Introduction to Kinetics Lecture 14

Reading in Chapter 5 Read sections 5.1 through (p.160 to p. 199) and section 5.7 (p ). We will probably skip the intervening sections – or cover them briefly. Book errata:

Kinetics Whereas thermodynamics concerns itself with equilibrium and the distribution of components between species and phases at equilibrium, kinetics concerns itself with the pathway to equilibrium, including the rates and mechanisms of reaction. Rates depend on temperature and at the surface of the Earth reaction rates are often so slow that equilibrium is never achieved. This can also be true at higher temperature - and we have mentioned one example (the spinodal). The microscopic perspective becomes somewhat more important in kinetics than it was in thermodynamics

Overall & Elementary Reactions The reaction: CaAl 2 Si 2 O 8 + 3H 2 O + CO 2 = CaCO 3 + 2Al(OH) 3 + 2SiO 2 describes a key process at the surface of the Earth, namely weathering igneous minerals (plagioclase) to form common sedimentary ones (calcite, gibbsite, and quartz). But does this overall reaction describe what actually happens? NO. In thermodynamics,we might not care, but in kinetics, we do. The first step in understanding reaction pathways and reaction mechanics is to breakdown overall reactions such as this into the elementary reactions. An elementary reaction is one that involves only one step a describes what occurs on the microscopic level.

Reaction Mechanisms We can begin to breakdown the overall reaction. Some steps are: CO 2(g) + H 2 O = CO 2(aq) + H 2 O CO 2(aq) + H 2 O = H 2 CO 3 H 2 CO 3 = H + + HCO 3 – Producing acidity necessary for weathering. Next step is likely absorption of H + to the surface: CaAl 2 Si 2 O 8 + 2H + = H 2 CaAl 2 Si 2 O 8 2+ Followed by replacement of the Ca by H: H 2 CaAl 2 Si 2 O 8 2+ = H 2 Al 2 Si 2 O 8 + Ca 2+ etc.

Defining Reaction Rates For a reaction such as: Ca 2+ + Mg CO 3 2– = CaMg(CaO 3 ) 2 We define the rate of reaction as the rate of production of the products, or equivalently, the rate of consumption of the reactants divided by the stoichiometric coefficient: Equivalently: The equation tell us nothing about what the reaction rate is, we are just defining what it means. o We’ll shortly see that rates generally do depend on concentrations or reactants and products, so don’t be confused.

Reaction Rates & Concentration Consider the gas phase reaction: N 0 + O 2 = NO + O 0 First thing that must happen is we must bring the reactants together. We can imagine a reference frame in which the N atom sweeps out a volume v × t (velocity times time). Whether a reaction will occur in that time will depend on whether or not the center of an oxygen molecule is present within that volume. Number of collisions (per N)will be: Overall collision rate will be:

For an elementary reaction, we expect the rate of reaction to depend on the concentration of reactants Bottom Line:

Dependence on Temperature Just because two people meet on a date, doesn’t mean they will tie the knot. o Kinda depends on how ‘hot’ the date was! Similarly, just because two atoms or molecules collide, doesn’t mean they will react. o Depends on whether the collision is energetic enough to overcome coulomb repulsion and the electron orbits can reorganize. o An energy barrier, E B, must be overcome. o That means it depends on temperature. Hence the date analogy!

Temperature and Barrier Energy Since energy levels are closely spaced, we can integrate, so the probability of a molecule having E ≥ E B is: Our reaction rate is now: Maxwell-Boltzmann Law gives ave. velocity in a gas as: where µ is reduced mass of gas: µ = m N m O2 /(m N + m O2 ) We suppose that a reaction will proceed if the N atom has at least certain energy, E ≥ E B. What function tells us how energy is distributed among molecules? Boltzmann Distribution Function.

Arrhenius Relation Our equation now is: Let: A describes the frequency of opportunity for reaction and is called the frequency factor. We can express the temperature dependence of the reaction rate as: This is known as the Arrhenius relation and describes the dependence of reaction rates on temperature.

The Rate Constant Arrhenius Relation k is known as the rate constant. o So many K’s! o We’ll use upper case roman K for the equilibrium constant o Lower case roman k for Boltzmann’s constant o Lower case italic k for the rate constant. We can now write the rate of our N+O 2 reaction as: R = kn N n O2

Reaction Rates and Temperature The Arrhenius Relation tells us that reaction rates depend exponentially on temperature (fits everyday experience). This is reason high-T rocks survive at the surface of the Earth out of equilibrium. In the gas phase reaction, A depended on square root of T - much weaker than the exponential factor. Other kinds of reactions show difference dependence of A on T. In many cases we can view A as a constant independent of T.

General Form of Rate Equation We may now write a general form of the rate equation for a reaction such as: aA + bB = cC +dD o (don’t confuse this with the definition of the rate). In the general case of overall reactions, the exponents can be any number (including 0). For the special case of elementary reactions, the exponents of the reactants are the stoichiometric coefficients and the exponents of the products are 0; i.e., rates of elementary reactions are independent of the concentrations of products. Hence if the above is elementary:

Order of the Reaction The order of the reaction is the sum of the exponents of the activities in the rate equation. For example, formation of carbonic acid CO 2 + H 2 O = H 2 CO 3 Rate should be (assuming ideality, and an elementary reaction): So this is a second order reaction. In this case, however, concentration of water will not change appreciably, so it is a pseudo-first order reaction:

Rates and Concentrations Knowing the rate constant (usually empirically determined), we can compute rate. Integrating rate of first order reaction gives: Graph shows how CO 2 concentration changes in the reaction CO 2 + H 2 O = H 2 CO 3

Distinguishing Elementary from Complex Reactions

Elementary or Not? Can’t always predict whether a reaction is elementary or not just by looking at it. The earlier rules about order of reaction provide a test. For example, 2NO 2 –> 2NO +O 2 Rate of reaction turns out to be What does does this tell us? The reaction is elementary.

Elementary or Not? Now consider2O 3 –> 3O 2 Rate of this reaction turns out to be: Since it depends on the concentration of a reactant, it is not an elementary reaction. o Indeed, it is a fairly complex one involving a reactive intermediate, O˚, which does not appear in the reaction. For example, in the stratosphere: