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 = $1$