Calculate the rate constant of a first-order reaction having a half-life of $1 \text{ minute } 40 \text{ seconds}$.

At $T(K)$,if the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,the time to reduce the initial concentration of the reactant to $1/10$ of its initial value in seconds is:

Azo isopropane decomposes according to the equation:
$((CH_3)_2CHN)_2N_{2(g)} \xrightarrow{250 - 290 \ ^oC} N_{2(g)} + C_6H_{14(g)}$
It is found to be a first order reaction. If the initial pressure is $P_o$ and the total pressure of the mixture at time $t$ is $P_t$,then the rate constant $K$ is given by:

The half-life of a first-order reaction is $10 \ minutes$. If the initial concentration is $0.08 \ mol/L$ and at some instant the concentration is $0.01 \ mol/L$,then the time elapsed is ...... minutes.

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 ........ $min$.

Ethylene is produced by $C_4H_8 (\text{Cyclobutane}) \xrightarrow{\text{Heat}} 2C_2H_4$. The rate constant is $2.3 \times 10^{-4} \text{ s}^{-1}$. In what time will the molar ratio of ethylene to cyclobutane in the reaction mixture attain the value $1$? ...... $\text{min}$