What time is required for $100 \ g$ of reactant to reduce to $25 \ g$ in a first order reaction having half life $5760 \ year$ (in $year$)?

The half-life of a first order reaction is $30 \, min$. The time required for $75 \, \%$ completion of the same reaction will be $..... \, min$

Identify $True$ $(T)$ and $False$ $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$I. \log \frac{[R]}{[R]_0} = -\frac{kt}{2.303}$
$II. \log \frac{[R]}{[R]_0} = \frac{kt}{2.303}$

How much time is required for a first-order reaction to be $3/4$ complete?

The half-life period of a first-order reaction is given by:

For the decomposition of $N_2O_5$ according to the equation $2N_2O_5(g) \to 4NO_2(g) + O_2(g)$,the reaction is of first order. After $30 \, \min$ from the start of the reaction in a closed vessel,the total pressure is $305.5 \, mm \, Hg$,and at the end of complete decomposition,the total pressure is $587.5 \, mm \, Hg$. Calculate the rate constant of the reaction.