Rate Laws and Temperature

The rate of a chemical reaction describes how quickly reactants are consumed or products are formed. For a reaction between two reactants, A and B, the rate law has the form rate = k[A]ᵐ[B]ⁿ, where k is the rate constant and the exponents m and n are the orders of the reaction with respect to A and B. The exponents cannot be found from the balanced equation and must be determined by experiment. The sum m + n is the overall order, and the units of k depend on the overall order.

The rate constant also depends on temperature. Reactions occur when molecules collide with enough energy to overcome an energy barrier called the activation energy, Ea. Raising the temperature increases the fraction of molecules with that much energy, and a catalyst provides a different pathway with a lower Ea. Neither of these changes the overall free energy change of the reaction.

Part 1. A chemist studies the reaction A + B → products in solution at 300 K. She measures the initial rate of the reaction for different starting concentrations, in moles per liter (M). The rate is given in M/s. Table 1 shows the results.

Table 1. Initial rates at 300 K.

Each rate is measured by following the disappearance of A with a spectrophotometer, because A absorbs light at a wavelength where B and the products do not. The cuvette is held at 300 K in a thermostated holder, and the reaction is started by adding B last.

Part 2. The chemist next measures the rate constant at different temperatures, using the same starting concentrations as in Experiment 1. She also repeats the 300 K measurement in the presence of a catalyst. Table 2 shows the results. The units of k are those of the rate law found in Part 1.

Table 2. Rate constant under different conditions.

A typical rule of thumb holds that many reactions at room temperature proceed about twice as fast for each 10 K rise in temperature, which is close to what the chemist sees. The chemist also notes that the reaction mixture is stirred to keep the concentrations uniform, and that each rate in Table 1 is measured before more than a few percent of the reactants have been used, so that the concentrations are close to their starting values.

In a mechanism, a reaction takes place through a series of elementary steps. The slowest elementary step determines the overall rate, and the rate law of an elementary step can be read directly from its molecularity. The chemist wants to propose a mechanism that is consistent with the rate law she finds, but she must remember that a proposed mechanism can only be disproved by experiment, not proved.