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METO 621

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METO 621

Lesson 20

- A quantum of radiative energy is called a photon, and is given the symbol hn . Hence in a chemical equation we write:
O3 + hn →O2 + O

- The energy of a photon in terms of its wavelength l is E=119625/l kJ mol-1 or 1239.8/ l eV
- To get enough energy to break up a molecule (dissociation) the wavelength must be in or below the ultraviolet. Thus dissociation typically occurs as the result of electronic transitions
- Small, light chemical species generally have electronic transitions at wavelengths shorter than those for more complex compounds, e.g. l<200 nm for O2,.

- Atmospheres tend to act as filters cutting out short wavelength radiation, since the absorptions of their major constituents are generally strong at the short wavelengths.
- As a result, photochemically active radiation that penetrates into an atmosphere is of longer wavelengths, and the chemistry is characterized by lower energies. For example, the dissociation of molecular oxygen, the ultimate source of ozone in the stratosphere, is limited to altitudes above 30 km.
- Absorption of a photon of photochemically active radiation leads to electronic excitation, represented as
AB + hn→AB*

- If the excited molecule then breaks apart, the quantum yield of such a reaction is defined as the number of reactant molecules decomposed for each quantum of radiation absorbed

- Two main mechanisms are recognized for dissociation, optical dissociation and pre-dissociation. These processes will be illustrated in the O2 and O3 molecules.
- Optical dissociation occurs within the electronic state to which the dissociation first occurs. The absorption spectrum leading to dissociation is a continuum.
- At some longer wavelength the spectrum shows vibrational bands. The bands get closer together as the limit is approached – the restoring force for the vibration gets weaker.
- The absorption from the ‘X’ to the ‘B’ state in O2 , is an example.

- Note that when the B state dissociates, one of the two atomic fragments is excited. One atom is left in the ground state (3P) and the other in an excited state (1D).
- Some fragmentation occurs in the B→X (Schumann-Runge) system before the dissociation limit. This occurs because a repulsive state crosses the B electronic state and a radiationless transition takes place. The repulsive state is unstable and dissociation takes place. Note that both atomic fragments are 3P.
- Although molecular oxygen has many electronic states, not all of the possible transitions between the states are allowed. The magnitude of the photon energy is not the only criteria
- Consideration of things such as the need to conserve quantum spin and orbital angular momentum indicate if the transition is possible.

- Let us take the reaction
O3 + hn → O2 + O

- The O2 molecule and atom can be left in several states if we consider energy alone, because any ‘extra’ energy can be used for kinetic energy of the products.
- For wavelengths about 310 nm or less, spin conservation allows the transition
O3 + hn → O2(1Dg) + O(1D)

- The O(1D) atom formed in this reaction plays a major role in atmospheric chemistry, for example
O(1D) + H2O → OH + OH

- OH, the hydroxyl radical, can break down hydrocarbons.

- Note that the onset of dissociation is not abrupt.
- The shape of the curve can be explained if the internal energy of the molecule (vibration and rotation) can be added to the photon energy to induce transitions.
- Transitions from vibrationally excited states can be important in the atmosphere.
- The solar spectrum shows a rapid increase above 310 nm, so any extension of the absorption cross section above this limit can lead to a significant increase in say the quantum yield of O1D

- We have already considered the potential energy diagram for a diatomic surface, which can be represented as a two dimensional surface.
- But for a polyatomic molecule we must consider a three dimensional potential energy surface.
- The next figure represents the potential energy surface for the reaction
A + BC → ABC* → AB + C

- The symbol * indicating that ABC has energy above that of the reactants A and BC, and therefore ABC* is unstable.
- ABC* will either drop back to A + BC or drop down to AB + C

- A reaction
A + B → products

proceeds at a rate proportional to the concentrations raised to some power

- k is the rate coefficient (rate constant).The powersa and b are the order of the reaction with respect to the reactants i.e.
- aA + bB → products
- If for example a=b=1 then the reaction is called a second order reaction (a+b=2) .

- If the concentration of B is very much greater then A then [B] can be considered a constant.
- One can now combine [B] with k to form a first order reaction rate

- k1 is called a pseudo first order rate coefficient

- As two reactants approach each other closely enough, the energy of the reaction system rises ( see the previous figure).
- The contours of the surface show that there is a valley that provides the lowest energy approach of the reactants, the dotted line in the figure is that lowest path.
- There comes a point , marked ‘*’ beyond which the energy starts to decrease again, and so product formation is now energetically favorable.
- The next figure shows the energy of the ABC system as a function of distance traveled along the lowest path for an exothermic reaction.

- In principle, if the potential surface is known, it is possible to calculate the rate coefficient, but in practice this a difficult problem.
- Two simplifications are adopted. The first is the collision theory, the second the Transition State theory.
- In the collision theory two conditions must be met, a collision between the reactants must occur, and the energy of collision along the line of centers must equal or exceed the energy required to overcome the energy barrier. The rate of reaction becomes

- The rate coefficient then becomes

- In this expression A is a constant whereas the mean velocity used in the collision theory depends on the square root of the temperature. So the two equations do not agree exactly.

- For typical molecular reactants, with collision radii of 400 picometers, and relative masses of ~30,sc is ~3E-10 cm-3 molecule-1 s-1 at 300K.
- This product is called the collision frequency factor. Except for the simplest systems, A is always less than this factor.

- 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.
- The q’s for AB and BC are obtained from spectroscopic constants. However this cannot be done for ABC*. Informed guess.

The partition functions may each have a different temperature dependence but the over all temperature dependence can be expressed as a power law.

Where A’ is the temperature-independent part of the pre-exponential function, and n is the exponent for the temperature dependence.

- 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.
- Droplets are much denser then the surrounding air, and reactants have to squeeze past solvent molecules in order to react
- 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.

- These are reactions that occur at the interface between condensed and gaseous phases, i.e. the surface
- In liquids, the reactions tend to be inside the particle. In solids, the diffusion from the surface is extremely small, and the reactions are confined to the surface.
- We now need to consider the case when two different species X and Y are absorbed on the surface and react
- If we assume that all surface sites are equivalent, and that there are no interactions between similar molecules, i.e. the number of sites ‘filled’ is small compared to the total number of sites, then we can apply the Langmuir adsorption isotherm.

- It can be shown that the surface coverage, qX, is given by
qX=bpX/(1+pX)

- b is the ratio of rate coefficients for adsorption onto the surface and desorption from it. p is the partial pressure of the gas.
- In general the value of pX is much smaller that 1. Hence we can write