The rate constant of a first order reaction is 6.9 × 10-3 s -1. How much time will it take to reduce the initial concentration to its 1 / 8 text th value?

Question

The rate constant of a first order reaction is 6.9 × 10-3 s -1. How much time will it take to reduce the initial concentration to its 1 / 8 text th value? (A) 100 s (B) 200 s (C) 300 s (D) 400 s

Tardigrade Admin · Accepted Answer

[ A ]=[ A ]0((1/2))n where [A]0= initial concentration (1/8)=1((1/2))n ; n=3 t1 / 2=(0.693/6.9 × 10-3)=100 sec ∴ T=n × t1 / 2=3 × 100=300 sec

Q. The rate constant of a first order reaction is $6.9 \times 1 0^{- 3} s^{- 1}$ . How much time will it take to reduce the initial concentration to its $1/ 8^{th}$ value?

$100 s$

$200 s$

$300 s$

$400 s$

$[A] = [A]_{0} (\frac{1}{2})^{n}$
where $[A]_{0} =$ initial concentration
$\frac{1}{8} = 1 (\frac{1}{2})^{n}; n = 3$
$t_{1/2} = \frac{0.693}{6.9 \times 1 0 ^{- 3}} = 100 sec$
$∴ T = n \times t_{1/2} = 3 \times 100 = 300 sec$

Q. The rate constant of a first order reaction is 6.9×10−3s−1. How much time will it take to reduce the initial concentration to its 1/8th value?

100s

200s

300s

400s