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METO 621 CHEM
Lesson 1
CHEMICAL FORMULA
• Each atom is given a symbol, N stands for nitrogen, O for
oxygen, Cl for chlorine.
• For molecules, the number of atoms is placed as a subscript,
for example Nitrogen Dioxide is written as NO2, and contains
one nitrogen atom and two oxygen atoms.
• We will deal with the simplest reactions, e.g.
NO + O3 → NO2 + O2
Nitric oxide (NO) reacts with Ozone (O3) to give Nitrogen
Dioxide (NO2) plus molecular oxygen (O2)
• The number of atoms for a particular species must be the
same on both sides of the equation.
Photochemical Change
• 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 but <300 nm for O3
Photochemical Change
• 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
Photochemical Change
Photodissociation
• 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.
Photodissociation
Photodissociation
Photodissociation
Photodissociation
• 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.
Photodissociation
• 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.
Wavelength Threshold for Dissociation of
Ozone
Quantum yield for Ozone
Quantum yield for Ozone
• 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
Potential Energy Surface
• 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
Potential Energy Surface
Chemical Kinetics
• A reaction
A + B → products
proceeds at a rate proportional to the concentrations raised to
some power
d [ A] d [ B]
Rate 

 k[ A] [ B]
dt
dt
• k is the rate coefficient (rate constant). The powers  and 
are the order of the reaction with respect to the reactants i.e.
A + B → products
• If for example 1 then the reaction is called a second
order reaction (+2) .
Chemical Kinetics
• 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
d [ A]
Rate 
 {k 2 [ B] }[ A]  k 1[ A]
dt
•
k1 is called a pseudo first order rate coefficient
Bimolecular reactions
• 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.
Bimolecular reactions
Bimolecular reactions
• 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
dnBC
dn A


 n A nBC c c exp(  Ec / RT )
dt
dt
Bimolecular reactions
• The rate coefficient then becomes
k   c c exp(  Ec / RT )
Many second - order rate constants are found to follow the
Arrhenius expression
k  A exp(  Ea / RT )
• 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.
More telling is the difference between A and c
Bimolecular reactions
• For typical molecular reactants, with collision radii of 400
picometers, and relative masses of ~30, c 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.
Transition State Theory
• For this theory we write the rate coefficient as
kT q ABC*
k
exp(  Ec / kT )
h q A qBC
• 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.
Transition State Theory
The partition functions may each have a different
temperature dependence but the over all
temperature dependence can be expressed as a
power law.
k  A T exp(  Ec / RT )
'
n
Where A’ is the temperature-independent part
of the pre-exponential function, and n is the
exponent for the temperature dependence.
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.
• 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.
Heterogeneous Reactions
• 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.
Heterogeneous Reactions
• 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
rate  kLq XqY  kLbX pX bY pY