Chemical Kinetics: Rate Laws and Reaction Orders

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Chemical Kinetics

Introduction to Rate Laws

Chemical kinetics is the study of reaction rates and the factors that affect them. The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. Understanding rate laws allows chemists to determine reaction mechanisms and predict how changes in conditions affect reaction speed.

Rate Law: An equation that relates the reaction rate to the concentrations of reactants, typically in the form .
Order of Reaction: The sum of the exponents in the rate law, indicating how the rate depends on reactant concentrations.
Rate Constant (k): A proportionality constant specific to a reaction at a given temperature.

Determining Rate Laws from Experimental Data

Methodology

To determine the rate law, initial rates are measured for different reactant concentrations. By comparing experiments where only one reactant concentration changes, the order with respect to each reactant can be deduced.

Keep all but one reactant concentration constant and observe how the rate changes.
Use the ratio method to solve for the order of each reactant.
Once the rate law is established, calculate the rate constant using any set of data.

Worked Examples

Example 1: BF3 + NH3 → F·BNH3

Experimental data for the reaction:

Experiment	[BF3] (M)	[NH3] (M)	Initial Rate (M/s)
1	0.250	0.250	0.2130
2	0.250	0.125	0.1065
3	0.200	0.100	0.0682
4	0.350	0.100	0.1193
5	0.175	0.100	0.0596

Rate Law: By comparing experiments, the rate law is determined to be .
Overall Order: The reaction is second order (1 + 1 = 2).
Rate Constant: Using any data set, .
Example Calculation: For [BF3] = 0.100 M and [NH3] = 0.500 M, .

Example 2: S2O82− + 3 I− → 2 SO42− + I3−

Experimental data:

Experiment	[S2O82−] (M)	[I−] (M)	Initial Rate (M/s)
1	0.018	0.036	2.6 × 10−5
2	0.027	0.036	3.9 × 10−5
3	0.036	0.054	7.8 × 10−5
4	0.018	0.072	1.4 × 10−4

Rate Law: (determined by comparing experiments).
Units of k: For overall third order, units are .
Example Calculation: For [S2O82−] = 0.025 M and [I−] = 0.050 M, .

Example 3: 2 NO(g) + O2(g) → 2 NO2(g)

Experimental data:

Experiment	[NO] (M)	[O2] (M)	Initial Rate (M/s)
1	0.0126	0.0125	1.41 × 10−2
2	0.0252	0.0125	5.64 × 10−2
3	0.0252	0.0250	1.13 × 10−1

Rate Law: .
Units of k: For overall third order, units are .
Example Calculation: For [NO] = 0.0750 M and [O2] = 0.0100 M, .

Example 4: 2 NO(g) + Br2(g) → 2 NOBr(g)

Experimental data:

Experiment	[NO] (M)	[Br2] (M)	Initial Rate (M/s)
1	0.10	0.20	24
2	0.25	0.20	150
3	0.10	0.50	60
4	0.35	0.50	735

Rate Law: .
Units of k: For overall third order, units are .
Example Calculation: For [NO] = 0.075 M and [Br2] = 0.25 M, .

Key Concepts and Definitions

Initial Rate: The rate of reaction measured at the very beginning, before significant changes in concentration occur.
Order with Respect to a Reactant: The exponent of a reactant's concentration in the rate law, determined experimentally.
Overall Order: The sum of the orders with respect to each reactant.
Units of Rate Constant: Depend on the overall order of the reaction. For a reaction of order n, units are .

Summary Table: Rate Law Determination Steps

Step	Description
1	Collect initial rate data for various reactant concentrations.
2	Compare experiments where only one reactant concentration changes.
3	Calculate the order with respect to each reactant.
4	Write the rate law using determined orders.
5	Calculate the rate constant using the rate law and any data set.

Applications

Predicting how changes in concentration affect reaction rate.
Determining reaction mechanisms.
Calculating rates for given concentrations.

Additional info: The above examples and tables are based on standard methods for determining rate laws in general chemistry. Calculations for rate constants and rates require substituting values into the determined rate law equations.