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 $year$)?

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.

The first order reaction $A_{(g)} \rightarrow B_{(g)} + 2C_{(g)}$ occurs at $25^{\circ} C$. After $24 \ min$,the ratio of the concentration of products to the concentration of the reactant is $1:3$. What is the half-life of the reaction (in $min$)? $(\log 1.11 = 0.046)$

Calculate the half-life of a first-order reaction in minutes if the rate constant is $1 \times 10^{-3} \ sec^{-1}$.

For a first order reaction $(A) \rightarrow$ products,the concentration of $A$ changes from $0.1 \ M$ to $0.025 \ M$ in $40 \ min$.
The rate of reaction when the concentration of $A$ is $0.01 \ M$ is ............$ \times 10^{-4} \ M/min$.

Which of the following graphs has an intercept equal to zero?