Question

A first order reaction is $10$% complete in $20$ min. The time taken for $19$% completion is:

• A. $30$ min
• B. $40$ min
• C. $50$ min
• D. $38$ min

Answer 1

The correct option is B $40$ min

For first order reaction:

Initially reaction is 10% complete, $x=10;t=20$min

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

let $a=100$

$20=\frac{2.303}{k}log\frac{100}{100-10}$

$20=\frac{2.303}{k}\times 0.0453$

$k=0.1151\times 0.0453=0.00521$

Substituting the value of $k$ and $x=19$

$t=\frac{2.303}{0.00521}log\frac{100}{100-19}$

$t=442.034\times 0.09131=40.3min$