For the reaction $A \rightarrow \text{products}$,the graph of $t_{1/2}$ versus $[A]_0$ is given below. The concentration of $A$ at $10 \ \text{minutes}$ is $.......... \times 10^{-3} \ \text{mol L}^{-1}$ $(nearest \ integer)$. The reaction was started with $2.5 \ \text{mol L}^{-1}$ of $A$.

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).

The order of reaction for which the units of rate constant are $mol \ dm^{-3} \ s^{-1}$ is

In the reaction,$A + B \to C + D$,the rate $\left( \frac{dx}{dt} \right)$ when plotted against time $t$ gives a straight line parallel to the time axis. The order and rate of reaction will be

If the slope of a line of the graph between dissociated concentration of reactant $([A]_0 - [A]_t)$ and time ($t$ in $min$) for a zero order reaction is $0.02 \ mol \ L^{-1} \ min^{-1}$,then calculate the initial concentration of reactant $([A]_0)$,if after $30 \ min$ its concentration $([A]_t)$ is $0.05 \ mol \ L^{-1}$. (in $M$)

The rate constant for a zero order reaction $A \rightarrow$ products is $0.0030 \ mol \ L^{-1} \ s^{-1}$. How long will it take for the initial concentration of $A$ to fall from $0.10 \ M$ to $0.075 \ M$ (in $s$)?