Reaction Kinetics in Air
Learning Objectives
Students will be able to:
- Define reaction rate and explain factors that influence reaction kinetics
- Write and interpret rate law expressions for atmospheric reactions
- Apply the Arrhenius equation to predict temperature effects on reaction rates
- Calculate half-lives for first-order decay of atmospheric pollutants
- Explain why reaction kinetics matter for indoor air quality management
The Big Question
"If a pollutant enters a room, how long does it take to react away? What determines this rate?"
Fundamentals of Reaction Kinetics
Chemical kinetics describes how fast reactions occur. In atmospheric and indoor chemistry, understanding reaction rates helps us predict pollutant lifetimes and transformation pathways.
The Rate Law
For a general reaction: aA + bB → Products
Rate = k[A]m[B]n
Where:
- k = rate constant (depends on temperature)
- [A], [B] = concentrations of reactants
- m, n = reaction orders (determined experimentally)
The Arrhenius Equation
The rate constant k depends on temperature according to the Arrhenius equation:
k = A · e-Ea/RT
| Variable | Meaning | Units |
|---|---|---|
| A | Pre-exponential factor (frequency factor) | Same as k |
| Ea | Activation energy | J/mol or kJ/mol |
| R | Gas constant | 8.314 J/(mol-K) |
| T | Temperature | Kelvin |
First-Order Reactions and Half-Life
Many atmospheric reactions follow first-order kinetics, where the rate depends only on one reactant concentration:
Integrated Rate Law
[A]t = [A]0 · e-kt
Concentration decreases exponentially with time
Half-Life
t1/2 = ln(2)/k = 0.693/k
Time for concentration to decrease by 50%
Atmospheric Reaction Examples
| Reaction | k (298 K) | Atmospheric Lifetime |
|---|---|---|
| OH + CO → H + CO2 | 2.4 x 10-13 cm3/molecule-s | ~2 months |
| OH + CH4 → CH3 + H2O | 6.3 x 10-15 cm3/molecule-s | ~9 years |
| O3 + NO → NO2 + O2 | 1.8 x 10-14 cm3/molecule-s | ~1 minute (indoor) |
| O3 + limonene → products | 2.0 x 10-16 cm3/molecule-s | ~10 minutes (indoor) |
Activity: Calculate Pollutant Lifetimes
Problem Set
-
Ozone Decay: Indoor ozone reacts with surfaces at a first-order rate constant of k = 0.001 s-1.
- Calculate the half-life of ozone due to surface reactions
- How long until 90% of the ozone has reacted?
-
Temperature Effect: A reaction has Ea = 50 kJ/mol and A = 1012 s-1.
- Calculate k at 20 degrees C (293 K) and 30 degrees C (303 K)
- By what factor does the rate increase with this 10 degree change?
- Indoor Relevance: Why does temperature control matter for managing indoor air quality? Consider both reaction rates and source emissions.
Connection to Indoor Air Quality
Pollutant Lifetimes
Kinetics determines how long pollutants persist before reacting or being removed
Secondary Formation
Reaction rates determine how fast primary pollutants transform into secondary products
Ventilation Design
Air exchange rates must be balanced against reaction rates for effective IAQ control
Key Takeaway
Reaction kinetics provides the quantitative framework for understanding how fast atmospheric reactions occur. The exponential dependence on temperature (Arrhenius equation) and the concept of half-life are fundamental tools for predicting pollutant behavior in indoor environments. In the next lesson, we will explore how light energy drives photochemical reactions that produce ozone and other oxidants.