The rate of a first order reaction is 0.4 mol L-1 sec-1 at 10 minutes and 0.04 mol L-1 sec-1 at 20 minutes after initiation. The half-life of the reaction is

Question

The rate of a first order reaction is 0.4 mol L-1 sec-1 at 10 minutes and 0.04 mol L-1 sec-1 at 20 minutes after initiation. The half-life of the reaction is (A) 2 minutes (B) 6.9 minutes  (C) 3.0 minutes (D) 3.3 minutes.

Tardigrade Admin · Accepted Answer

Let the reaction starting at 10 minutes k=(2.303/t) log (a/a-x) , (Time = 20 - 10 = 10 minutes) =(2.303/10) log (0,4/0.04) =(2.303/10 ) t1/ 2 =(0.693/k) =(0.693×10/2.303) 3.0 minutes

Q. The rate of a first order reaction is $0.4 m o l L^{- 1} se c^{- 1}$ at $10$ minutes and $0.04 m o l L^{- 1} se c^{- 1}$ at $20$ minutes after initiation. The half-life of the reaction is

$2 min u t es$

$6.9 min u t es$

$3.0 min u t es$

$3.3 min u t es .$

Let the reaction starting at $10$ minutes
$k = \frac{2.303}{t} l o g \frac{a}{a - x}, (T im e = 20 - 10 = 10 min u t es)$
$= \frac{2.303}{10} l o g \frac{0 , 4}{0.04} = \frac{2.303}{10}$
$t_{1/2} = \frac{0.693}{k} = \frac{0.693 \times 10}{2.303} 3.0 min u t es$

Q. The rate of a first order reaction is 0.4molL−1sec−1 at 10 minutes and 0.04molL−1sec−1 at 20 minutes after initiation. The half-life of the reaction is

2minutes

6.9minutes

3.0minutes

3.3minutes.