Question

In a first order reaction, the concentration of the reactant is reduced to $12.5\%$ in one hour. When was it half completed ?

• A. 3 hr
• B. 20 min
• C. 30 min
• D. 15 min

Answer 1

Answer: (B)

20 min

Answer 2

Key concept If initial amount of reactant is taken $100 \%$, then after three half-lifes it will remain $12.5 \%$. Hence, on dividing the given time i.e. $1 hr$ $(60 min )$ by 3, we get half-life of the reactant.

Time
Concentration

$t=0\,\,\, t=t_{1/2}$
$100]\,50]$ 1 half-life

$t=2t_{1/2}$
25] 1 half-life

$t=3t_{1/2}$
12.5] 1half-life

Total 3 half-lifes]
Total time taken for ]
3 half -lifes ] $\to \, 1hr=60\,min$
Time taken for 1 half-life $=\frac{60}{3}=20 \,min$