Question

A reaction is $50\%$ completed in $2$ hours and $75\%$ completed in $4$ hours. The order of the reaction is:

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

A reaction is 50% completed in 2 hours and 75% completed in 4 hours, so $\text{t}_{3 / 4} \, =2\text{t}_{1 / 2}$ .
Integrated rate equation for first order kinetics:
$t=\frac{2 . 303}{k}log\left(\frac{C_{0}}{C_{t}}\right)t_{75 \%}=\frac{2 . 303}{k}log\left(\frac{100}{25}\right)t_{50 \%}=\frac{2 . 303}{k}log\left(\frac{100}{50}\right)\frac{t_{75 \%}}{t_{50 \%}}=\frac{2}{1}$
$\text{t}_{3 / 4} \, = 2 \text{t}_{1 / 2}$ for first-order reaction.
Order = $1$