For a zero-order reaction,the correct expression for rate constant $(k)$ at half-life time $(t_{1/2})$ is ($[R_0] =$ initial concentration of reactant).

For a given reaction,the half-life $t_{1/2}$ varies with different initial concentrations $a$. If $t_{1/2} \propto a$ is constant,then the order of the reaction will be .......

Consider the reaction $aX \to bY$, for which the rate constant at $30^\circ C$ is $1 \times 10^{-3} \text{ mol L}^{-1} \text{ s}^{-1}$. Which of the following statements are true?
$A$. When concentration of $X$ is increased to four times, the rate of reaction becomes $16$ times.
$B$. The reaction is a second order reaction.
$C$. The half-life period is independent of the concentration of $X$.
$D$. Decomposition of $N_2O_5$ is an example of the above reaction.
$E$. $\ln \frac{[R]_0}{[R]}$ vs time is valid for the above reaction.

Find the percentage of unreacted reactant for a zero order reaction in $90 \ s$ having a rate constant of $1 \ mol \ dm^{-3} \ s^{-1}$. (in $\%$)

At $T \ K$,if the rate constant for a zero order reaction is $2.5 \times 10^{-3} \ M \ s^{-1}$,the time required for the initial concentration of reactant $R$ to fall from $0.10 \ M$ to $0.075 \ M$ at the same temperature in seconds is:

Derive an expression to calculate the time required for the completion of a zero order reaction.