Question

The time for half life period of a certain reaction, $A\to \text{Products}$ is 1 hour. When the initial concentration of the reactant 'A', is $2.0{\text{mol L}}^{-1}$, how much time (in hour) does it take for its concentration to come from $0.50{\text{mol L}}^{-1}$ to $0.25{\text{mol L}}^{-1}$, if it is a zero order reaction?

Answer 1

Given,
Half life period for the reaction, $t_{\frac{1}{2}}=1\text{hr}$
Initial concentration, $\left[A_o\right]=2{\text{mol L}}^{-1}$
Again, order of the reaction is zero.
Thus, $t_{\frac{1}{2}}=\frac{\left[A_o\right]}{2k}$
$\Rightarrow k=\frac{\left[A_o\right]}{2t_{\frac{1}{2}}}=\frac{2}{2\times 1}=1{\text{mol L}}^{-1}{\text{hr}}^{-1}$

For, zero order reaction,
$k=\frac{1}{t}\left(\right[A_o]-[A\left]\right)$
$\Rightarrow t=\frac{1}{k}\left(\right[A_o]-[A\left]\right)=\frac{1}{1}[0.50-0.25]=0.25\text{hr}$