The rate constant for a first order reaction is 60 s^-1. How much time will it take to reduce the initial concentration of the reactant to its \(\frac{1}{10}\)th value?

0.0383

k = 60 s^-1, t = ?
If initial concentration is [A₀]

Then one tenth of the initial concentration will be \(\frac{[A_o]}{10}\)

Using expression for first order reaction,

t = \(\frac{2.303}{k}\)log\(\frac{[A_o]}{[A]}\)

t = \(\frac{2.303}{60}\)log\(\frac{[A_o]}{[A_o/10]}\)

t = \(\frac{2.303}{60}\)log10

t = 0.0383 s