Rate Laws

Rate laws are equations that quantify the rate of a chemical reaction. In general, the rate of a chemical reaction depends on a number of variables, including:

• Temperature

• Reactant Concentration

• Pressure

For the general chemical reaction given below:

$aA + bB \rightarrow cC + dD$

(where capital letters A, B, C, and D indicate chemical species – products and reactants- and lower case letters indicate stoichiometric coefficients) a general power law form of the reaction rate law can be written as follows

$-r_{A} = k{C_{A}}^{\alpha}{C_{B}}^{\beta}$       (Equation 1)

where –r_A is the rate of disappearance of species A, k is the specific reaction rate constant, C_A and C_B are the concentrations of reactants A and B, respectively, and α and β are the reaction orders. The reaction orders indicate the functional dependence of the rate of reaction on each species concentration. Though often thought of as (and determined) as fitting parameters, these reaction orders are more formally the net, macroscopic dependence on concentration that results from the actual elementary mechanism.

The main effect of temperature on the rate of a chemical reaction comes through the specific rate constant, k. The effect of temperature on k is described by the Arrhenius law, which states

$k = Aexp \left ( \frac{-E_a}{RT} \right)$        (Equation 2)

where A is the pre-exponential factor (related to the entropy changes associated with forming the transition state from the initial reactants) and E_a is the activation energy, or the energy barrier that must be surmounted in order to form products.

More information on rate laws and determining rate law parameters can be found in chapter 3 and 5 of Elements of Chemical Reaction Engineering, by H. S. Fogler and in Chemical Kinetics, by K. J. Laidler.