For a first-order reaction $A \to B$,what will be the slope of the graph of $t$ versus $\log(a - x)$?

$A$ first order reaction has a rate constant $1.15 \times 10^{-3} \, s^{-1}$. How long will $5 \, g$ of this reactant take to reduce to $3 \, g$?

The thermal decomposition of a molecule follows a first-order reaction. The molecule decomposes $50\%$ in $120 \text{ minutes}$. How many minutes will it take for $90\%$ decomposition?

The reaction,$N_2O_5 \longrightarrow 2NO_2 + \frac{1}{2} O_2$ is of first order for $N_2O_5$ with rate constant $6.2 \times 10^{-4} \ s^{-1}$. What is the value of rate of reaction when $[N_2O_5] = 1.25 \ mol \ L^{-1}$?

$A$ first-order reaction decomposes such that the time taken for $1/8$ and $1/10$ of the initial concentration to decompose are $t_{1/8}$ and $t_{1/10}$ respectively. Find the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$. (Given: $\log_{10} 2 = 0.3$)

What is the numerical value of the rate constant of a first-order reaction that is $20 \%$ completed in $10 \ min$ (in $min^{-1}$)?