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

$(a)\;4\;hr \\ (b)\;0.5\;hr \\(c)\;0.25\;hr \\(d)\;1\;hr$

For a zero order reaction ,k= rate constant
When $t= t_{y_2},$ then $x= \large\frac{|A|_o}{2}$
Given that $[A_0]= 2M$
$t_{y_2}=1 hr,K=1$
$\therefore K= \large\frac{|A|_0}{2 \times ty_2} =\frac{2}{2 \times 1}$
$\qquad= 1 mol .L^{-1}.hr^{-1}$
Now, change in conc $(x)=0.50 -0.25$
$\qquad= 0.25\;M$
$\therefore t= \large\frac{x}{k} =\frac{0.25}{1}$$=0.25\;hr$
Hence c is the correct answer.