The Rate Law
Objectives:
• To understand what a rate law is
• To determine the overall reaction order from
a rate law
CLE 3224.3.3
Initial Reaction Rate
One way of studying the effect of concentration
on reaction rate is to determine the way in
which the rate at the beginning of the
reaction(the initial rate) depends on the starting
concentrations.
Consider the following reaction:
NH4+ (aq) + NO2-(aq) N2(g) + 2H2O(l)
We might study the rate of this reaction by
measuring the concentration of NH4+ or NO2as a function of time or by measuring the
volume of N2 collected. Because the
stoichiometric coefficients on NH4+ , NO2- , and
N2 are the same, all of the rates will be equal.
NH4+ (aq) + NO2-(aq) N2(g) + 2H2O(l)
The data indicates that changing either [NH4+] or [NO2−] changes the reaction rate. Notice that if
we double [NH4+] while holding [NO2−] constant, the rate doubles( look at experiments 1 and 2).
If [NH4+] is increased by a factor of 4 with [NO2−] left unchanged(look at experiments 1 and 3),
the rate changes by a factor of 4.
When [NO2−] is varied while [NH4+] is held constant,
the rate is affected in the same manner. The
reaction rate is directly proportional to the
concentration of both [NO2−] and[NH4+]. We
express the way the rate depends on the
concentration of these reactants as
Rate = k [NO2−] [NH4+]
An equation such as this which shows how the rate
depends on the concentrations of the reactants is
called a rate law.
General Form of the Rate Law
For a general reaction,
aA + bB  cC + dD
The rate law generally has the form
Rate = k[A]m[B]n
The constant k in the rate law is called the rate
constant. The exponents m and n are typically
small whole numbers.
Calculating k
If we know the rate law for a reaction and its
rate for a set of concentrations, we can calculate
the value of k, the rate constant.
NH4+ (aq) + NO2-(aq) N2(g) + 2H2O(l)
If we know the rate law for a reaction and its rate for a set of concentrations,
we can calculate the rate law.
Rate = k [NO2−] [NH4+]
We can use any of the data from the six experiments to calculate k.
Study Check
Use the data from any of the six experiments to
calculate k for this reaction:
NH4+ (aq) + NO2-(aq) N2(g) + 2H2O(l)
Rate law =k [NO2−] [NH4+]
Other Facts About k, the Specific Rate
Constant
• The value of k does not change for different
concentrations of reactants or products
• The value of k is for the reaction at a specific
temperature ; if we increase the temperature
of the reaction, the value of k increases.
• The value of k becomes larger if a catalyst is
present
Study Check
1. What is a rate law?
2. What is the name of k in any rate law?
Reaction Orders: The Exponents in the
Rate Law
The rate laws for most reactions have the
general form
Rate = k[reactant 1]m[reactant 2]n
The exponents m and n in a rate law are called
reaction orders.
Determination of Overall Reaction
Order
Consider the following rate law:
Rate = k [NO2−] [NH4+]
Because the exponent of [NH4+] is 1, the rate is first
order in NH4+. The rate is also first order in
NO2− . (The exponent 1 is not shown in rate laws)
The overall reaction order is the sum of the orders
with respect to each reactant in the rate law. This
rate law has an overall reaction order of 1+ 1=2,
and the reaction is second order overall.
The exponents in a rate law indicate how the
rate is affected by the concentration of each
reactant. Because the rate at which NH4+ reacts
with NO2− depends on [NH4+ ] raised to the first
power, the rate doubles when [NH4+ ] doubles,
triples when [NH4+ ] triples, and so forth.
If a rate law is second order with respect to a
reactant( i.e.[A]2), then doubling the
concentration of [A] causes the reaction rate to
quadruple(22=4 ) and tripling the concentration
causes the reaction rate to increase by 9
times(32= 9).
Zero Order
If the concentration of a reactant has no effect
on the reaction rate, the reaction is zero order in
that reactant. Anything raised to the zero power
is one, so changing the concentration of a
reactant that has a zero order will not affect the
rate.
Additional Rate Laws
2N2O5(g) -- 4NO2(g) +O2(g) rate = k[N2O5]
H2(g) + I2(g)  2HI(g) rate = k[H2][I2 ]
Note that although the exponents in a rate law
are sometimes the same as the coefficients in
the balanced equation, this is not necessarily
the case. The values of these exponents must
be determined experimentally.
Study Check
For the following reaction,
2NO(g) + 2H2(g)  N2(g) + 2H2O(g)
the rate law is
Rate = k[NO]2[H2]
Determine:
1. The order of each reactant in the rate law
2. The overall reaction order