A reaction A→B is of the order 2.5 with respect to A. The half-life of the reaction will be given

A reaction $A \to B$ is of the order 2.5 with respect to A. The half-life of the reaction will be given

A
$0.693 / k$
B
$1 / ([A]_{0} k)$
C
$k / [A]_{0}$
D
$[1 / (1.5 k [A]_{0}^{1.5})] (2^{1.5} - 1)$

Solution:

$- \frac{d [A]}{d t} = k [A]^{2.5} .$

Hence, $- \frac{d [A]}{[A]^{2.5}} = k d t .$

Thus

$\frac{1}{[A]^{1.5}} - \frac{1}{[A]_{0}^{1.5}} = (1.5) k t$

For $t_{0.5}, [A] = [A]_{0} / 2$

Hence

$\frac{1}{{([A]_{0} / 2)}^{1.5}} - \frac{1}{[A]_{0}^{1.5}} = 1.5 k t_{0.5} \Rightarrow t_{0.5} = \frac{1}{1.5 k [A]_{0}^{1.5}} (2^{1.5} - 1)$

Related content

SBTET Full Form

What is CSS Scholarship – Know About CSS (Central Sector Scholarship) Scholarship 2023

International Coffee Day

International Day for the Elderly

MPL Full Form – Mobile Premier League

How to Prepare for NTSE 2023-24: Best NTSE Preparation Tips?

RRB NTPC Eligibility 2023

NTSE (National Talent Search Exam) Scholarship Scheme: Details, Amount, Eligibility, Selection Process

Casual Leave Application for Office, Teachers, Government Offices with Format and Samples

NCVT Full Form – National Council for Vocational Training