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Chemical Kinetics

Question

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

Solution

Given that
Initial quantity, [R]^o= 5 g
Final quantity, [R] = 3 g
Rate constant, k = 1.15 x 10⁻³ s⁻¹
Formula of 1^st order reaction,
We know that

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

t = \frac{2.303}{1.15 \times 10^{- 3}} \log (\frac{5}{3}) = \frac{2.303}{1.15 \times 10^{- 3}} (\log 5 - \log 3) = \frac{2.303}{1.15 \times 10^{- 3}} (0.6990 - 0.4771) = \frac{2.303 \times 0.2219}{1.15 \times 10^{- 3}} = \frac{2.303 \times 0.2219 \times 1000}{1.15} = 444 \sec .