Reaction Rates

Collision Theory: We assume that particles must collide in order to react. Thus a first understanding of reaction rates is based on understanding what influences the frequency of collisions.

• Can have different molecularites. This refers to the numbers of molecules (or particles - can also be atoms or ions) involved in the collision.
  • unimolecular - only one molecule involved (there is no collision)
  • bimolecular - 2 body collision
  • termolecular - 3 body collision (this is very rare, essentially never get more than three body collisions)
• Since particles must collide to react, the rate will depend on concentration. Thus
  • rate = k[A][B] for the reaction of A and B.
• But not all collisions will lead to reaction. At least two additional factors are important:
  • Activation energy, E_a. This is the energy needed to overcome repulsion, bond strength etc. At any given temperature the number of particles with a particular energy is given by N = e^-(E/RT). Note that
    • as E_a increases the fraction decreases.
    • as T increases, the fraction with sufficient energy for reaction (E>E_a) increases. Arrhenius Equation, k = Ae^-(E/RT). Can plot fraction of particles with KE vs. KE. [sketch or overhead]. A crude relation, which holds for many average reactions is the so called Q₁₀. This states that for every 10 °C increase in temperature we get a doubling of reaction rate.
  • Orientation of collision. The steric factor or probability factor (p) is the fraction of collisions which have orientations favorable for reaction. Can range from very small numbers (one atom or molecule must hit another at a very specific place) to about 1.

• Note that for kinetics the stoichiometry of the reaction is not necessarily related to the rate law, rather the rate law is related to a single slow step in the reaction process.

Transition States and Reaction Progress (Reaction Coordinate) Diagrams.

Reaction with a negative free energy (-G) - products are favored:

.

How do we interpret this diagram?

• The x-axis can be thought of a time axis for a single reaction, starting with the reacting molecules and ending with the product molecules.
  • Thus as the reaction progresses the energy in the particles goes up (they become less stable) as they are "pushed together" in a collision.
  • The upward slope represents the energy of repulsion and bond stretching.
  • The downward slope represents the formation of the new bonds and the separation of the products.
  • The top of the peak represents the "transition state" (TS) a high energy combination of atoms which can go to either reactants or products.
• The y-axis represents the energy of the species during the reaction. In these diagrams we are plotting the so-called free energy, G= delta G. The free energy tells us how much energy is available to do work, and so is the most common energy measure used by chemists and biologists.
  • The energy difference between the reactants and the TS is called the activation energy, E_act. This is the energy the reacting species must have (as kinetic energy etc.) in order to overcome the barriers to reaction (repulsion, bond energy). The greater the value of E_act the slower the reaction, because fewer molecules have enough energy to react. If E_act is very low (not much of a hill) then the reaction will proceed readily and rapidly.
  • The energy difference between the reactants and the products (G) tell us how far the reaction will go (that is, the fractions of reactants and products in equilibrium with each other). If the change is negative (products have less energy than reactants as seen on the diagram above), then products are favored (the reaction will go to mostly product. If, on the other hand, the products are at a higher energy then G will be positive, and the reactants will be favored (the reaction will stay mostly reactants, and little product will be made - see the diagram below). If G is zero, then the reaction mixture will end up with equal amounts of reactant and product,

    Reaction with a positive free energy (+G) - reactants are favored:

    

• Thus the size and sign of G tells us how far a reaction will proceed, while the size of E_act tells us how fast the reaction will be. Note that reactions can be thermodynamically very favorable (go nearly completely to product and release lots of energy), but kinetically unfavorable (they react very slowly). We say the reactants are thermodynamically unstable, but kinetically stable.
• Catalysts make reactions go faster without affecting how far they go (G is unchanged - the equilibrium is unchanged). They do this by
  • making it easier to achieve the activation energy (they reduce E_act), or
  • change the mechanism to one with one or more lower E_act's.

Equilibria

Chemical equilibria occur when the rates of the forward and the reverse reactions of a chemical system are identical.

Regardless of initial concentrations, systems will approach and reach equilibrium given time [see Figure 12.15, p 474] (overheads, approach to equilibria by carbon monoxide + water vs. carbon dioxide + hydrogen)

Vast numbers of chemical reactions operate at equilibrium in the natural world, and it is frequently essential to be able to understand and to predict their behavior. Qualitatively we can get an idea of how an equilibrium system will behave by using Le Châtelier's Principle.

Le Châtelier's Principle: If stress is applied to a system at equilibrium, the equilibrium will shift in such a way as to relieve the stress. e.g. if the pressure of carbon dioxide is increased over a solution of carbon dioxide in water, more carbon dioxide will dissolve, reducing the pressure increase.

Let's look at an equilibrium system, and try to predict its response using Le Châtelier's Principle and/or the equilibrium expression.

Example: Consider the reaction

CO + NO₂ NO + CO₂ + heat (226 kJ)

Note that heat appears on the product side - the system is giving up heat, H is negative, H = - 226 kJ

So, what will happen to [CO₂] if:

• CO is added?
• NO₂ is added?
• NO is added?
• T is increased?
• V is increased?
• Ar is added?

 

C107 Laboratory

C107 Home

C107 Lecture Notes

© R A Paselk

Last modified 19 November 2009