Chemical Kinetics

Definition

The change in concentration of a reactant or a product per unit of time.

Explanation

Think of a reaction like a group of people leaving a room. The "rate" is simply how many people exit every minute. If reactants are being consumed, the rate is measured by their disappearance. If products are being formed, it's measured by their appearance.

• Rate is always positive: Expressed as a positive value.
• Unit: mol L⁻¹ s⁻¹ (concentration per time).
• Average Rate: Measured over a large time interval.
• Instantaneous Rate: Measured at a specific moment in time.

Examples

• The decomposition of N₂O₅ over a period of minutes.
• The fizzing of an antacid tablet in water (the rate of CO₂ production).

Real-Life Use: Automotive Safety

Airbag Deployment: When a car crashes, the chemical reaction inside the airbag (sodium azide decomposition) must happen at an incredibly precise and high rate. If it's too slow, the passenger hits the dashboard; if it's too fast, the bag might burst.

Explanation

Various physical and chemical conditions that speed up or slow down a reaction by changing how often and how hard molecules hit each other.

• Concentration: Higher concentration $\rightarrow$ more particles $\rightarrow$ more collisions $\rightarrow$ faster rate.
• Temperature: Higher temperature $\rightarrow$ more kinetic energy $\rightarrow$ more effective collisions $\rightarrow$ faster rate.
• Surface Area: Smaller particles (larger surface area) $\rightarrow$ more contact points $\rightarrow$ faster rate.
• Catalyst: Provides an alternative path with lower energy $\rightarrow$ faster rate.

Examples

• Using crushed limestone instead of large chunks in industrial processes.
• Keeping milk in the refrigerator to slow down bacterial growth.

Real-Life Use: Industrial Manufacturing

Haber Process: In the production of Ammonia, engineers balance temperature and pressure. Kinetics helps find the "sweet spot" for maximum speed and efficiency.

Definition

• Order: The sum of powers of the concentration terms in the rate law equation (Experimental).
• Molecularity: The number of reacting species that must collide simultaneously (Theoretical).

Comparison Table

Real-Life Use: Pharmacology

Drug Metabolism: Doctors need to know the "order" of a drug's breakdown. If a drug follows zero-order kinetics, your body processes it at a constant rate regardless of dose, which is crucial for preventing toxicity.

A. Zero-Order Reactions

The rate of reaction is independent of the concentration of the reactant.

• Formula: [A]ₜ = -kt + [A]₀
• Half-life (t₁/₂): t₁/₂ = [A]₀ / 2k

B. First-Order Reactions

The rate depends on the concentration of only one reactant.

• Formula: k = (2.303 / t) log ([A]₀ / [A]ₜ)
• Half-life (t₁/₂): t₁/₂ = 0.693 / k

Real-Life Use: Food Preservation

By knowing the rate constant (k) of spoilage reactions (often first-order), food scientists calculate exactly how long a product will stay safe to eat.

Explanation

A reaction that is actually higher-order (e.g., second order) but behaves like a first-order reaction because one reactant is in massive excess.

Example

Hydrolysis of cane sugar: Water is in huge excess. The rate depends on sugar, but since water concentration is constant, it looks first-order.

Collision Theory

For a reaction to happen, molecules must hit each other with enough "oomph" (Activation Energy) and in the right direction.

Arrhenius Equation

k = A e^(-Ea / RT)

• k: Rate constant
• A: Arrhenius factor (frequency of collisions)
• Ea: Activation Energy (the "energy barrier")
• R: Gas constant
• T: Temperature (in Kelvin)

Logarithmic Form for Calculations

log (k₂/k₁) = (Ea / 2.303R) * [(T₂ - T₁) / (T₁T₂)]

Real-Life Use: Chemical Engineering

Engineers use the Arrhenius equation to predict "runaway reactions" in large plants, preventing explosions by controlling temperature-driven rate increases.

Problem 1 (First Order)

A first-order reaction has a rate constant k = 5.5 × 10⁻¹⁴ s⁻¹. Find the half-life of the reaction.

Problem 2 (Arrhenius)

The rate constant of a reaction is 2.0 × 10⁻² at 300 K and 4.0 × 10⁻² at 310 K. Calculate the Activation Energy (Ea). (Given R = 8.314 J/K/mol)

• Spectroscopy (FTIR/UV-Vis): Used to monitor reactant concentrations in real-time.
• Computational Chemistry: Simulating collisions to predict Ea before lab work.
• Automated Process Control: Sensors in refineries adjusting T and P instantly.

