Question

Half- life of a reaction is found to the inversely proportional to the fifth power of its initial concentration, the order of reaction is

• A. 5
• B. 3
• C. 6
• D. 4

Answer 1

The Correct Option is C

The half-life of a reaction is a measure of the time it takes for the concentration of a reactant to decrease by half.
The relationship between the half-life and the order of a reaction can be expressed mathematically as:
\(t_{1/2} \propto \frac{1}{{[A]}^{(n-1)}}\)
where \(t_{1/2}\) is the half-life,\( [A] \) is the initial concentration of the reactant, and n is the order of the reaction.
Given that the half-life is inversely proportional to the fifth power of the initial concentration, we can rewrite the equation as:
\(t_{1/2} \propto \frac{1}{{[A]}^5}\)
Comparing this equation with the general form, we can see that \(n - 1 = 5\), which implies that n = 6.
Therefore, the order of the reaction is (C) 6.

Answer 2

Given: Half-life \( t_{1/2} \propto \frac{1}{a^5} \) 

For an n^th order reaction (where \( n \ne 1 \)), the half-life is given by:

$$ t_{1/2} \propto \frac{1}{a^{n - 1}} $$

Comparing with the given relation: $$ \frac{1}{a^{n - 1}} = \frac{1}{a^5} \Rightarrow n - 1 = 5 \Rightarrow n = 6 $$

Correct answer: 6