“K”
Chemistry
(part 1 of 3)
Chapter 13:
Reaction Rates and Kinetics
Reaction Rates
• The rate of a chemical reaction is a measure of
how fast the reaction occurs
• A slow reaction will have a small fraction of
molecules reacting and forming products
• A fast reaction will have a large fraction of
molecules reaction and forming products
• As the reactants react and form the products,
the concentrations of each change as a
function of time
Rate Calculations
• For a balanced chemical reaction:
aA + bB  cC + dD
Practice
• Consider the following balanced chemical equation:
H2O2(aq) + 3 I-(aq) + 2 H+(aq)  I3-(aq) + 2 H2O(l)
• In the first 10.0 seconds of the reaction , the
concentration of I- dropped from 1.000 M to 0.868 M.
(a) Calculate the average rate of this reaction in this time
interval
(b) Predict the rate of change in the concentration of H+
(Δ[H+] / Δ t) during this time interval
Practice
• Using the above reaction, predict the rate of
change in concentration of hydrogen peroxide
and the I3-1 during the same time interval
Rate Laws
• The rate of a reaction depends on the concentration of
one or more of the reactants
• For example (a simple decomposition reaction):
A  Products
• As long as the reverse reaction is negligibly slow (or
non existent), we can write a relationship (a rate law)
Rate = k [A]n
Rate Laws
Rate = k [A]n
• k is the proportionality constant called the
rate constant
• n is a number called the reaction order
– IT IS NOT NUMBER OF MOLES OR THE
STOICHIOMETRY COEFFICIENT!!!
– It MUST be determined experimentally!!
Reaction Order, n
• If n = 0, the reaction is zero order and the rate is
independent of the concentration of A
– By mathematical definition, [A]0 = 1 so the rate law
(Rate = k [A]0) is equal to k regardless of the
concentration of A
• If n = 1, the reaction is first order and the rate is
directly proportional to the concentration of A
• If n = 2, the reaction is second order and the rate
is proportional to the square of the
concentration of A
Zero-Order Reaction
Rate = k [A]0 = k
• For a zero order reaction,
the concentration of the
reactant decreases
linearly with time
• The rate is constant
because it does not slow
down as the [A]
decreases
First-Order Reaction
Rate = k [A]1
• For a first order, the rate
is directly proportional to
the concentration of the
reactant
• Consequently, the rate
slows as the
concentration of the
reactant decreases
Second-Order Reaction
Rate = k [A]2
• For a second order
reaction, the rate of the
reaction is proportional to
the square of the
concentration of the
reactant
• Consequently, the rate is
even more sensitive to the
reaction concentration
Quick Tip
• The “order of the reactant” refers to only the
reactant of focus
A  Products
Rate = k [A]n
• This reaction is nth order with respect to “reactant A”
• A “reaction order” is the sum of all the exponents
Determining the Order of the Reaction
• The order of the reaction can only be
determined by experiment
• Uses a method called the method of initial
rates
– The rate for a short period of time at the
beginning of the reaction is measured using
different initial reactant concentrations to
determine the effect of [A] has on the rate
Method of Initial Rates
[A] (M)
Initial Rate (M/s)
0.10
0.015
0.20
0.030
0.40
0.060
• Notice for this data:
– When the concentration of A doubles, the rate is
directly proportional… the rxn is therefore first
order with respect to “reactant A”
The Value of the Rate Constant, k
• The rate constant, k, can be calculated using this
experimentally determined data after the
determination of the orders (the exponents)
Rate = k [A]1
k = rate/[A] = (0.015 M*s-1) / (0.10M) = 0.15s-1
• NOTICE THAT: the rate constant for a first-order
reaction is s-1
Data for Zero-Order
[A] (M)
Initial Rate (M/s)
0.10
0.015
0.20
0.015
0.40
0.015
• Notice for this data:
– The initial rate is independent for the reactant
concentration – the rate is the same at all
measured initial concentrations
Data for Second-Order
[A] (M)
Initial Rate (M/s)
0.10
0.015
0.20
0.060
0.40
0.240
• Notice for this data:
– The initial rate quadruples for a doubling of a
reactant concentration. The relationship between
concentration and rate is quadratic.
