Why most drugs clear at a constant fraction
First-order elimination means a constant percentage of the drug present is removed per unit time, so the absolute amount cleared rises and falls with concentration. Because the rate scales with how much drug is in the body, the plasma curve falls in a smooth exponential decay and the half-life stays the same regardless of starting dose. Most medicines behave this way at normal therapeutic concentrations because the enzymes and transporters handling them are nowhere near saturation.
Zero-order elimination is different: a fixed amount is cleared per unit time because the clearing machinery is already working at capacity. Here the decline is linear rather than exponential, and there is no single half-life that describes the whole curve.
Alcohol and phenytoin as the classic exceptions
Ethanol is the textbook zero-order example: alcohol dehydrogenase saturates at low blood concentrations, so the body metabolises roughly a fixed quantity per hour rather than a fixed fraction. Phenytoin shows mixed kinetics, behaving first-order at low levels but shifting toward zero-order within its therapeutic range, which is one reason small dose increases can produce disproportionately large concentration jumps.
This distinction matters clinically because saturable elimination makes blood levels harder to predict from dose alone. This is general educational information, not medical advice; dosing of drugs with saturable kinetics should be guided by a qualified prescriber and, where appropriate, blood-level monitoring.