kinetics and is given by $O_{3(g)} \longrightarrow O_{2(g)} + O_{(g)}$. The rate constant for this reaction is $1.0 \times 10^{-3} \ s^{-1}$. The initial pressure of $O_{3(g)}$ is $100 \ atm$. What will be the partial pressure (in $atm$) of $O_3, O_2, O$ respectively after $38.38 \ minutes$?

The rate constant for the decomposition of $H_2O_2$ is $3.66 \times 10^{-3} \ s^{-1}$. If the initial concentration of $H_2O_2$ is $0.882 \ M$,then in how many seconds will its concentration become $0.600 \ M$?