Introduction

As chemists we are concerned about two things when studying reactions. That is the rate at which a reaction will proceed and to what extent the reaction will be product-favored. These two concerns can be addressed by studying chemical kinetics. Chemical kinetics is the study of the reaction rates and reaction mechanisms. In studying the chemical kinetics of a system we are interested in what the reaction rate means, how to determine the reaction rate experimentally, how temperature affects the reaction rate, how concentration affects the reaction rate and the detailed pathway taken by the atoms as the reaction proceeds forwards.

Thermodynamics and Kinetics

Before we study chemical kinetics further lets remind ourselves of the laws of thermodynamics. The laws of thermodynamics allow the prediction of the favored direction in a given reaction.  A common illustration is the equilibrium reaction between two different solid carbon structures.

C_{(s, diamond)}  <=> C_{(s, graphite)}    

Unfortunately, thermodynamics tells us that the above reaction is strongly favored to the right. Therefore, the diamond(s) in a ring, watch, etc., will eventually be converted to the thermodynamically more stable product, graphite. Why isn’t this prediction commonly observed?  Because, thermodynamics considers factors such as heat content, pressure, phase (solid, liquid, gas, plasma), entropy (disorder), and temperature, but not time or rate of the reaction (the chemical kinetics.) A reaction rate is the velocity with which reactants are used up and products produced.  This velocity is expressed as the change in concentration of reactant or product per unit time.  A reaction mechanism is the pathway by which reactants are converted to products. 

Measuring Rates Experimentally

The fundamental observation in reaction kinetics is of the reaction occurring in a given time interval.  Concentration data may then be used to calculate the rate of reaction for a given experiment according to the following equations.

or

In order to measure a reaction rate, there must be some method of determining the concentration of reactants or products at the beginning and at the end of a time period.  For most reactions, the rate decreases continuously with the progress of the reaction. This is due to decreasing concentrations of kinetically significant reactants.  For example, assume a reaction of the general type:

A + B <=> 2C       

The rate law would be expressed as follows:

Assuming the superscripts m and n are positive integers, the rate of the reaction will decrease as the number of moles of A and B diminish (thus their concentrations decrease) as they form C. Both m and n are determined experimentally and cannot be deduced from the overall stoichiometric reaction equation. The exponents m and n in the above equation are called reaction orders and their sum is the overall reaction order. For example, if m = n = 1, the reaction order in A is 1, the reaction order in B is 1; the reaction is first order in A and B; and the overall reaction order is 1 + 1 = 2 or second order. 

The Iodine Clock Reaction

In this experiment we will investigate the kinetics of the following reaction, known as the “iodine clock":

 and determine the value of the coefficients in the rate law:

rate = k[I^-1]^m[S₂O₈^-2]ⁿ

To determine the rate law we must first determine the rate of the reactions. The computation of the rate is complicated by the need to allow for continuous change in the rate. However, for the "clock reaction" it is possible to find concentrations of reactants such that the rate remains constant until one reactant, the limiting reagent, is entirely consumed. Under these conditions the calculation of the rate be­comes the following:

If the number of moles of limiting reagent put into the reaction solution at the start of the reaction is known, as well as the total volume of the reaction solution, the initial concentration can be calculated. The time (in seconds) required for the complete reaction (at constant rate), is then recorded in lab and the rate of the reaction can then be determined. Typically, reactions occur in more than one step. The slow step will essentially determine the rate. The "clock reaction" consists of a slow step and a fast step to determine the overall reaction:

The overall reaction will be observed in lab by using the reaction of iodine and starch. This reaction forms a blue complex as it progresses. The time at which the blue complex is formed is an indication that the reaction is complete. In setting up the "clock reaction", the thiosulfate ion (S₂O₃^2-) is the limiting reactant. Peroxydisulfate ion (S₂O₈^-2) is used in large excess so its concentration re­mains essentially constant throughout the reaction.

From the above reactions, it is reasonable to assume that as soon as iodine (I₂) is formed in the slow step it will be immediately reconverted to iodide (I^-1) ion in the fast step. Therefore, the concentration of iodide ion remains constant as long as any S₂O₃^2- is left. Since the concentrations of both reactants in the slow step will remain essentially constant, the rate of the slow step remains constant until the S₂O₃^2- is used up. In other words, the limiting reagent is used up, because the rate limiting step, the slow step, does not involve this ion.

Colorimetric Determination

When has the limiting reagent been consumed? Iodine is formed in the slow step, but is removed rapidly by the reaction with the limiting reagent S₂O₃^2-. When all of the S₂O₃^2- is used up, I₂ begins to accumulate. Since I₂ is yellow in aqueous solution, the appearance of a yellow color indicates I₂ because the other reactants and products are colorless. However, the iodine color is faint and difficult to observe. Sensitivity can be improved by using starch as an indicator. In the presence of a suitably prepared starch solution, I₂ forms a deep blue starch-tri-iodide complex. In effect, the starch indicator amplifies the color of the iodine. At exactly the time when all of the thiosulfate (S₂O₃^2-) has been consumed the solution will change from colorless to blue. We are measuring the rate of slow step reaction because the reaction shown in the fast step is too fast.

