This page supplements the second handout on the "clock reaction." You should have your copy of the handout available as you look over this page. If you need a spare, or just want an electronic (pdf) version, click the link below.
A "Clock" Reaction: Temperature effect
MAIN IDEAS: Activation energy and the effect of temperature
While it is somewhat intuitive that chemical reactions are faster at higher temperatures, a real understanding of why this is true and how to express "faster" mathematically was a long time coming (and in fact some reactions are slower at higher temperature, but they are pretty rare). The first sucessful theory of the effect of temperature on reaction rates was put forward in 1889 by the Swedish physical chemist Svante Arrhenius, who won the Nobel Prize in Chemistry in 1903. (He won for his earlier work on ionic dissociation in aqueous solutions, work that established the existance of ions in solution. He was also the first to propose that atmospheric CO2 would have an effect on the Earth's climate, what we now call the Greenhouse Effect. You can click on his picture to read more about him.)
Photo © 1999 The Nobel Foundation
But to get back to the clock reaction, recall that we determined in class the reaction rate law and its rate constant, k, at one temperature. The effect of temperature on reaction rates is almost always entirely contained in k. (We say "almost always," because rates also depend on concentrations, and concentrations can change with temperature, too. In solution, the change is way too small to be important, but in the gas phase, if we keep the pressure constant, then gas concentrations will change with temperature. Remember the Ideal Gas Equation, PV = nRT? Written as P = (n/V)RT, we see that if P is to stay constant while T changes, then the concentration, n/V, must change, too.)
The Arrhenius Equation states
k = A exp(Ea / RT)
where A is a constant with the same dimensions as k called the pre-exponential factor, Ea is a constant with dimensions of energy per mole called the activation energy, and R and T are the Universal gas constant and the absolute temperature, respectively. This equation predicts that a graph of the natural log of the rate constant plotted against the reciprocal of the absolute temperature should be a straight line with a slope given by
slope = Ea / R
We will measure the rate constant in class at three temperatures and construct such a graph. Data from a previous year gave the results shown below. The data are the blue dots, and the purple line is there to allow you to measure a slope and, from the slope, an activation energy. (You will do this again in the second week of the kinetics lab, so now is a good time to practice. You may even get a third chance to interpret such a graph on the first exam...)
When I estimated the activation energy from this graph, I got a value around 56 kJ mol1. If you are having trouble getting a value anywhere close to this, see me.
Finally, here's a page that discusses the snowy tree cricket, a chirping, common cricket that follows the Arrhenius expression in a macroscopic way!