The half-life of a reaction is inversely proportional to the square of the initial concentration of the reactant. Then the order of the reaction is

Question

The half-life of a reaction is inversely proportional to the square of the initial concentration of the reactant. Then the order of the reaction is (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

For nth order reaction, t1/2 propto(1/an-1) Given, t1/2 propto (1/a2) On comparing, an-1 = a2 n-1 = 2 ∴ n = 3 Hence, the order of reaction is 3.

Q. The half-life of a reaction is inversely proportional to the square of the initial concentration of the reactant. Then the order of the reaction is

0

1

2

3

0.5

For nth order reaction,
$t_{1/2} \propto \frac{1}{a ^{n - 1}}$
Given, $t_{1/2} \propto \frac{1}{a ^{2}}$
On comparing,
$a^{n - 1} = a^{2}$
$n - 1 = 2$
$∴ n = 3$
Hence, the order of reaction is 3.

Q. The half-life of a reaction is inversely proportional to the square of the initial concentration of the reactant. Then the order of the reaction is

0

1

2

3

0.5

For nth order reaction, t1/2​∝an−11​ Given, t1/2​∝a21​ On comparing, an−1=a2 n−1=2 ∴n=3 Hence, the order of reaction is 3.

For nth order reaction,
$t_{1/2} \propto \frac{1}{a ^{n - 1}}$
Given, $t_{1/2} \propto \frac{1}{a ^{2}}$
On comparing,
$a^{n - 1} = a^{2}$
$n - 1 = 2$
$∴ n = 3$
Hence, the order of reaction is 3.