METO 637 Lesson 5 Transition State Theory Quasiequilibrium

METO 637 Lesson 5

Transition State Theory • Quasi-equilibrium is assumed between reactants and the ABC molecule, in order to calculate the concentration of ABC*. • The rate of the reaction can then be obtained from the rate at which ABC* passes to products. • Equilibrium constants are then expressed in statistical thermodynamic terms

Transition State Theory • For this theory we write the rate coefficient as • The q’s are statistical thermodynamic terms or partition functions. Basically the internal motions neglected in the collision theory are specifically taken into account. • One can get q. A and q. BC from spectroscopic constants measured in the laboratory , but q. ABC has to be ‘estimated’

Transition State Theory • Both theories give identical algebraic expressions for two identical atoms (hard spheres) • The three total partition functions are ecah the product of translational, rotational and vibrational partition functions • The temperature dependence of each partition function can be evaluated as a power law. Hence the rate coefficient can be written as:

Unimolecular and termolecular reactions • Consider the combination of two O(3 P) atoms. • If the two atoms have no translational energy then the newly formed O 2 molecule has the O+O bond energy stored in it, i. e. we actually have O 2* at its dissociation limit. • Unless some energy is removed within one vibrational period the molecule will fall apart • Energy can be removed by collisions, and we usually represent the collision partner as M

Unimolecular and termolecular reactions

Unimolecular and termolecular reactions • If kr >> ks[M] the reaction is third order • If kr << ks[M] the reaction is second order • Sometimes the excess energy can be removed by radiation. • For example O + NO → NO 2 + hν • This gives rise to continuum emission in the atmosphere. However the three body combination (O + NO + M) is much more efficient, except at very low pressures.

Condensed phase, surface and heterogeneous reactions • Reactions within liquids and droplets are important in several aspects of tropospheric chemistry, especially in the formation of acid rain. • Particles such as sulfate aerosols or clouds formed from water-ice and hydrates of nitric acid – polar stratospheric clouds (PSC), are a major cause of the observed polar ozone holes. • The chemistry takes place at the interface between gas and condensed phases and is known as heterogeneous chemistry.

Liquid Phase Reactions • In such areas as the formation of acid rain, reactions that take place within a droplet are extremely important. • Henry’s Law will determine the rate at which the reactant gases enter the droplet. Solubilities of gases at low pressures obey the law: [X(s)] = HXpx • Droplets are much denser then the surrounding air, and reactants have to squeeze past solvent molecules in order to react

Liquid Phase Reactions • Liquid-phase kinetics can be viewed in two ways • First, the rate determining process is the diffusion of the reactants through the solvent – a diffusion controlled reaction. • Second, the kinetics are controlled by the rate of reaction within the droplet – an activation controlled reaction

Heterogeneous Reactions • These are reactions that occur at the interface between condensed and gaseous phases, i. e. the surface • The first parameter that we consider is the uptake parameter, γ, which is the ratio of the number of molecules that stick on the surface to the number that strike the surface. • If the rate of collision of a molecule X on an area A is w then the rate of loss of X per unit volume, -d[X]/dt is equal to γ. w/V, where V is the volume of the system. • The kinetic theory of gases shows that:

Heterogeneous Reactions • The equation developed for the uptake coefficients can be applied to more than one species, which in turn can interact chemically on the surface. • For example the reaction between hydrogen chloride and chlorine nitrate on the surface of polar stratospheric clouds HCl + Cl. ONO 2 → HNO 3 + CL 2 is the major source of chlorine atoms in the polar spring.