Order Of Reaction And Half Life : Chemical Kinetics

📘 Introduction

Chemical reactions proceed at different rates depending on the concentration of reactants. This relationship is described using the concept of Order of Reaction. Understanding zero, first, and second order reactions is critical in predicting product formation, controlling reaction speed, and interpreting real-world chemical behavior. An equally important concept is Half-Life, which tells us how long it takes for half the reactant to be consumed.

🟢 Zero Order Reaction

In zero-order reactions, the rate of reaction does not depend on the concentration of the reactant.
Rate law: Rate = k
Unit of rate constant (k): mol L^-1 s^-1

Example: Decomposition of NH₃ on platinum surface.
Graph: [A] vs Time is linear with negative slope.

🔵 First Order Reaction

In a first-order reaction, the rate depends linearly on the concentration of one reactant.
Rate law: Rate = k[A]
Unit of k: s^-1

Example: Radioactive decay, hydrolysis of ester.
Graph: ln[A] vs Time gives a straight line.

🟡 Second Order Reaction

The rate of a second-order reaction depends on the square of one reactant or the product of two reactants.
Rate law: Rate = k[A]² or Rate = k[A][B]
Unit of k: L mol^-1 s^-1

Example: 2NO + O₂ → 2NO₂
Graph: 1/[A] vs Time gives a straight line.

🧭 Half-Life (t_½) Concept

Half-life is the time required to reduce the concentration of a reactant to half its initial value.

• Zero order: t_½ = [A]₀/2k
• First order: t_½ = 0.693/k (independent of concentration)
• Second order: t_½ = 1/k[A]₀

Zero Order Reaction

In zero order reactions, the rate of reaction is independent of the concentration of reactants. The concentration decreases linearly with time.
Example: Photochemical decomposition of HI on a gold surface.

First Order Reaction

In first order reactions, the rate of reaction is directly proportional to the concentration of one reactant. The graph shows an exponential decrease in concentration.
Example: Decomposition of N₂O₅.

Second Order Reaction

In second order reactions, the rate depends on the square of the concentration of the reactants. The graph of [R] vs. time shows a curve that decreases steeply.
Example: Reaction between NO₂ and CO or 2A → Products.

⚙️ Applications in Real Life

• 📺 Radioactive decay in carbon dating is a first-order reaction.
• 💊 Drug elimination from the body often follows first-order kinetics.
• 🧪 Enzyme-catalyzed reactions exhibit zero-order behavior at saturation.
• 🚗 Pollution breakdown reactions can follow second-order kinetics.

🔟 IIT-JEE Style Conceptual Questions

1. A reaction is zero-order in [A]. What happens to rate if [A] is doubled?

2. Half-life of a first-order reaction is 10 mins. How long for 75% to decay?

3. For a reaction: Rate = k[A]². What is the unit of k?

4. For a first-order reaction, ln[A] vs time gives a straight line. What does the slope represent?

5. If [A]₀ = 0.5 M and after one t_½ it becomes 0.25 M, what is the order?

6. In which order reaction, t_½ is inversely proportional to initial concentration?

7. Rate = k. What type of reaction is this?

8. For a second-order reaction, what is the shape of [A] vs time graph?

9. What is the dimension of rate constant for first-order reaction?

10. Which reaction order has a constant half-life?

MCQ for IIT JEE

🧪 IIT-JEE Quiz: Reaction Order & Half-Life

1. For a zero-order reaction, the rate of reaction:

A. Increases with concentration
B. Decreases with concentration
C. Remains constant
D. Depends on catalyst only

✔ Answer: C. Remains constant

2. The unit of rate constant for a first-order reaction is:

A. mol L⁻¹ s⁻¹
B. s⁻¹
C. L mol⁻¹ s⁻¹
D. No units

✔ Answer: B. s⁻¹

3. For a second-order reaction, half-life is:

A. Directly proportional to [A]₀
B. Inversely proportional to [A]₀
C. Independent of [A]₀
D. Proportional to square of [A]₀

✔ Answer: B. Inversely proportional to [A]₀

4. In a first-order reaction, time to complete 75% is:

A. 2t½
B. t½
C. 3t½
D. 4t½

✔ Answer: C. 3t½

5. A reactant decreases linearly with time. The reaction is:

A. First-order
B. Second-order
C. Zero-order
D. Third-order

✔ Answer: C. Zero-order

6. t½ = 10 min for a 1st order reaction. Time for 87.5% reaction:

A. 20 min
B. 30 min
C. 40 min
D. 50 min

✔ Answer: B. 30 min

7. Integrated rate law for 2nd-order A → Product:

A. [A] = [A]₀ - kt
B. ln[A] = ln[A]₀ - kt
C. 1/[A] = 1/[A]₀ + kt
D. [A] = [A]₀e⁻ᵏᵗ

✔ Answer: C. 1/[A] = 1/[A]₀ + kt

8. ln[A] vs time gives a straight line for:

A. Zero-order
B. First-order
C. Second-order
D. All of these

✔ Answer: B. First-order

9. For k = 0.693 s⁻¹ in a 1st-order reaction, t½ is:

A. 1 s
B. 0.5 s
C. 10 s
D. 100 s

✔ Answer: A. 1 s

10. Which is incorrect for zero-order reactions?

A. Rate is independent of [A]
B. [A] vs time is a straight line
C. Half-life increases with [A]₀
D. Half-life is constant

✔ Answer: D. Half-life is constant

🔗 Internal Links

🎮 Reaction Order Game
📊 Rate vs Concentration Graph
🧠 Colligative Property Game

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