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AIEEE 2010 Solved Paper

Section: Chemistry

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Question : 21 of 89

Marks: +1, -0

The time for half life period of a certain reaction

A \rightarrow

products is 1 hour. When the initial concentration of the reactant '

A

2.0\ \mathrm{mol}\ \mathrm{L}^{-1}

, how much time does it take for its concentration to come from

0.50

0.25\ \mathrm{mol}\ \mathrm{L}^{-1}

if it is a zero order reaction?

$4\ \mathrm{h}$
$0.5\ \mathrm{h}$
$0.25\ \mathrm{h}$
$1\ \mathrm{h}$

Solution:

For the reaction

A \rightarrow

Product ; given

t_{1/2}=1

hour

for a zero order reaction

\;t_{\;\text{completion }\;}= \frac{[A_0]}{k}= \frac{\;\text{ initial conc. }\;}{\;\text{ rate cons }\; \tan t}

\;\therefore\;\; t_{1/2}= \frac{[A_0]}{2K}

or

k= \frac{[A_0]}{2 t_{1/2}} = \frac{2}{2 \times 1} = 1

mol lit

^{-1} h r^{-1}

Further for a zero order reaction

\;k= \frac{dx}{dt}= \frac{\;\text{ change in concentration }\;}{\;\text{ time }\;}

\;I= \frac{0.50-0.25}{\;\text{ time }\;}

\;\therefore\;\; \;\text{ time }\; = 0.25 \mathrm{hr} .

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