Zero-Order Integrated Rate Law

A zero-order reaction consumes reactant at a fixed rate no matter how much is left, so a plot of concentration against time is a straight line of slope −k. This looks strange until you see the mechanism: it happens when something other than the reactant is the bottleneck — a saturated enzyme, a fully covered catalyst surface, or a photochemical step limited by the lamp. Start at 0.500 M with k = 0.0100 mol/(L·s) and after 20 s exactly 0.200 M has gone, leaving 0.300 M.

Ethanol metabolism is the everyday example: alcohol dehydrogenase saturates at very low blood alcohol levels, so the liver clears roughly 0.015% blood alcohol per hour regardless of how much you drank — which is why "one drink per hour" advice works and why doubling the dose doubles the sobering-up time rather than leaving it unchanged. The unique feature of zero order is that it genuinely runs out: set [A] = 0 and the reaction stops dead at t = [A]₀/k, unlike first-order decay which merely approaches zero forever. Note that k here carries units of mol/(L·s), not the s⁻¹ of a first-order constant.