Case Study: The Stability of Aspirin

In the pharmaceutical industry, determining the shelf-life of a drug is critical. Aspirin undergoes hydrolysis when exposed to moisture, breaking down into salicylic acid and acetic acid.

Researchers find that this degradation follows First-Order Kinetics. By measuring concentration drops (e.g., from 100% to 95% in 6 months), they use the integrated rate law to find k. Using the Arrhenius Equation, they can even predict how much faster the drug will degrade in tropical climates vs. temperate ones. This kinetic data dictates the "Expiration Date" on every bottle.

1. The unit of rate constant for a zero-order reaction is:
   a) s⁻¹   b) mol L⁻¹s⁻¹   c) L mol⁻¹s⁻¹   d) mol⁻¹L s⁻¹
   Ans: b
2. If the concentration of a reactant is doubled and the rate becomes four times, the order is:
   a) 0   b) 1   c) 2   d) 3
   Ans: c
3. The temperature dependence of the rate constant is explained by:
   a) Collision Theory   b) Arrhenius Equation   c) Both a & b   d) None
   Ans: c
4. A catalyst increases the rate of reaction by:
   a) Increasing Eₐ   b) Decreasing Eₐ   c) Increasing temperature   d) Increasing concentration
   Ans: b
5. For a first-order reaction, the half-life is:
   a) Dependent on [A]₀   b) Independent of [A]₀   c) Proportional to [A]₀   d) None
   Ans: b
6. Molecularity of a reaction can be:
   a) 0   b) 1.5   c) 2   d) -1
   Ans: c
7. Pseudo-first order reactions are actually:
   a) Zero order   b) Second order   c) Third order   d) First order
   Ans: b
8. The rate of reaction is fastest when:
   a) Temperature is low   b) Surface area is low   c) Concentration is high   d) Catalyst is removed
   Ans: c
9. In the Arrhenius equation, 'A' represents:
   a) Activation energy   b) Frequency factor   c) Gas constant   d) Temperature
   Ans: b
10. If a reaction is zero order, the plot of [A] vs time is:
    a) A curve   b) A straight line   c) A circle   d) A parabola
    Ans: b

1. Q: Distinguish between Order and Molecularity. (3 Marks)
   Answer: Order is experimental and can be fractional; it applies to all reactions. Molecularity is theoretical, always an integer, and applies only to elementary reactions.
2. Q: Define Activation Energy. How does a catalyst affect it? (2 Marks)
   Answer: Activation energy is the minimum energy required for a collision to result in a reaction. A catalyst lowers this energy barrier.
3. Q: Derive the expression for half-life of a first-order reaction. (3 Marks)
   Answer: Using ln([A]ₜ/[A]₀) = -kt, at t=t₁/₂, [A]ₜ = [A]₀/2. Thus, ln(1/2) = -kt₁/₂ $\rightarrow$ ln(2) = kt₁/₂ $\rightarrow$ t₁/₂ = 0.693/k.
4. Q: What is a Pseudo-first order reaction? Give an example. (2 Marks)
   Answer: A reaction behaving as first-order due to one reactant being in massive excess. Example: Hydrolysis of ester in water.
5. Q: Explain Collision Theory in brief. (3 Marks)
   Answer: For a reaction to occur, particles must collide with sufficient kinetic energy (Activation Energy) and proper orientation.
6. Q: Why does the rate of reaction increase with temperature? (2 Marks)
   Answer: Increased temperature increases kinetic energy, leading to more frequent and more energetic (effective) collisions.
7. Q: A reaction is second order with respect to A. How does the rate change if [A] is tripled? (2 Marks)
   Answer: Rate = k[A]². If [A] becomes 3[A], Rate' = k(3[A])² = 9k[A]². The rate increases by 9 times.
8. Q: What happens to the rate constant when the temperature increases? (1 Mark)
   Answer: The rate constant (k) increases.
9. Q: Define Rate of Reaction. (1 Mark)
   Answer: The change in concentration of reactants or products per unit time.
10. Q: Write the Arrhenius equation in its logarithmic form. (1 Mark)
    Answer: log (k₂/k₁) = (Ea / 2.303R) * [(T₂ - T₁) / (T₁T₂)]

• Factors affecting Rate: "C-T-S-C"
  • Concentration
  • Temperature
  • Surface Area
  • Catalyst
• Order vs Molecularity:
  • Order = Observational (Experimental).
  • Molecularity = Mechanical (Theoretical/Mechanism).