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JEE Main levelOne or more correct optionsDifficulty 2 of 3ck086

Select the correct statement(s) about the dependence of half-life $t_{1/2}$ on the initial concentration $a$ for reactions of order $n$ .

AFor $n = 0$ , $t_{1/2}$ is independent of $a$ .
BFor $n = 1$ , $t_{1/2}$ is independent of $a$ .
CFor $n = 2$ , $t_{1/2} \propto 1/ a$ .
DFor any order $n \neq = 1$ , $t_{1/2} \propto a^{1 - n}$ .

Answer: B, C, D

The general result for

n \neq = 1

is

t_{1/2} = \frac{2 ^{n - 1} - 1}{k ( n - 1 )} a^{1 - n}

. Putting

n = 2

gives

1/ a

,

n = 1

gives no

a

dependence, and

n = 0

gives

t_{1/2} = a /2 k \propto a

, so the zero order statement is false.

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