A second order reaction in which both the reactants have same con… - Vidyadip

Question

A second order reaction in which both the reactants have same concentration, is $20\%$ completed in $500$ seconds. How much time it will take for $60\%$ completion?

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Answer

The second order equation when both the reactants have same concentration is
$k =\frac{1}{t} \cdot \frac{x}{a(a-x)}$
If $a =100, x =20,1=500$ seconds
Then $k =\frac{1}{500} \times \frac{20}{100 x(100-20)}$
When
$a =100 $
$x =60 $
$t =? $
$t =\frac{1}{k} \frac{60}{100 \times 40}$
Substituting the value of $k$,
$t =\frac{500 x 100 x 80}{20} \times \frac{60}{100 x 40}$
or
$t =3000 \text { seconds }$

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