6.2 The Rate Law: Reactant Concentration and Rate
In general, the rate of a reaction increases when the concentrations of reactants increase. This
relationship can be expressed in a general equation
Rate Law Equation
For any reaction, the rate law equation expresses the relationship between the concentrations of the
reactants and the rate of reaction
K = a proportionality called the rate constant (there is a different rate constant for each reaction at any given
temperature)
m and n must be determined by experiment (they do not necessarily correspond to stiochiometric
coefficients. Usually 1 or 2 but 0 and 3 or fractions can occur)
Rate order
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


The values of the exponents in the rate law equation establish the order
If a given reactant is found to have the exponent of 1 the reaction is called a First order
If the exponent of a reactant is 2 the reaction is a Second order
The sum of the exponents (m + n) is the overall reaction order.

Ex
would be a third order
The Rate Constant (k)



Indicates the speed of reaction
Small rate constants would be slow reactions, large numbers would be fast
As a reaction proceeds, the reaction rate decreases because concentrations of reactants will be
decreasing.
For a given reaction under constant conditions the value of k remains constant
If the temperature changes so does k because rates of reaction depends on temperature. Chemists
studying reaction rates must work at constant temperature
Defining First-Order Reactions

Have an overall order of 1
2N2O5(g) → 4NO2(g) 5O2(g)
Ex
Experiments have shown this to be a first order reaction. And the rate Law equation would look like
Rate k[N2O5]1
Reactions with more than one reactant can also be first order
Ex (CH3)3CBr(aq) H2O(_) → (CH3)3OH(aq) Haq) Br(aq)
Experiments have shown that (CH3)3CBr is 1st order and water is 0th order and the reaction rate does not
depend on the concentration of water.
Rate law equation
Rate k[(CH3)3CBr]1[H2O]0
2nd order Reactions
 Have an overall order of 2
 Ex 2HI(g) → H2(g) I2(g) Scientists have determined this is second order
 The rate would be Rate k[HI]2


NO(g) O3(g) → NO2(g) O2(g)
Rate k[NO]1[O3]1
Summary
 Values of exponents in a rate law equation are determined experimentally
 Chemists determine values of m and n by carrying out a series ofexperiments by varying
concentrations of reactants
 All other factors (temp remain the same)
To determine m chemists perform different reactions with different initial concentrations of
reactants
Determining m
Determining rate constant k
a.
Determine the order
b. The rate law equation
c. Determine the rate law exponents (m and n)
d. Determine the Rate constant (k)