If the half-life of a first-order reaction is $6.93$ minutes, then the time required for the completion of $99\%$ of the reaction will be . . . . . . minutes. (Given: $\log 2 = 0.3010$)

For the reaction $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$,the rate law is $R = k[A]$. At the start $(t = 0)$,the total pressure is $100 \ mm$ and after $t = 10 \ min$,the total pressure is $120 \ mm$. The rate constant $(min^{-1})$ is:

$A$ first-order reaction takes $30$ minutes for $75\%$ decomposition. Calculate its rate constant. (in $\text{ min}^{-1}$)

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: $\log_{10}(5) = 0.6989$)

For which of the following graphs of a first-order reaction will the value of the slope be $\frac{K}{2.303}$?

For a first order reaction,show that the time required for $99 \%$ completion is twice the time required for the completion of $90 \%$ of the reaction.