Question

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

• A. $\frac{1}{6}$ of initial concentration
• B. $\frac{1}{64}$ of initial concentration
• C. $\frac{1}{12}$ of initial concentration
• D. $\frac{1}{32}$ of initial concentration

Answer 1

The correct option is B $\frac{1}{64}$ of initial concentration

Given: $t_{1/2}=10\text{min.}$
For the first order reaction, the amount of reactant left $C_t$ after $n$ half lives $=\frac{C_0}{2^n}$
where, $C_0$ is initial concentration.

Number of half life, $n=\frac{60\text{min.}}{10\text{min.}}=6$

$C_t=\frac{C_0}{(2{)}^6}=\left(\frac{C_0}{64}\right)$