![Q.5 Among the following diagrams, the one that correctly describes a zero order reaction (X → product) is (Given: [X]o = initial concentration of reactant X; [X] = concentration of reactant X at time t and t1/2 = half-life period of reactant X)](https://www.letstalkacademy.com/wp-content/uploads/2026/01/slide_5-5.png)
Q.5 Among the following diagrams, the one that correctly describes a zero order reaction
(X → product) is
(Given: [X]o = initial concentration of reactant X; [X] = concentration of reactant X at time t
and t1/2 = half-life period of reactant X)
Introduction
Chemical kinetics questions frequently test conceptual understanding of reaction order and graphical relationships.
One such common problem is identifying the correct graph for a zero order reaction using half-life
and concentration relationships.
In this article, we analyze the given diagrams and determine which correctly represents a zero order reaction
(X → product), with a clear explanation of why the other options are incorrect.
Key Concepts: Zero Order Reaction
For a zero order reaction, the rate is independent of reactant concentration.
Rate Law
Rate = k
Integrated Rate Law
[X] = [X]0 − kt
Half-Life Expression
t1/2 =
[X]0 / 2k
🔑 Important conclusion:
- The half-life is directly proportional to the initial concentration [X]0
- This is a unique feature of zero order reactions
Expected Graphical Relationships for Zero Order Reactions
| Quantity | Relationship |
|---|---|
| [X] vs t | Straight line with negative slope |
| t1/2 vs [X]0 | Straight line through origin |
| 1/[X] vs t | ❌ Not linear |
| t1/2 vs 1/[X]0 | ❌ Inverse (not correct) |
Analysis of the Given Options
Option (A): 1/[X] vs t
A straight line between 1/[X] and time is characteristic of a second order reaction.
❌ Not valid for zero order kinetics.
Option (B): t1/2 vs [X]0 (Horizontal line)
This implies half-life is independent of initial concentration.
This behavior is true for first order reactions.
❌ Incorrect for zero order reactions.
Option (C): t1/2 vs 1/[X]0
Suggests half-life is inversely proportional to initial concentration.
No standard reaction order follows this trend.
❌ Incorrect.
Option (D): t1/2 vs [X]0 (Straight line with positive slope) ✅
Matches the zero order half-life equation:
t1/2 = [X]0 / 2k
Shows direct proportionality between half-life and initial concentration.
✔ Correct representation of a zero order reaction.
✅ Correct Answer
Option (D)
Final Takeaway
📌 For a zero order reaction, the most important identifying feature is that:
Half-life increases linearly with initial concentration.
Any graph showing t1/2 ∝ [X]0 correctly represents zero order kinetics.
Exam Tip (CSIR NET / GATE) 🎯
- If you see constant half-life → first order
- If you see half-life proportional to concentration → zero order
- If you see 1/[X] vs t linear → second order
Master these three and most kinetics graph questions become instant solves 💡
