Question

In a first order reaction the reacting substance has half-life period of ten minutes. What fraction of the substance will be after an hour the reaction has occurred?

• A. 1/6 of initial concentration
• B. 1/64 of initial concentration
• C. 1/12 of initial concentration
• D. 1/32 of initial concentration

Answer 1

Answer: (B)

1/64 of initial concentration

The half-life of a reaction is the time required during which amount of reactant has reacted becomes half of its initial amount.

So, after one half life,

Amount of reactant left unreacted= $\frac{A_0}{2}$

if $A_0$ is the initial amount.

Amount of reactant left after two half lives= $\frac{A_0}{2^2}$

Amount of reactant left after three half lives =$\frac{A_0}{2^3}$

In general,

Amount of reactant left after $n$ half lives= $\frac{A_0}{2^n}$

Given, half life of first order reaction as $10$ minutes.

So, No. of half lives in $60$ minutes=$\frac{60}{10}=6$

Amount of reactant left after $6$ half lives= $\frac{A_0}{2^6}$

= $A_0/64$

So, after $6$ half-lives, the fraction of reactant left will be $\frac{1}{64}$ of the initial concentration.