Rate Laws
Rate Laws
• Rate law – an equation that describes the
effect of concentration on a reaction
– used to calculate rate given concentration
• rate laws are defined for specific temperatures
and pressures
– why?
– changes in temperature and pressure cause
changes in reaction rate so they must be held
constant for the rate law to hold true
• Consider the following reaction.
• Why would it be important to determine a
rate law from the initial conditions rather than
later in the reaction?
Determining a Rate Law Equation
• Consider the reaction AB
• k = rate constant
• every unique reaction has its own rate constant
• [A] = concentration of reactant A
• x = reaction order
– defines the degree to which a reaction is affected
by concentration of the reactant
Example: rate = k[H2O2]
• x=1
– reaction is first order in H2O2
– Reaction rate changes in direct proportion to the
concentration of H2O2
– ie 2 x [H2O2] = 2 x rate
– halving concentration halves the rate, etc
Reaction Order
• In general the overall order of a reaction is
the sum of the orders for individual reactants
• Consider the reaction
• Aproducts
– rate = k[A]2
– overall 2nd order
– 2nd order in A
Reaction Order
• Consider the reaction
• A + B products
– rate = k[A][B]
– overall 2nd order
– 1st order in A and 1st order in B
Reaction Order
• Consider the reaction
• A + B products
– rate = k[A]3[B]2[C]
• What is the overall order?
• What is the order of the individual reactants?
– overall 6th order
– 3rd order in A
– 2nd order in B
– 1st order in C
Effect of Reaction Order
• A specific example would be:
• rate = k[NO]2[H2]
• If [NO] doubles rate quadruples
– 22 = 4
• If [H2] doubles rate doubles
Effect of Reaction Order
• Below is a table summarizing the effect of
reaction order on rate of reaction
Determining Reaction Order
• Reaction order must be determined
experimentally!
• This is done using the method of initial rates
• method of initial rates – performed by
comparing the initial rates of reactions when
concentrations of reactants are varied
Example
• consider the reaction A + B  products
• hold one reactant constant and observe the
effect of concentration change on the other
reactant
Example
• consider the reaction A + B  products
• When [B] is constant and [A] doubles the rate
doubles therefore the reaction is 1st order in A
• rate = k[A][B]y
Example
• consider the reaction A + B  products
• When [A] is constant and [B] doubles the rate
quadruples therefore the reaction is 2nd order in
B (22 = 4)
• rate = k[A][B]2
Example
• consider the reaction A + B  products
• rate = k[A][B]2
• overall reaction is 3rd order
Zero Order
• Sometimes a reactant’s concentration has not
effect on reaction rate:
• rate = k[A]0[B]2
• rate = k(1)[B]2
• rate = k[B]2 is the rate law
• In these cases that reactant does not appear
in the rate law equation
Determining the Rate Constant
• After experimentally determining the rate law
the rate constant can be determined by
substituting the experimental data into the
rate law
Determining the Rate Constant
Determining the Rate Constant
• Therefore the overall rate law is:
• rate = 2[A][B]2
• Note: the units for k depend on the units used
in the calculation
Example:
• For the reaction:
• the following data was obtained:
• Find the rate law and rate constant for this
reaction