1.1 The rate of chemical reactions
1.2 The rate expression and order of reaction
1.3 Determining the rate equation
1.4 The rate determining step

1.1 Rate of chemical reactions
Learning objectives:
1. Explain what rate of reaction means.
2. Calculate the rate of a reaction using experimental results.

Rate of Reaction = Speed of the reaction

How do we measure speed of reaction?
• Definition – change in concentration (of either reactant or product) with unit time
• Unit – mol dm -3 s -1 , moles per dm 3 per second
• Usually follow the change in product at constant temperature.

Measuring Rate Experimentally
1. Measure concentration at regular time intervals.
2. Plot concentration over time on a graph.
3. Measure the gradients of the tangents to the line.
The gradient of the tangent line is the rate of the reaction.

1.2 The rate expression
Learning Objectives:
1. Write a rate expression.
2. Describe the order of a reaction.
3. Calculate the units for the rate constant.

Rate expression
• Tells us how the concentrations of each substance in the chemical equation contributes to the rate .
• What might affect the rate of a reaction?
• Each reaction will have a different rate equation depending on the particular reaction and the conditions.

The rate expression and rate constant
Example:
Rate = k[A][B] 2
Rate constant = varies depending on the temperature

The order of reaction
• Definition – describes how much a species contributes to the overall rate
• Example: Rate = k[A][B] 2
The rate is first order with respect to [A], doubling A doubles the rate .
The rate is second order with respect to [B], doubling B quadruples the rate.
The overall order of the reaction is the sum of the orders for all species .
The overall order is three .

Units of the rate constant
• The units for the rate constant are unfortunately NOT constant.
• They need to be calculated using the rate expression.

1.3 Determining the rate equation
Learning Objective:
1. Determine the order of the rate equation by experiment.
a. using rate/concentration graphs.
b. using the initial rate method.

Using a Rate-Concentration Graph
• Start with a concentration-time graph.
• Draw tangents to the curve at various intervals to determine the rate at particular concentrations.
• Plot a graph of rate-concentration.
• The shape of the graph will tell you the order of the reaction.
• This only works with respect to one particular species, not the overall order of the reaction.

Initial Rate Method
• For this method a series of experiments is done with varying starting concentrations .
• The initial rate is measured for each experiment.
• A pair of experiments is compared to see what effect changing the concentration of one species has on the rate.
• ie: if I double concentration of A, does the rate 1) stay the same (zero order), 2) also doubles (first order), or 3) quadruples (second order)

Practice Time!
• For the following data determine:
1. Order with respect to [NO]
2. Order with respect to [O
2
]
3. Rate equation
4. Overall order of the reaction

3
4
5
Experiment
Number
1
2
Initial [NO]
1.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
Initial [O
2
]
1.0 x 10 -3
1.0 x 10 -3
1.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
Initial rate
7 x 10 -4
28 x 10 -4
63 x 10 -4
56 x 10 -4
189 x 10 -4

3
4
5
Experiment
Number
1
2
Initial [NO]
1.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
Initial [O
2
]
1.0 x 10 -3
1.0 x 10 -3
1.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
Initial rate
7 x 10 -4
28 x 10 -4
63 x 10 -4
56 x 10 -4
189 x 10 -4

3
4
5
Experiment
Number
1
2
Initial [NO]
1.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
Initial [O
2
]
1.0 x 10 -3
1.0 x 10 -3
1.0 x 10 -3
2.0 x 10 -3
3.0 x 10 -3
Initial rate
7 x 10 -4
28 x 10 -4
63 x 10 -4
56 x 10 -4
189 x 10 -4

• When we doubled the [NO], the rate increased x4 .
• The rate is second order with respect to [NO].
• When we doubled the [O
2
], the rate also doubled .
• The rate is first order with respect to [O
2
].
• The rate expression is: rate = k[NO] 2 [O
2
]
• The overall rate is third order .

Calculating the rate constant
• To find out the rate constant, simply plug in values from any of the experiments and solve for k.
• Try it now. Don’t forget units!
• k = 7 x 10 5 mol -2 dm 6 s -1
• Remember that the k value is only valid for a specific temperature.

The effect of temperature on k
• Small changes in temperature produce large changes in reaction rates.
• General rule of thumb:
10 K rise = doubles k
• Example: 2HI  I
2
+ H
2
Temperature (K)
633
666
697
715
781 k/mol -1 dm 3 s -1
0.0178 x 10 -3
0.107 x 10 -3
0.501 x 10 -3
1.05 x 10 -3
15.1 x 10 -3

Why?

1.4 The rate determining step
Learning Objectives:
1. Describe what is the rate determining step of a reaction.
2. Describe the connection between the rate equation and the reaction mechanism.

The rate determining step
• Most reactions take place in multiple steps.
• We represent these reactions by an overall chemical equation.
• One step must follow another because the products of one step are the reactants of the next.
• The slowest step is the rate determining step as it causes a
“bottleneck”.

The rate equation can be used to find the rate determining step
• Example: Nucleophilic Substitution of C
4
H
9
Br with OH -
• Overall equation: C
4
H
9
Br + OH  C
4
H
9
OH + Br -
• Is this a one step mechanism? Or two steps (forms carbocation as an intermediate)?
Step 1: C
4
H
9
Br  C
4
H
9
+ + Br -
Step 2: C
4
H
9
+ + OH  C
4
H
9
OH

• Three isomers of C
4
H
9
Br.
• 1-bromobutane reacts with rate equation rate = k[C
4
H
9
Br][OH ]
• Which mechanism does this suggest?
• 2-bromo-2-methylpropane reacts with rate equation
Rate = k[C
4
H
9
Br]
• Which mechanism does this suggest?
In the two step mechanism, which is the rate determining step?