Question

In a first order reaction ,if $25\%$ of the reaction is completed in $50$ minutes $50\%$ of the total reaction is completed in _________ minutes (approx):

• A. $120$
• B. $100$
• C. $80$
• D. $150$

Answer 1

The correct option is A $120$

Given:

First order reaction- $25$% complete in $50minutes$

Then $50$% of reaction will complete in ?

For the first order reaction,

$k=\frac{2.303}{t}\frac{Loga}{a-x}$

Here $a=100$%, $x=25$% $t=50minutes$

so $k=\frac{2.303}{50}\frac{log100}{100-25}$

$k=\frac{2.303}{50}\frac{log100}{75}$

$k=\frac{2.303}{50}\frac{log4}{3}$------------(1)

In Second case $a=100$%, $x=50$% $t=?minutes$

so $k=\frac{2.303}{t}\frac{log100}{100-50}$

so $k=\frac{2.303}{t}\frac{log100}{50}$

so so $k=\frac{2.303}{t}log2$----------------(2)

Compare (1) and (2) we will get:

$\frac{2.303}{50}\frac{log4}{3}$=$\frac{2.303}{t}log2$

on solving we will get $t=120minutes$ approximately

Option A is correct.