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?

Answer 1

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