Equilibrium & Kinetics 5/21/2019 ENV 4101 Elements of Air Pollution ENV 5105 Foundations of Air Pollution Equilibrium & Kinetics Prepared by: Ying Li

Equilibrium & Kinetics 5/21/2019 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)

5/21/2019 Equilibrium Constant Consider Reaction: Equilibrium constant

5/21/2019 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.

Gibbs free energy and equilibrium 5/21/2019 Gibbs free energy and equilibrium Consider Reaction: Gibbs free energy of reaction: When not at equilibrium Reaction proceeds forward Reaction proceeds backward At equilibrium

5/21/2019 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 (@298 K) ΔHf (@298 K) NO 86.55 kJ/mol. 90.25 kJ/mol. O2 NO2 51.29 kJ/mol. 33.18 kJ/mol.

Effect of Temperature on Keq 5/21/2019 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?

Effect of Temperature on Keq 5/21/2019 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?

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]

Air Pollution Chemistry 5/21/2019 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?

Air Pollution Chemistry 5/21/2019 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?

Activation Energy (Ea) and Catalysis 5/21/2019 Activation Energy (Ea) and Catalysis

Temperature Effect on Reaction Rate 5/21/2019 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?

Determining the Activation Energy 5/21/2019 Determining the Activation Energy Collect data for k as a function of T k T

Quick Reflections Equilibrium Kinetics Equilibrium constant 5/21/2019 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)