Humboldt State University ® Department of Chemistry

Richard A. Paselk

Chem 109 - General Chemistry - Spring 2011

Lecture Notes 35: 18 April

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Chemical Kinetics, cont.

So how do we determine the order of a reaction? cont.

Last time looked at an algebraic method to detrmine rate law. We can also determine the order graphically. If we plot ri = d[P]/dt vs. [P] for 0 - 3rd order we see the plots below:

reaction order plot

Its fairly easy to distinguish 0 order & first-order (linear), but the others can be difficult since they are all curves with only slightly different basic shapes (if we adjust the x-axis to fit them, they come fairly close for eye-balling). However, they are readily distinguished via linear plots.

Thus, the various orders can be linearized:

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.

 

r = p (e-(Ea/RT)) Zo[A][B]

r = k [A][B]

Reaction Rates vs. Temperature

We know that reaction rates are influenced by temperature - wood reacts with oxygen much faster in a fire than at room temperature. From the expressions above it is also obvious that rate should be influenced by temperature.

Recall the distribution of KE in a population of molecules (the Maxwell-Boltzman Distribution). [overhead, Figure 12.12, p 588 in Zumdahl] Note that for this plot higher temperatures for Xe would look very similar to the plots for the smaller gases.

Plot of Maxwell-Boltzman Distribution of oxygen at three different temperatures

 

At higher temperatures more molecule will have KE's exceeding Ea, thus the reaction rate will increase. So how can we determine the magnitude of this effect?

k = A e-(Ea/RT)

where A = pZo

ln k = (-Ea/R) (1/T) + ln A

  • A plot of ln k vs. 1/T will then give a slope of -Ea/R, from which Ea is readily obtained.

Arrhenius plot

public domain image via Wikipedia Creative Commons

  • Alternatively, k values can be obtained at two different temperatures. Subtracting the resultant equations (and recalling that ln a - ln b = ln a/b) then gives:

ln k1/k2 = -Ea/R (1/T1 - 1/T2)

Transition States and Reaction Progress (Reaction Coordinate) Diagrams

Reaction with -DeltaG:

Reaction Progress diagram for favorable reaction

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, Eact. 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 Eact the slower the reaction, because fewer molecules have enough energy to react. If Eact 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 (DeltaG) 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 DeltaG 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 DeltaG is zero, then the reaction mixture will end up with equal amounts of reactant and product.

Reaction with +DeltaG:

Reaction Progress diagram for unfavorable reaction

Thus the size and sign of DeltaG tells us how far a reaction will proceed, while the size of Eact tells us how fast the reaction will be. Note on this plot that Eact 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.

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© R A Paselk

Last modified 20 April 2011