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JEE Advanced levelSingle correct optionDifficulty 3 of 3ck046

In a first order reaction, $75%$ of the reactant is decomposed in $40 min$ . The percentage decomposed in $100 min$ is

A $93.75%$
B $98.4%$
C $87.5%$
D $96.9%$

Answer: D

75%

decomposed means

25% = (1/2)^{2}

remains, so two half-lives take

40 min

and

t_{1/2} = 20 min

. In

100 min

there are 5 half-lives, so

(1/2)^{5} = 0.03125

remains and

96.9%

is decomposed.

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