Question

Given that for a reaction of $n^{th}$ order, the integrated rate equation is:
$K=\frac{1}{t(n-1)}[\frac{1}{C^{n-1}}-\frac{1}{C_0^{n-1}}]$
where, C and $C_0$ are the concentration of reactant at time t and initially respectively. The $t_{3/4}$ and $t_{1/2}$ are related as: ($t_{3/4}$ is time required for C to become $C_1/4$)

• A. $t_{3/4}=t_{1/2}[2^{n-1}+1]$
• B. $t_{3/4}=t_{1/2}[2^{n-1}-1]$
• C. $t_{3/4}=t_{1/2}[2^{n+1}+1]$
• D. $t_{3/4}=t_{1/2}[2^{n+1}-1]$

Answer 1

The correct option is A $t_{3/4}=t_{1/2}[2^{n-1}+1]$

As we know,
$t_{3/4}=(4{)}^{n-1}-1$
$t_{1/2}=2^{n-1}-1$
$t_{3/4}/t_{1/2}=2^{n-1}+1$