ZERO-ORDER VS FIRST-ORDER DEGRADATION

Arvind Sharma30 Oct 2026 7 min read Faculty reviewed

ZERO-ORDER VS FIRST-ORDER DEGRADATION

UPSC Drug Inspector 2026 — High-Yield Revision Notes

1. Introduction

Definition: Drug degradation kinetics describes the rate at which a drug decomposes or loses its potency with time under specified conditions.

The two important kinetic models in pharmaceutical sciences are zero-order and first-order degradation.

2. Zero-Order Degradation

Definition: Zero-order degradation is a process in which the rate of degradation is independent of the concentration of the drug remaining.

Key principle: A constant amount of drug is degraded per unit time.

Rate equation

$-\frac{dC}{dt}=k_0$

Integrated equation

$C=C_0-k_0t$

Where

C = Drug concentration at time t
C₀ = Initial drug concentration
k₀ = Zero-order rate constant
t = Time

Characteristics of Zero-Order Degradation

The degradation rate remains constant.
Equal amounts of drug are degraded in equal time intervals.
Drug concentration decreases linearly with time.
The plot of concentration versus time gives a straight line.
The plot of log concentration versus time gives a curved line.
Half-life depends on the initial drug concentration.
The rate constant has units of concentration per unit time.

Zero-Order Degradation Graph

Reaction rate and order · Image: pharmacy180.com

Reference graph: Zero-order concentration-versus-time graph (PNG)

Graph interpretation: The concentration decreases by equal amounts over equal time intervals.

Time (hours)	Concentration (mg/L)
0	100
2	80
4	60
6	40
8	20

The concentration decreases by 20 mg/L every 2 hours.

Exam point: Concentration versus time gives a straight line with slope −k₀.

Half-Life Formula

$t_{1/2}=\frac{C_0}{2k_0}$

Shelf-Life Formula

$t_{90}=\frac{0.1C_0}{k_0}$

Numerical Example

A drug has an initial concentration of 100 mg/L and a zero-order degradation rate constant of 10 mg/L/hour.

$t_{1/2}=\frac{100}{2\times10}$

$\boxed{t_{1/2}=5\text{ hours}}$

If the initial concentration doubles to 200 mg/L

$t_{1/2}=\frac{200}{2\times10}=10\text{ hours}$

Conclusion: In zero-order degradation, half-life increases with initial concentration when the rate constant remains unchanged.

3. First-Order Degradation

Definition: First-order degradation is a process in which the rate of degradation is directly proportional to the concentration of the drug remaining.

Key principle: A constant fraction of drug is degraded per unit time.

Rate equation

$-\frac{dC}{dt}=kC$

Integrated equation

$\ln C=\ln C_0-kt$

Alternatively

$\log C=\log C_0-\frac{kt}{2.303}$

Where

C = Drug concentration at time t
C₀ = Initial drug concentration
k = First-order rate constant
t = Time

Characteristics of First-Order Degradation

The degradation rate depends on drug concentration.
The rate decreases as the concentration decreases.
Equal fractions of drug are degraded in equal time intervals.
Drug concentration decreases exponentially with time.
The plot of concentration versus time gives a curved line.
The plot of log concentration versus time gives a straight line.
Half-life is independent of initial drug concentration.
The rate constant has units of inverse time.

First-Order Degradation Graph

Clinical pharmacokinetics | IUPHAR · Image: pharmacologyeducation.org

Reference graph: First-order concentration-versus-time graph (PNG)

Graph interpretation: The concentration decreases by equal fractions over equal time intervals.

Illustrative data when half-life is 2 hours

Time (hours)	Concentration (mg/L)
0	100
2	50
4	25
6	12.5
8	6.25

The concentration decreases by 50% every 2 hours.

Exam point: Log concentration versus time gives a straight line with slope −k when natural logarithms are used.

Half-Life Formula

$t_{1/2}=\frac{0.693}{k}$

Shelf-Life Formula

$t_{90}=\frac{0.105}{k}$

Numerical Example

A drug follows first-order degradation kinetics with a rate constant of 0.1 hour⁻¹.

$t_{1/2}=\frac{0.693}{0.1}$

$\boxed{t_{1/2}=6.93\text{ hours}}$

The half-life remains 6.93 hours if the rate constant and reaction conditions remain unchanged, regardless of the initial concentration.

