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)