1. Equilibrium & Kinetics
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ENV 4101 Elements of Air Pollution
ENV 5105 Foundations of Air Pollution
Equilibrium & Kinetics
Prepared by: Ying Li

2. Equilibrium & Kinetics
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Equilibrium & Kinetics
Equilibrium
Equilibrium constant
Free energy
Temperature effect
Kinetics
Order of Reactions (1st, 2nd, and pseudo 1st order)
Air Pollution Reactions
Lifetime, Half-life
Temperature effect (Arrenhius Equation)

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Equilibrium Constant
Consider Reaction:
Equilibrium constant

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Definitions:
Internal energy, U: the total of the kinetic energy due to the motion of molecules (translational, rotational & vibrational) for a closed system.
Enthalpy or heat content, H: description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant conditions.
Gibbs free energy, G: The greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies.
Standard state: pure material at a pressure of 1 atm and at given temperature
Standard free energy of formation : energy change when 1 mole of the species in its standard state is formed from its constituent elements.
Standard enthalpy of formation : heat change when 1 mole of the species in its standard state is formed from its constituent elements.

5. Gibbs free energy and equilibrium
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Gibbs free energy and equilibrium
Consider Reaction:
Gibbs free energy of reaction:
When not at equilibrium
Reaction proceeds forward
Reaction proceeds backward
At equilibrium

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Equilibrium
Example:
Calculate the equilibrium constant, Keq, for the conversion of nitric oxide (NO) to nitrogen dioxide (NO2) in the presence of oxygen at 25 °C.
Cmpd
ΔGf K)
ΔHf K) NO
86.55 kJ/mol.
90.25 kJ/mol. O2
NO2
51.29 kJ/mol.
33.18 kJ/mol.

7. Effect of Temperature on Keq
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Effect of Temperature on Keq
Van’t Hoff Equation
- enthalpy of reaction
Assuming
does not change in the range of temperature interested
Can you find the equilibrium constant for the conversion of NO to NO2 in presence of O2 at 325 °C?
Is the reaction favorable at higher or lower temperature?

8. Effect of Temperature on Keq
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Effect of Temperature on Keq
Concentrations of NO and NO2 at equilibrium in exhaust
What can you tell from this table about the equilibrium concentrations of NO and NO2?

9. Kinetics Order of Reaction First-Order Reaction Second-Order Reaction
How to determine the order of reaction based on experimental data?
Order of Reaction
First-Order Reaction
ln [A] t k
Second-Order Reaction
1/[A] k t
Pseudo First-Order Reaction
When [B] >> [A]

10. Air Pollution Chemistry
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Air Pollution Chemistry
Photodissociation (or Photolysis) Reactions
What is the order of the reaction?
Lifetime, τ, is the time for the concentration of a compound to reach a concentration that is 1/e times the initial concentration
Half life, t1/2, is the time for the concentration of a compound to reach a concentration that is half of the initial concentration
How do you express the lifetime and half life of a photolysis reaction as a function of the rate constant?

11. Air Pollution Chemistry
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Air Pollution Chemistry
Reactions of a compound with an atmospheric oxidant
What is the order of the reaction?
How do you express the lifetime of a compound with respect to reaction with an atmospheric oxidant?
Concentration of oxidants in an unpolluted atmosphere
Species
Conc. (molecules cm-3)
OH
1×106
NO3
5×108 O3
7×1011
The rate constant for the reaction of propene with OH at 1 atm pressure and 298 K is 2.6×10-11 cm3 molecule-1 s-1. What is the lifetime of propene with respect to removal by OH in the atmosphere?

12. Activation Energy (Ea) and Catalysis
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Activation Energy (Ea) and Catalysis

13. Temperature Effect on Reaction Rate
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Temperature Effect on Reaction Rate
The Arrenhius Equation
k = Reaction rate constant (is it a real constant?)
A = Frequency factor
Ea = Activation energy (always +)
R = Ideal gas constant
T = Absolute temperature
Does the reaction rate increase or decrease as the temperature increases?

14. Determining the Activation Energy
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Determining the Activation Energy
Collect data for k as a function of T k T

15. Quick Reflections Equilibrium Kinetics Equilibrium constant
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Quick Reflections
Equilibrium
Equilibrium constant
Free energy
Temperature effect
Kinetics
Order of Reactions (1st, 2nd, and pseudo 1st order)
Air Pollution Reactions
Lifetime, Halflife
Temperature effect (Arrenhius Equation)