4. Comparison Table: Zero-Order vs First-Order Degradation

Feature	Zero-Order Degradation	First-Order Degradation
Definition	Rate independent of concentration	Rate proportional to concentration
Rate equation	−dC/dt = k₀	−dC/dt = kC
Rate of degradation	Constant	Decreases as concentration decreases
Amount degraded per unit time	Constant	Variable
Fraction degraded per unit time	Variable	Constant
Integrated equation	C = C₀ − k₀t	ln C = ln C₀ − kt
Half-life	Depends on initial concentration	Independent of initial concentration
Half-life formula	C₀/(2k₀)	0.693/k
Shelf-life formula	0.1C₀/k₀	0.105/k
Concentration vs time plot	Straight line	Exponential curve
Log concentration vs time plot	Curved line	Straight line
Rate constant unit	Concentration/time	Time⁻¹
Typical example	Certain constant-rate release processes	Many drug degradation reactions under applicable conditions

5. Important Straight-Line Plots

Kinetic order	Straight-line plot	Slope
Zero order	C versus t	−k₀
First order	ln C versus t	−k
First order	log ₁₀C versus t	−k/2.303

Reference graphs

Zero-order degradation graph (PNG)
First-order degradation graph (PNG)

6. Half-Life and Shelf-Life

Half-life (t_1/2): The time required for the drug concentration to decrease to 50% of its initial value.

Shelf-life (t₉₀): The time required for the drug concentration to decrease to 90% of its initial value, corresponding to 10% degradation.

Parameter	Zero Order	First Order
Half-life	C₀/(2k₀)	0.693/k
Shelf-life	0.1C₀/k₀	0.105/k
Dependence on initial concentration	Yes	No

These formulas assume that the stated kinetic model applies and the rate constant remains unchanged.

7. Numerical Questions

Example 1: First-Order Half-Life

A drug has a first-order rate constant of 0.2 hour⁻¹. Calculate its half-life.

Formula

$t_{1/2}=\frac{0.693}{k}$

Calculation

$t_{1/2}=\frac{0.693}{0.2}$

$\boxed{t_{1/2}=3.465\text{ hours}}$

Example 2: Zero-Order Half-Life

A drug has an initial concentration of 80 mg/L and a zero-order rate constant of 8 mg/L/hour. Calculate its half-life.

Formula

$t_{1/2}=\frac{C_0}{2k_0}$

Calculation

$t_{1/2}=\frac{80}{2\times8}$

$\boxed{t_{1/2}=5\text{ hours}}$

Example 3: First-Order Shelf-Life

A drug has a first-order rate constant of 0.05 hour⁻¹. Calculate its shelf-life.

Formula

$t_{90}=\frac{0.105}{k}$

Calculation

$t_{90}=\frac{0.105}{0.05}$

$\boxed{t_{90}=2.1\text{ hours}}$

8. UPSC DI 2011 Previous-Year Question

Q. All of the following statements about first-order degradation are true, EXCEPT.

Its rate is dependent on the concentration.

Its half-life is a changing parameter.

A plot of the log of concentration versus time yields a straight line.

Its t₉₀ is constant and independent of the concentration.

Correct Answer: B. Its half-life is a changing parameter.

Explanation: First-order degradation has a constant half-life that is independent of the initial drug concentration. Its rate depends on concentration, and both half-life and t₉₀ remain constant when the rate constant and reaction conditions remain unchanged.

9. Exam Memory Tricks

Zero order: Constant amount degraded per unit time.
First order: Constant fraction degraded per unit time.
Zero-order half-life: Depends on initial concentration.
First-order half-life: Independent of initial concentration.
Zero-order straight-line plot: Concentration versus time.
First-order straight-line plot: Log concentration versus time.
Zero-order rate constant: Concentration/time.
First-order rate constant: Time⁻¹.
First-order half-life: 0.693/k.
First-order shelf-life: 0.105/k.

10. One-Minute Final Revision

Remember	Zero Order	First Order
Rate depends on concentration	No	Yes
Amount lost per unit time	Constant	Variable
Fraction lost per unit time	Variable	Constant
Half-life	Depends on C₀	Independent of C₀
Straight-line plot	C versus t	Log C versus t
Rate constant	k₀	k

Most important exam trap: Do not confuse half-life with shelf-life. For first-order degradation, t₉₀ = 0.105/k; for zero-order degradation, t₉₀ = 0.1C₀/k₀.

UPSC DI takeaway: If a question states that half-life changes with initial drug concentration, the behaviour is consistent with zero-order rather than first-order kinetics.

11. References for Further Study

Aulton’s Pharmaceutics: The Design and Manufacture of Medicines — pharmaceutical stability and degradation kinetics.
Lachman, Lieberman and Kanig: The Theory and Practice of Industrial Pharmacy — pharmaceutical stability.
Martin’s Physical Pharmacy and Pharmaceutical Sciences — reaction kinetics and pharmaceutical stability.
Relevant pharmaceutical analysis and physical pharmacy textbooks prescribed by the university.

🎯 Exam Tip: The graphs and numerical examples are illustrative teaching materials. For examination questions, use the kinetic model and conditions stated in the question.

ZERO-ORDER VS FIRST-ORDER DEGRADATION

Arvind Sharma30 Oct 2026 7 min read Faculty reviewed