The Rate Law, or more exactly the Rate-Law Expression, is a description of how the rate of a
reaction depends on its concentration. Rate Laws are individual to each reaction they describe, and must be derived experimentally. The rate-law expression for a reaction in which A, B,... are reactants has the general form:
rate=k[A]x[B]y...
The
variable 'k' represents the specific rate
constant for the reaction, which is entirely dependant upon the reaction at hand. Though its value is unknown until experimental evidence has been gathered, 'k' will not change once it has been determined and should apply to any value of the reaction under the given conditions (if
these conditions change, 'k' will change). No element of the rate-law expression is dependant on the
coefficients of the
balanced chemical equation, nothing will give you the full picture until you actually perform some experiments (although molecular simulation software can help predict its value).
Rate-law expressions possess two 'orders', the first corresponding to the value of the exponent. For example, 'A' in the above equation is in the 'xth' order. The second order corresponds to the overall sum of orders for the equation, so the above equation is in the 'x+yth' order overall. The overall order of the equation determines the units for 'k'.
A rate-law expression for an equation can be found by performing series of reactions in which the balance of reactants is changed in various ways as well as the initial rate of formation for the product. Using Algebra these rates can be compared and rate ratios are determined. For example, in the reaction A + 2B --> C
Exp# Initial [A] Initial [B] Rate of Form. C
-----------------------------------------------------------
1 1.0 * 10-2 M 1.0 * 10-2 M 1.5 * 10-6 M*s-1
2 1.0 * 10-2 M 2.0 * 10-2 M 3.0 * 10-6 M*s-1
3 2.0 * 10-2 M 1.0 * 10-2 M 6.0 * 10-6 M*s-1
Between experiments one and two, Initial [A] remains the same will Initial [B] changes, so these values can be used to calculate the ratio of [B]. 2.0 * 10
-2 M / 1.0 * 10
-2 M = 2.0. Looking at the initial rate of formation for C, this also has a ratio of 2.0. Therefore, the exponent to which the concentration of [B] is raised is 1. The same process results in an exponent of 2 for [B]. So the final rate-law expression is rate=k[A]²[B].
Once the rate-law expression is derived, plugging in known values from experimental data reveals the value of the constant 'k'. Any of the three experiments can be used, all will result through Algebraic manipulation in yielding a constant of 1.5 M-2*s-1. The value of the molarity's exponent is determined by the overall order of the rate-law expression, in this case three.
Thanks for help from Professor Pi