Rate Law

Rate law is an equation that relates the reaction rate to the concentration of the reactants.  Meaning it is dependent on the concentration of the reactants not the coefficient in the balanced chemical equation.  It can be determined experimentally and with the use of elementary steps.  For a general equation,

aA  +  bB  →  cC  +  dD

the rate law has the general form of

Rate = k[A]^m[B]ⁿ

where  

           k = is the rate constant

           [A] = concentration of reactant A

           [B] = concentration of reactant B

           m and n = typically small whole number (0,1, or 2)

The constant k in the rate law is called the rate constant.  The magnitude of k changes with temperature and therefore determines how temperature affects rate.    If we know the rate law and the rate of the reaction including the concentration of the reactants, rate constant can be calculated.

Sample Exercise:

1.  The initial rate of a reaction A +  B  → C, was measured for several different starting concentrations of A and B , and the results are as follows:

Using the data above, determine a) the rate law for the reaction; b) the magnitude of the rate constant; c) the rate of the reaction when [A] = 0.050 M and [B] = 0.100 M.

Solution:

a.  To determine the rate law, we need to analyze the table given, experiment 1 and 2 has constant concentration of A, therefore using this two  experiment number can give us the relationship between the rate and the concentration of B. While experiment 1 and 3 having constant value of [B] will give the relation between rate and [A].

This is how to get the value of n,

Using the relationship of rate above,

Therefore the value of n = 0, because any number raised to 0 equals 1.

To get the value of m we will analyze experiment 3 and 1:

Using the relationship of rate 3 and rate 1 above,

The value of m = 2, since the square of 2 equals 4 (2^m = 4).

The rate law now will be

Rate= k[A]²[B]⁰ = k[A]²

b.  For the magnitude of rate constant:

c.  Using the rate law in a:

Rate =k[A]² = (4.0 x 10^-3 M^-1 s^-1)(0.050 M)² = 1.0 x 10^-5 M/s

Exponents in the Rate Law

The exponent m and n in the rate law is called reaction orders.  Reaction orders can be first order,  second order with respect to reactants. It depends on the exponent of the reactants.  First order when the exponent is raised to 1 and second order if raised to 2. In the example above, reactant A is  second order and the overall reaction order is also second order overall.  The overall reaction order is the sum of the reaction orders with respect to each reactant in the rate law.


Units of Rate Constants

The units of rate constant is dependent on the overall reaction order of the rate law.  Third order overall will have different unit with that of second order overall.  In the above sample problem, the units of rate constant is M^-1 s^-1, that is for second order overall rate law.  For the third order overall will have the unit as shown below:

TRY THIS:

The following data were measured for the reaction of nitric oxide with hydrogen:

2NO(g)  +  2H₂(g)  →  N₂(g)  +  2H₂O(g)

a) Determine the rate law for this reaction.
b) Calculate the rate constant.
c) Calculate the rate when the [NO] = 0.050 M, [H₂]= 0.150 M