Determining the Rate Law

Once we have determined the rate of the reaction we want to determine the rate law for the reaction. A rate law of a reaction is a mathematical expression relating the rate of a reaction to the concentration of either reactants or products. The rate law may be theoretically determined from the rate determining step (slow step) of the reaction mechanism. Many chemical reactions actually require a number of steps in order to break bonds and form new ones. The rate law of a reaction must be proven experimentally by looking at either the appearance of products or the disappearance of reactants.

The following examples shows how the rate law can be determined for a reaction similar to that of the “Iodine Clock:”

Example Problem

Consider the following overall chemical reaction:

Here is an example of a rate law for the above reaction:

In this rate law, the rate of disappearance of NO and O₂ is proportional to the concentrations of NO and O₂, where k is a rate constant (a proportionality constant). The exponent associated with each concentration term is referred to as the partial order. The sum of the partial orders gives the overall order of the reaction. In the above rate law, the partial order for NO is 2 and is often referred to as 2nd order. The partial order for O₂ is 1 and is often referred to as 1st order. The overall order is 3 (3rd order). It is important to note that the coefficients found in the balanced equation are not necessarily related to the exponents found in the rate law.

Let's look at a set of experimental data from which the rate law may be deduced. In this case, we will consider examining the rate in terms of the disappearance of reactants. Experimentally one compiles the reaction rates relative to initial concentrations of reactants:

Where the rate is determined by:

where [reactant]_i is the initial concentration of the limiting reactant and Dt is the time it takes for the reaction to run to completion.

The rate law can be determined using two methods. The first method is by examining the experimental data. Pick two trials to compare in which the concentration of one reactant is doubled while the concentration of the other reactant is held constant. We will be determining the partial order for the reactant whose concentration has changed. By keeping the concentration of the other reactant constant, we insure that the rate will not be affected by that reactant.

Let's begin by choosing the results for Trial 1 and Trial 2. In these two trials the concentration of NO is held constant while the concentration of O₂ has been doubled. Also, note that doubling the concentration of O₂ also doubles the rate of the reaction. This may be mathematically expressed as:

For the equality to hold true, x must equal 1. This makes the partial order for O₂ first order.

The same procedure is used to determine the partial order of NO. Pick two trials in which the concentration of O₂ is held constant while the concentration of NO is varied. These criteria are met with Trial 1 and Trial 3.

The concentration of O₂ is held constant while the concentration of NO has tripled. Under these conditions, the rate of the reaction is increased nine fold. This may be expressed mathematically as:

For the equality to hold true, x must be 2. This makes the partial order for NO second order. We are now able to write the rate law: Rate = k[NO]²[O₂], where k is the rate constant. To solve for the rate constant, choose any experimental trial, and substitute for the rate, and concentrations of NO and O₂. Trial 1 data will be arbitrarily chosen in this case:

Thus the rate law becomes:  Rate = 1.2 x 10^-5 M^-2 s^-1[NO]²[O₂]

The rate law for the above reaction can also be determined graphically by expressing the rate law equation in a straight-line form WHICH IS WHAT YOU WILL BE DOING IN THIS EXPERIMENT:

By rearranging the rate equation and taking the log of each side and assuming one concentration is a constant:

Graphing the log of the rate (y-axis) versus the log of the [NO] (x-axis) should result in a straight-line graph with a slope equal to x, the reaction order for NO.  This same process can be done for both reactants, simply by holding the concentration of one reactant constant each time. 

Once the rate orders have been determined, the rate constant k can be determined by inputting the data for each run and solving for k.  If the data is good the k values should all be reasonably the same and the average k for all the runs can be reported.

Temperature Effects on Rate

In this experiment we will also be collecting data at several temperatures, this will allow us to calculate the reaction’s activation energy. The mathematical relationship between temperature and activation energy is a variation of the Arrhenius Equation:

Where A is a constant called the frequency factor and is related to the frequency of collisions and the probability that the collisions are favorably oriented, R is the universal gas constant, E_a is the activation energy, T is the temperature in Kelvin and k is the rate constant. The above version of the Arrhenius Equation is in the form of a straight line, thus a plot of ln(k) on the y-axis vs 1/T on the x-axis will give a straight line. The slope of the line will equal –E_a/R and the y-intercept equals ln A. Therefore we can use the Arrhenius Equation to determine the activation energy and frequency factor for the “Iodine Clock” Reaction.

The chemical kinetics of the “Iodine Clock” can be studied by simply measuring the rate of the reaction. Once the rate of the reaction is determined one can mathematically determine the rate constant for the reaction at the given conditions and the amount of energy it takes to activate the reaction.

Copy the following Table into your lab notebook for use during class: