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JEE Main levelOne or more correct optionsDifficulty 2 of 3ck043

Select the correct statements for a first order reaction $A products$ (use $ln 2 = 0.693$ and $ln 1000 = 6.908$ where needed).

AThe half-life does not depend on the initial concentration.
BThe unit of $k$ is $s^{- 1}$ (time inverse).
CAbout 10 half-lives are needed for $99.9%$ completion.
D $t_{1/2} = [A]_{0} /2 k$ .

Answer: A, B, C

For first order

t_{1/2} = 0.693/ k

, independent of

[A]_{0}

, and

k

has the unit of inverse time. For

99.9%

completion

t = ln 1000/ k = 6.908/ k

, which is

6.908/0.693 = 9.97 \approx 10

half-lives. The expression

[A]_{0} /2 k

is the half-life of a zero order reaction.

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