# Determining of the Rate Law of a Reaction

In Chemical Kinetics, one of the first steps is to determine the order of the reaction. There are several methods used to determine the order of a reaction, but we will focus on the Isolation method.

### Isolation method

If there is more than one type of reactant involved in a reaction, all the concentrations of the reactants can be kept constant except for one reactant. You can then measure the rate of the reaction as a function of its concentration. Any change in the rate is due to the reactant whose concentration was not constant. After determining the rate of this reaction, you can isolate another reactant and determine its rate. This method is called the Isolation Method because you are isolating one reactant’s concentration to calculate the overall rate of the reaction. The Isolation Method is used to determine first, second, and zero order reactions.

The rate law,  of a reaction is an equation that expresses the rate of the reaction in the form of concentrations. We can use the following general formula to determine the rate law of a reaction.

The rate constant, k, is a coefficient that is independent of the concentration of the reactant but depends on temperature. The units for the rate constant are always given in a form where you can express the rate of the reaction as a change in concentration over time.

One of the main components of air pollution is nitrogen dioxide. The combination of nitrogen and oxygen heated in combustion engines is the source for polluted air. Nitrogen monoxide rapidly forms nitrogen dioxide in the presence of oxygen.

2 NO (g) + O2 (g) ? 2 NO2 (g)

Using this formula, you can determine that the rate law of the nitrogen dioxide is

The reaction rates are second order for nitrogen monoxide, first order for oxygen, and third order overall.

In reactions using gases, we can use the same approach for determining the rate law. The rate constant for the reaction would have units expressed in cm-3 molecule-1 s-1. We can also use the same approach for determining the units for the rate constant.

### Pseudo-first-order reactions

If one of the reactants of a second-order reaction is in excess, the concentration of the other reactant would be negligible compared to the reactant with a lower concentration. For example, in the reaction.

the rate law is Y is in excess. Because the concentration of Y is high, it is negligible because it remains fairly constant. The rate law is then <nob[X] </nobr>. The reaction would then appear to follow first-order kinetics and is called a pseudo-first-order reaction and k’ is called the effective rate constant. Pseudo-second-order reactions are easier to interpret than the complete rate law.

### Method of Initial Rates

The method of initial rates is commonly used with the isolation method to measure the rate at the beginning of a reaction for several different initial concentrations of reactants. For example, suppose that you have a reaction that the rate law for this reaction. The initial concentrations for X are known and the initial rate of the reaction, , is measured, you can solve for k. By taking the logarithm of the entire equation, we get:

Plotting the logarithms of the initial rates against the logarithms of the initial concentrations gives us straight lines with slopes that are equal to the order of the reaction.

Example 2

The following data was obtained on the initial rate of binding nitrogen monoxide and chloride:

<nobr>[NO]0</nobr>/(mmol L-1)     1.00 2.00 4.00 8.00
<nobr>0</nobr>/(mol L-1 s-1)   (a) 4.0 6.5 14.6 22.4
(b) 8.0 13.0 26.0 33.5
(c) 16.0 29.0 69.5 98.0

The concentrations of Cl2 are (a) 1.0mmol L-1 (b) 2.5 mmol L-1 (c) 5.0 mmol L-1. The initial rate law has the form <nobr>0=k[NO]0x</nobr>, with <nobr>  k’  =  k  [Cl2]0y </nobr>. The equation we would be using is: <nobr>log0=log  k’  +xlog[NO]0 </nobr>.

The data give the following points on the graph

<nobr>log[NO]0</nobr>/(mol L-1)   -3.00 -2.70 -2.40 -2.10
<nobr>log0</nobr>/(mol L-1 s-1) (a) 0.602 0.813 1.16 1.35
(b) 0.903 1.11 1.41 1.53
(c) 1.20 1.46 1.84 1.99

### References

• Atkins, Peter and Julio de Paula. Physical Chemistry for the Life Sciences. 2006. New York, NY: W.H. Freeman and Company. p. 244-5, 247-9.
• Atkins, Peter and Julio de Paula. Physical Chemistry. 2002. 7th ed. New York, NY: W.H. Freeman and Company. p. 869.
• Chang, Raymond. Physical Chemistry for the Biosciences. 2005. Sausalito, Ca: University Science Books. p. 312-3, 324.
• Kotz, John C., Paul M. Treichel, Jr., and Patrick A. Harman. Chemistry & Chemical Reactivity. 5th ed. 2003. United States of America: Thomson Learning, Inc. p. 611, 907.

### Contributors

• Stacy Huynh

17:17, 24 Mar 2014

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