Atmospheric chemistry Lecture 2: Photochemistry & kinetics Dr. David Glowacki University of Bristol,UK david.r.glowacki@bristol.ac.uk

Quick review of yesterday We discussed atmospheric structure Temperature & pressure gradients, as well as Coriolis forces are related to atmospheric transport Today… We’ll gain some insight into the relationship between atmospheric structure and atmospheric chemistry Atmospheric chemistry depends on sunlight, temperature, and pressure; Today we’ll learn about Photochemistry Chemical kinetics

The Atmosphere is a low temperature chemical reactor Important Chemistry: UV Stratosphere O3 layer UV absorption by O3 visible Troposphere Tropopause -70oC 14 km IR absorption by Greenhouse gases (H2O, CH4, CO2) Surface emissions resulting in O3 and aerosol formation, and acid rain Regional and global biogenic emissions (CH4) Urban Anthropogenic emissions Surface O3

Atmospheric Chemistry starts with sunlight E = hv v = c/l l Energy/kJ mol-1 Red 700 170 Orange 620 190 Yellow 580 210 Green 530 230 Blue 470 250 Violet 420 280 Near UV 400-200 300-600 Far UV 200-50 600-2400 visible Breaking chemical bonds requires energy Sunlight has energy If sufficient energy is deposited in the bond, then it will break O3 has a bond energy of ~105 kJ mol-1

Photoexcitation gives excited molecules, A* Photoexcitation may result in a number of processes: Initial photoexcitation Dissociation Fluorescence Collisional relaxation Ionization * Photochemistry depends on temperature, pressure, and the wavelength of the absorbed light

Photoexcitation kinetics The rate of formation of A* is written: where jA is the photochemical rate constant Competition between subsequent processes is determined by the quantum yield, ϕ, for each process where: Dissociation yield =Φ1 Fluorescence yield =Φ2 Collisional relaxation yield =Φ3 Ionization =Φ4

Understanding the photolysis rate Quantum yield: efficiency at which absorbed photons result in the molecular process of interest absorption cross section: number of photons absorbed by a molecule at a particular wavelength Spectral actinic flux: density of photons in the atmosphere at a particular wavelength need to integrate over the entire wavelength range

Understanding photolysis rates Atmospheric actinic flux O3 absorption cross section Photochemical processes depend on: temperature (absorption cross sections & quantum yields) Pressure (collisional relaxation) Altitude (actinic flux)

Atmospheric absorption of light Gases absorb light The absorption of light depends on the concentration of the gas, N, its absorption cross section, σ, & the path length, l,through the gas May be described by the Beer-Lambert law

Atmospheric absorption of light The Beer Lambert law: Explains the altititude dependence of actinic flux Is often used to measure atmospheric trace gas concentrations DOAS (differential optical absorption spectrometry) FTIR spectrometry

Chemical Kinetics

Kinetics depends on the potential energy surface (PES) What molecules do is determined by their potential energy landscapes – energy as a function of coordinates Stable molecules are minima on a PES Potential energy surfaces (PES) are multidimensional, but we usually think about their motion projected in one dimension T dependence of reaction rate coefficients well described by the Arrhenius equation:

First order Unimolecular kinetics

Mechanisms with more than one chemical reactions: exact solutions Coupled chemical reactions, often result in mechanisms of the sort: For this system we can write three rate equations, one for each species: A B k1 B C k2 In matrix form:

Chemical Mechanisms with Coupled Chemical Reactions: Coupled differential Equations Analytic solutions exist for this eigenvalue problem to solve for concentration vs. time If the initial concentration of every species but [A] is zero, the solutions are Concentration vs time when k2/k1=0.5 B changes a lot; Not low or constant Concentration vs time when k2/k1=10 B doesn’t change much Low and ~constant

Chemical Mechanisms with Coupled Chemical Reactions: Steady State Approximation Consider again the following mechanism: Steady state approximation: assume the rate of change of intermediate B is zero A B k1 B C k2 Approximate Steady state solution Equivalent when k2 >> k1 making [B] low & ~constant Exact solution

Chemical Lifetimes A B B C Often we are interested in the average lifetime of a molecule before it reacts away Lifetime has units of time The interplay between chemical lifetimes and atmospheric mixing processes determines much of atmospheric chemistry A B k1 B C k2

Collision Theory Molecules are constantly moving Molecular gases are constantly colliding with each other with a T & P dependent collision frequency Each collision has a particular amount of energy associated with it This energy may lead to chemical reaction Threshold energy

Bimolecular Kinetics Atmospheric chemistry involves both unimolecular and bimolecular processes Bimolecular kinetics depend on pressure, [M] A reasonable model for a bimolecular reaction is

Visualizing bimolecular pressure dependence: O + O2 + M  O3 + M M O OO M = O2 or N2 O3 O + O2 reaction coordinate

Bimolecular Kinetics: The Low & High pressure Limits The total bimolecular process: We want to know the rate of AB formation Write rate equations for AB* Assume AB* is in steady state Solve for AB* and plug into the first equation

Bimolecular Kinetics: The Low & High pressure Limits Low Pressure Limit [M] is very small k4 >> k5[M] k5[M] goes to zero Overall reaction rate depends linearly on [M] High Pressure Limit [M] is very large k4 << k5[M] k4 goes to zero Overall reaction rate is independent of [M] Instantaneous stabilization

T & P dependent kinetic effects Laboratory measurements of rate coefficients give rise to T & P dependences which are well described by the kinetic master equation

Quick Summary Atmospheric chemistry dominated by photolysis Molecular motion on a potential energy surface (PES) determines reactivity In the atmosphere, simple reactions combine to form kinetic networks (i.e., coupled sets of important reactions) The steady state approximation is a useful simplification for short lifetimes Chemical reactions depend on both pressure & temperature, and are determined through a combination of experimental & theoretical approaches