A reaction has a half life of 1 min. The time required for 99.9% completion of the reaction is _________ min. (Round off to the Nearest Integer). [Use : ln 2 = 0.69; ln 10 = 2.3]

Solution

Chemistry ma’am · 3 steps

Treat it as first order, find k from the half-life, then ask how long until only 1 part in 1000 is left.

1. Rate constant. A fixed half-life with no concentration given points to a first-order reaction, where t_(1/2) = (ln 2)/k. So k = 0.69/(1 min) = 0.69 min⁻¹.
2. Fraction left. At 99.9% completion, only 0.1% of the reactant remains. So [A]₀/[A] = 100/0.1 = 1000.

   t = 1/k ln[A]₀/[A] = (ln 1000)/0.69 = (3 × 2.3)/0.69 = 6.9/0.69

3. So. t = 10 min, so the answer is 10.

The common slip: 7. Using 99% completion, so a ratio of 100 instead of 1000, gives 4.6/0.69 ≈ 6.7, which rounds to 7 rather than 10.

The idea to keep. For first order, the time for 99.9% completion is always 10 t_(1/2), and for 99% it is 20/3 t_(1/2). Use the fraction left, not the fraction used up.

Answer from the NTA final answer key. Solution by PrepWiser.