Kinetics

To understand kinetics, it is useful to understand the relationship between kinetics and thermodynamics.

Thermodynamics: The study of energy changes of chemical reactions.
Kinetics: The study of the rates of chemical reactions.

Put another way, thermodynamics determines whether or not a reaction is 'possible', and kinetics indicates how quickly a reaction can occur.

Reaction energy diagrams, such as the one shown below, are a useful way of indicating this relationship. In these diagrams, the x-axis is the reaction coordinate, which is a measure of the extent of reaction. Thus, reactants (starting materials) are on the left, and products are on the right. For the reaction to proceed, it is necessary to pass through one or more transition states. The higher the transition state, the slower the reaction.

Reaction diagrams can be used to indicate the energy change (ΔG or ΔH) associated with a reaction, and the height of the reaction barrier (E_a). In the diagram shown above, ΔG is 50 - 150 = -100 kcal/mole. The negative sign indicates that the reaction is energetically favored (i.e. - it goes 'downhill'). The activation energy (E_a) is 450-150 = 300 kcal/mole. E_a values are always positive (it is always uphill).

Rate Laws

The rate of a chemical reaction can be defined as:

rate = (change in conc.) / (change in time)

This is commonly fit to a rate law of the form:

rate = k [A]ⁿ Where k is the rate constant, [A] is the concentration of reactant A, and n is the reaction order.

Using this equation, plots for zeroth, first, and second order plots are shown below. (Rate laws involving other orders or that depend on the concentration of more than one reactant will not be considered in this class).

Factors that Affect Chemical Reaction Rates

Concentration: Reaction rates almost always (except for 0^th order reactions) increase with increasing concentration.
Temperature: For all cases that we will consider, reaction rates are faster at higher temperatures.
Catalyst: Addition of a catalyst increases the rate of a chemical reaction by lowering E_a.

Equilibrium

A reaction is at equilibrium if:

rate_{(forward reaction)} = rate_{(reverse reaction)}

At equilibrium:

The rates of the forward and reverse reactions are equal.
The concentrations of reactants and products are not equal.
The reaction has not 'stopped'.

For equilibrium reactions, we can write an equilibrium expression:

K_eq = (products)/(reactants) *(Concentrations must be raised to the appropriate powers).*

We can write the equilibrium constant express for the following reaction as:

2 SO₂ + O₂ _←^→ 2 SO₃ K_eq = ( [SO₃]² ) / ( [SO₂]² [O₂] )

It should be noted that solids are not included in these equilibrium constant expressions.

Le Chatelier's Principle

Le Chatelier's principle states that if a 'stress' is applied to a system at equilibrium, the position of the equilibrium will shift to minimize this 'stress'. This is probably best illustrated by example.

C_(solid) + H₂O_(gas) _←^→ CO_(gas) + H_{2 (gas)} ΔH = +31 kcal/mol

Increase [H₂O]: Equilibrium should shift ↠
Increase [CO]: Equilibrium should shift ↞
Decrease [H₂]: Equilibrium should shift ↠
Increase [C_(solid)]: Should not affect equilibrium, since solids do contribute to K_eq.
Increase Temperature: Since heat is a reactant, adding heat should shift equilibrium ↠
Increase Pressure: Since the products contain more gas than reactants, increasing pressure should cause equilibrium to shift ↞
Adding a Catalyst: Catalysts have no effect on the position of equilibrium (although they may allow a reaction to reach equilibrium faster).