A first order reaction has a rate constant
Question:

A first order reaction has a rate constant 1.15 10−3 s−1. How long will 5 g of this reactant take to reduce to 3 g?

Solution:

From the question, we can write down the following information:

Initial amount = 5 g

Final concentration = 3 g

Rate constant = 1.15 10−3 s−1

We know that for a 1st order reaction,

$t=\frac{2.303}{k} \log \frac{[\mathrm{R}]_{0}}{[\mathrm{R}]}$

$=\frac{2.303}{1.15 \times 10^{-3}} \log \frac{5}{3}$

$=\frac{2.303}{1.15 \times 10^{-3}} \times 0.2219$

= 444.38 s

= 444 s (approx)