For a first order reaction the rate constant is 6.909 min-1. The time taken for 75% conversion in minutes is

Question

For a first order reaction the rate constant is 6.909 min-1. The time taken for 75% conversion in minutes is (A) (3/2) log 2 (B) (2/3) log 3 (C) (2/3) log 2 (D) (3/2) log (3/4)

Tardigrade Admin · Accepted Answer

For first order reaction, k = (2.303/t) log (a/a-x) 6.909 = (2.303/t) log (100/100-75) t = (2.303/6.909) log 4 = (1/3) log 22 = (2/3) log 2

Q. For a first order reaction the rate constant is 6.909 $mi n^{- 1}$ . The time taken for 75% conversion in minutes is

$\frac{3}{2} l o g 2$

$\frac{2}{3} l o g 3$

$\frac{2}{3} l o g 2$

$\frac{3}{2} l o g \frac{3}{4}$

$\frac{2}{3} l o g \frac{4}{3}$

For first order reaction,
$k = \frac{2.303}{t} l o g \frac{a}{a - x}$
$6.909 = \frac{2.303}{t} l o g \frac{100}{100 - 75}$
$t = \frac{2.303}{6.909} l o g 4$
$= \frac{1}{3} l o g 2^{2}$
$= \frac{2}{3} l o g 2$

Q. For a first order reaction the rate constant is 6.909 min−1. The time taken for 75% conversion in minutes is

23​log2

32​log3

32​log2

23​log43​

32​log34​

For first order reaction, k=t2.303​loga−xa​ 6.909=t2.303​log100−75100​ t=6.9092.303​log4 =31​log22 =32​log2