IV. Kinetics Introduction (Pseudo) First Order Approx. Steady State Approximation

Role of Kinetics Atmosphere is an open system- equilibrium does not apply Determine chemical fate of a species Determine concentration of a species Compare time scales for processes –Chemical –Physical –Meteorological

Simple Kinetics vs. Complex Models Simple Kinetics (here) Approximations to give insight Complex Models Quantitative but –Numerical solutions –Transport –Lack of insight

First Order Kinetics Photochemistry (J is 1 st order rate constant) O 3 + h → O 2 + O Lifetime,  = 1/J What is the photolysis lifetime of O 3 at 10 km?

Elementary versus Complex Reactions Elementary – balanced reaction reflects molecular-level events (mechanism): CH 4 + OH → CH 3 + HOH So the Rate Law reflects the mechanism Complex – multiple elementary reactions CH O 2 → CO H 2 O

Pseudo-First Order Approximation Reduces 2 nd order to 1 st order [O 3 ] >> [Cl] Major trace species vs. highly reactive radical [O 3 ] effectively constant k’ = pseudo-1 st order rate constant

Lifetimes and Halflife photochemistry  = 1/J Pseudo-1 st order rxn.  = 1/k’ Halflife (t 1/2 ) =  k Cl+O3 = 8.8 x cm 3 molecule -1 s -1 (218 K) [O 3 ] = 5 x molecule cm -3 (25 km) What is the lifetime of Cl with respect to reaction with O 3 ?

Rate Constants Sources – JPL Data Evaluation, IUPAC, NIST Arrhenius (empirical) k(T) = Ae -Ea/RT A = Arrhenius pre-exponential factor E a = activation energy For Cl + O 3 : k(T) = 2.9 x e -2.2 kJ/mole/RT cm 3 molecule -1 s -1 e -Ea/RT = e -(Ea/R)/T k(T) = 2.9 x e -260/T cm 3 molecule -1 s -1 What is k at 218 Kelvin ?

Steady State Approximation Applied to ClO, means [ClO] changing very slowly:

Steady State Approximation, con’t Local noon, [radicals] at daily maximum, changing slowly  Steady State Approximation okay

Key Points Pseudo-first order approximation Steady state approximation Data sources abound