KEY THINGS!!
• The rate constants for zero- and second-order
reactions have different units than first-order
NOTICE THAT:
– the rate constant for a zero-order reaction is M*s-1
– the rate constant for a first-order reaction is s-1
– the rate constant for a second-order reaction is M-1*s-1
Reaction Order for Multiple Reactants
(not a simple decomp.)
aA + bB  cC + dD
• Again, as long as the reverse is negligibly slow (or
non-existent), the rate law can be defined as:
Rate = k [A]m[B]n
• m is the reaction order with respect to A
• n is the reaction order WRT B
• The overall order is the sum of the exponents (m+n)
Example
• The reaction between hydrogen gas and
iodine has been experimentally determined to
be first order WRT both reactants… and thus
second order OVERALL
H2(g) + I2(g)  2HI(g)
Rate =k[H2]1[I2]1
• The exponents ARE NOT THE COEFFICIENTS!!
Example
• The reaction between hydrogen and nitrogen
monoxide has been experimentally determined to
be first order WRT hydrogen and second order WRT
to nitrogen monoxide
2H2(g) + 2NO(g)  N2(g) + 2H2O(g)
Rate = k[H2]1[NO]2
**Notice the exponents are the ‘experimentally
determined’ orders… NOT THE COEFFICIENTS!!
Practice Calculating Orders
Consider the following reaction between NO2 and CO:
NO2(g) + CO(g)  NO(g) + CO2(g)
The initial rate of the reaction was measured at several different
concentrations if the reactants with the following results:
[NO2] (M)
[CO] (M)
Initial Rate (M/s)
0.10
0.10
0.0021
0.20
0.10
0.0082
0.20
0.20
0.0083
0.40
0.10
0.033
• Calculate the rate law for the reaction AND the rate
constant (k)
[NO2] (M)
[CO] (M)
Initial Rate (M/s)
0.10
0.10
0.0021
0.20
0.10
0.0082
0.20
0.20
0.0083
0.40
0.10
0.033
• Look for anything held constant!!
– If you compare the rates while one reactant is held
constant than you can assume the reaction rate is
CAUSED by the reactant that is changing!!
• The [NO2] doubled while the rate quadrupled
– Implies this rxn is second order WRT to NO2
• The [CO] (while the [NO2] is constant) doubles
while the rate is unchanged… implying zero order
[NO2] (M)
[CO] (M)
Initial Rate (M/s)
0.10
0.10
0.0021
0.20
0.10
0.0082
0.20
0.20
0.0083
0.40
0.10
0.033
Rate = k[NO2]2[CO]0 = k[NO2]2
• Now, calculate the k –
plug in any two corresponding data points
= 0.21 M-1*s-1
**Notice the UNITS!!
Practice #2
• Consider the following reaction:
CHCl3(g) + Cl2(g)  CCl4(g) + HCl(g)
[CHCl3] (M)
[Cl2] (M)
Initial Rate (M/s)
0.010
0.010
0.0035
0.020
0.010
0.0069
0.020
0.020
0.0127
0.040
0.040
0.027
Calculate the rate law for the reaction AND the rate
constant (k)
Half Life (t1/2)
• Read through
pages 584-587
and work out the
half life problems
– In a nutshell, the
half life is the time
it takes for half of
a sample to
disappear (break
down /
decompose)
RATE LAW SUMMARY
• Effects of Temperature –
• Effects of Pressure (for gases) –
• Activation Energy –
• Catalysis –
– Enzymes –
• Collision Theory –
• Rate Determining Step –
End of Chapter 13 
• WORK THROUGH THE PRACTICE PROBLEMS!!!