If compound A reacts with B following first order kinetics with rate constant . The time taken by A (in seconds) to reduce from 7 g to 2 g will be ______. (Nearest integer) [log 5 = 0.698, log 7 = 0.845, log 2 = 0.301] [2023]

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Solution

Q.
If compound A reacts with B following first order kinetics with rate constant $2.011 \times 10^{- 3} s^{- 1}$ . The time taken by A (in seconds) to reduce from 7 g to 2 g will be ______. (Nearest integer) [log 5 = 0.698, log 7 = 0.845, log 2 = 0.301] [2023]

Ans.
(623)

$K = \frac{1}{t} \ln (\frac{a}{a - x})$

$K = \frac{1}{t} \ln (\frac{W_{0}}{W_{t}})$

$t = \frac{1}{K} \ln (\frac{7}{2})$

$t = \frac{2.303}{K} [\log 7 - \log 2]$

$= \frac{2.303}{K} [0.845 - 0.301]$

$= \frac{2.303}{2.011 \times 10^{- 3}} \times 0.544 = 622.989 sec$

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