JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Chemical Kinetics

t_{87.5}

is the time required for the reaction to undergo

87.5%

completion and

t_{50}

is the time required for the reaction to undergo 50% completion. The relation between

t_{87.5}

and

t_{50}

for a first order reaction is

t_{87.5} = x \times t_{50}

The value of

x

____

(Nearest integer)

Answer: 3

Solution

For a first-order reaction, if 87.5% is complete, then 12.5% remains, which is

\frac{A _{0}}{8}

. This corresponds to 3 half-lives:

A_{0} t_{1/2} \frac{A _{0}}{2} t_{1/2} \frac{A _{0}}{4} t_{1/2} \frac{A _{0}}{8}

Therefore,

t_{87.5} = 3 t_{1/2}

. Since

t_{50} = t_{1/2}

for a first-order reaction, we have

t_{87.5} = 3 t_{50}

, giving

x = 3

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Integer answer