If the rate constant of a reaction is 0.03 , how much time does it take for 7.2 mol concentration of the reactant to get reduced to 0.9 mol ? (Given: log 2 = 0.301) [2025]

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Solution

Q.
If the rate constant of a reaction is 0.03 $s^{- 1}$ , how much time does it take for 7.2 mol $L^{- 1}$ concentration of the reactant to get reduced to 0.9 mol $L^{- 1}$

(Given: log 2 = 0.301) [2025]

1 210 s

2 21.0 s

3 69.3 s

4 23.1 s

Ans.
(3)

Rate constant, $k = 0.03$ $s^{- 1}$

For $1^{st}$ order reaction, $k = \frac{2.303}{t} \log \frac{a}{a - x}$

So, $t = \frac{2.303}{0.03} \log \frac{7.2}{0.9} = \frac{2.303}{0.03} \log 8 = \frac{2.303}{0.03} \times 3 \log 2$

$= \frac{2.303}{0.03} \times 3 \times 0.301$ $[Given, \log 2 = 0.301]$

$= 69.32$ $s$

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