Zero Order Half-life

Question

For a zero order reaction with initial concentration 0.10 M and rate constant 0.005 mol L^-1 s^-1, what is the half-life of the reaction?

RankGuru · Accepted Answer

For a zero order reaction the integrated rate law is [A] = [A_0] - kt, and the half-life is the time taken for the concentration to fall to half its initial value. Setting [A] = [A_0]/2 gives [A_0]/2 = [A_0] - k t_(1/2), which rearranges to t_(1/2) = [A_0]/(2k). Substituting [A_0] = 0.10 M and k = 0.005 mol L^-1 s^-1 yields t_(1/2) = 0.10/(2 × 0.005) = 0.10/0.010 = 10 s. Notably, unlike first order reactions, the zero order half-life depends directly on the initial concentration. Option 5 s omits the factor of two in the denominator incorrectly. Option 20 s doubles the correct value. Option 40 s misuses the rate constant. This concentration-dependent half-life is a distinguishing NCERT feature of zero order kinetics. Carefully relating the data to the governing principle ensures the reasoning remains valid even when the numbers or species in the question are changed. Examiners frequently test whether a student can connect integrated rate law with the underlying principle rather than merely recalling an isolated fact. Plausibility check: a constant consumption rate of 0.005 mol L^-1 s^-1 removes 0.05 M in 10 s, exactly half of 0.10 M, confirming the half-life.

Zero Order Half-life

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