For a zero-order reaction $A \rightarrow \text{Product}$,the half-life is $1 \ h$. If the initial concentration of reactant $A$ is $2.0 \ mol \ L^{-1}$,how many hours will it take for the concentration to decrease from $0.50 \ mol \ L^{-1}$ to $0.25 \ mol \ L^{-1}$?

$A$ zero-order reaction,$A \rightarrow \text{Product}$,with an initial concentration $[A]_0$ has a half-life of $0.2 \ s$. If one starts with the concentration $2[A]_0$,then the half-life is $.... \ s$

What is the concentration (in $mol \ L^{-1}$) of the product $B$ after $20 \ s$ in the following reaction? Given that $A \longrightarrow 3B$,rate $= k[A]^0$. The data is provided in the table below:
| Time $(s)$ | Concentration of reactant $A$ $(mol \ L^{-1})$ |
| :--- | :--- |
| $0$ | $0.1$ |
| $15$ | $0.05$ |
| $20$ | $0.1 - x$ |

For a zero order reaction,the plot of concentration $(a-x)$ $Vs$ time is linear with

$5$ milli-moles of a solid $A$ was dissolved in $5$ moles of $H_2O$. On adding to the solvent,$A$ starts polymerising into another insoluble solid following zero order kinetics. On adding $6$ milli-moles of another solid solute $C$ (after $20$ minutes) the polymerisation completely stops. The insoluble solid polymer is removed and the resulting solution was cooled to a temperature less than $-0.186\,^{\circ}C$ (melting point of solution) to cause solidification of some liquid water. Calculate the value of $'X'$ if rate constant for polymerisation reaction is represented as $10^{-X}\,moles/minute$. $[K_f(H_2O) = 1.86\, K\, Kg\,mol^{-1}]$

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 .......