Half-life

Question

The half-life of a first order reaction is 20 minutes; what fraction of the original reactant remains after 60 minutes have elapsed?

RankGuru · Accepted Answer

For a first order reaction the half-life is constant and independent of concentration, so the reactant falls to half its amount during each successive half-life period. In 60 minutes the number of half-lives is 60/20 = 3. After each half-life the remaining fraction is multiplied by one-half, so after three half-lives the fraction left is (1/2)^3 = 1/8. Therefore one-eighth of the original reactant remains. The option one-half corresponds to a single half-life only. One-quarter corresponds to two half-lives. One-sixteenth would require four half-lives, or 80 minutes. The constancy of half-life is a defining feature of first order kinetics emphasised in NCERT. A common JEE pitfall is to ignore the role of half-life, yet it is exactly this factor that distinguishes the correct answer from the tempting alternatives. Plausibility check: three successive halvings give 1 → 1/2 → 1/4 → 1/8, confirming that one-eighth remains after three half-lives.

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