Question

The reaction $A⟶B$ follows first order kinetics. The time taken for $0.8$ mole of $A$ to produce $0.6$ mole of $B$ is $1h$. What is the time taken for conversion of $0.9$ mole of $A$ to produce $0.675$ mole of $B$?

• A. $0.25h$
• B. $2h$
• C. $1h$
• D. $0.5h$

Answer 1

The correct option is C $1h$

$\Rightarrow$ $k=\frac{2.303}{t}\log \frac{A_0}{A_t}$
or $k=\frac{2.303}{1}\log \frac{0.8}{0.2}....\left(i\right)$

Remaining moles of $A=0.9-0.675$
$=0.225$

$k=\frac{2.303}{t_1}\log \frac{0.9}{0.225}....\left(ii\right)$

From eq. $\left(i\right)$ and $\left(ii\right)$

$\frac{2.303}{1}\log \frac{0.8}{0.2}=\frac{2.303}{t_1}\log \frac{0.9}{0.225}$
$t_1=1h$