1. Zero-order vs First-order elimination graph
Zero-Order vs First-Order Degradation
UPSC Drug Inspector 2026 — High-Yield Revision Table
Feature | Zero-order degradation | First-order degradation |
|---|---|---|
Definition | Rate of degradation is independent of drug concentration. | Rate of degradation is directly proportional to drug concentration. |
Rate equation | −dC/dt = k0 | −dC/dt = kC |
Rate of degradation | Constant | Decreases as drug concentration decreases |
Amount degraded per unit time | Constant | Decreases with time |
Concentration remaining | Decreases linearly with time | Decreases exponentially with time |
Integrated equation | C = C0 − k0t | ln C = ln C0 − kt |
Half-life (t1/2) | Depends on initial concentration | Constant; independent of initial concentration |
Half-life formula | t1/2 = C02k0 | t1/2 = 0.693k |
Shelf-life (t90) | t90 = 0.1C0k0 | t90 = 0.105k |
Plot of concentration vs time | Straight line | Curved line |
Plot of log concentration vs time | Curved line | Straight line |
Unit of rate constant | Concentration/time (e.g., mg/L/hour) | Time⁻¹ (e.g., hour⁻¹) |
Examples | Constant-rate drug release; some degradation processes under special conditions | Many drug degradation reactions under conditions where first-order kinetics apply |
Visual understanding
Zero-order kinetics
Equal amounts are lost in equal time intervals.
Illustrative zero-order degradation
Example: 100 → 80 → 60 → 40 mg at equal 2-hour intervals.
First-order kinetics
An equal fraction is lost in equal time intervals.
Illustrative first-order degradation
Example: 100 → 50 → 25 → 12.5 mg when the half-life is 2 hours.
Important numerical example
Suppose a drug has a first-order degradation rate constant k = 0.1 hour−1.
Its half-life remains 6.93 hours even if the initial concentration changes, provided k stays the same.
For a zero-order process with C0 = 100 mg/L and k0 = 10 mg/L/hour:
If the initial concentration doubles to 200 mg/L, the half-life becomes 10 hours.
UPSC DI exam memory tricks
Zero order: Zero dependence on concentration; constant amount degraded per unit time.
First order: Rate depends on concentration; constant fraction degraded per unit time.
Zero order: Half-life depends on initial concentration.
First order: Half-life is independent of initial concentration.
First-order straight-line plot: log concentration vs time.
Zero-order straight-line plot: concentration vs time.
Most important exam trap: Do not confuse half-life with shelf-life. For first-order degradation, t90 = 0.105/k, whereas for zero-order degradation, t90 = 0.1C0/k0.