Chemical Kinetics, cont.

Transition States and Reaction Progress (Reaction Coordinate) Diagrams

Reaction with -G:

How do we interpret this diagram?

• The x-axis can be thought of as 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 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 +G:

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 on this plot that E_act goes from the lower blue line (reactant energy) to the top of the peak. 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.

Reaction Mechanisms

Most chemical reactions take place via a series of sequential steps. A reaction mechanism is a possible description of these steps written by us in an attempt to model the reaction.

A proper mechanism is characterized by:

1. a series of elemental steps which when combined give the stoichiometry of the reaction.
2. the steps are consistent with the rate law for the reaction (for us the rate determining step, rds, or slowest step, gives the order of the reaction).

   For example, for the reaction:

A + B C + D, where r = k[A]²

we could write

2 A C + X

B + X A + D

---

A + B C + D

• Note that the first step, 2 A C + X, will satisfy the rate law, that is there are 2 A's in the collision. Thus the first step is the rate determining step.
• And the two steps add up to give the overall stoichiometry, as shown.

Finally, let's look at a couple of example reactions (you don't need to know the chemistry, these are just to demonstrate the possibilities) showing two different reaction orders with the same stoichiometric ratios.

Look at the general reaction:

A + B C + D

specifically

R₃CX + Y^- R₃CY + X^-

• First Order: r = k [A]; & r =-d [A]/dt = d [C]/dt. Example: :S_N1 from organic chemistry, as in the hydroxylation of t-alkylchloride:

  

   

• Second order: r = k [A][B]. Example: S_N2 from organic chemistry, as in the hydroxylation of primary alkylchlorides (reverse of mechanism shown):

  

Chemical Equilibrium

As a general statement can say that all chemical reactions are equilibrium reactions and go toward a state of equilibrium or approach equilibrium. Some reactions reach equilibrium rapidly, some slowly, and some favor products to such an extent that the reactions "go to completion." Regardless of initial concentrations, systems will reach equilibrium given time.

What is an equilibrium - very dynamic situation in chemistry (Great Crabapple War overheads)

Let's look at some classic examples of reactions approaching equilibrium.

• Ammonia synthesis Gas phase at high temperature and pressure (Fig 13.5, Zumdahl, p 615: Ammonia syn.):

N_{2 (g)} + 3 H_{2 (g)} 2 NH_{2 (g)}

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.

Quantitatively we can look at the relationship in a reaction at equilibrium represented by

A C

A C characterized by a constant, k₁ to give a rate, r₁ = k₁[A]

A C characterized by a constant, k₂ to give a rate, r₂ = k₂[C]

The Equilibrium Expression is then:

Generalizing for the equation (Note that the simple derivation above does not generalize, since rates and stoichiometry are not generally correlated - the relationships between rates at equilibrium and stoichiometry are beyond our study.):

aA + bB + ... cC + dD + ...

K_eq = [C]^c[D]^d/ [A]^a[B]^b.

A similar expression is the Mass Action Expression:

The mass action expression is algebraically identical to the equilibrium expression, but it applies to a more general case. That is, the equilibrium expression requires that the values in the expression give the equilibrium constant, whereas the mass action expression allows any set of values. Thus the mass action expression is used to describe a system which has not yet reached equilibrium, while the equilibrium expression is a special case of the mass action expression for a system at equilibrium.

Syllabus / Schedule

C109 Home

C109 Lecture Notes

© R A Paselk

Last modified 20 April 2009