Kinetics: The Reaction of I^- with H₂O₂ Using Pseudo-Order Methods (Version 1)

This experiment was developed by Profs LH Berka and NK Kildahl, WPI, based on a commercially available experiment.

1 lab period; work in pairs. Complete the Preparation before laboratory.

• To explore the kinetics of a slow redox reaction
• To determine the rate law
• To explore the effect of a catalyst on the reaction rate

Kinetics and Thermodynamics. The distinction between kinetics and thermodynamics is an important one. Kinetics is the study of the rate at which (and the path by which) a chemical reaction occurs. Thermodynamics deals with the extent to which the reaction occurs. There is no necessary connection between the rate, measured by a rate constant k (see below), and the extent, measured by an equilibrium constant K_eq. Thus, a reaction in which 99.9% of the reactant molecules are eventually consumed may take years to reach that stage. Conversely, it may take just milliseconds for 0.1% of a reactant to be converted to products, but with no further reaction over an extended period of time. The former is an example of a slow reaction (small k) that occurs essentially to completion (large K_eq); the latter is a fast reaction of limited extent.

The Differential Rate Law. For the general reaction (1), the rate is expressed as the change of concentration with respect to time, t, of any reactant or product.

Since A is consumed and F is produced by (1), their derivatives have opposite signs. Thus we introduce a minus sign in front of d[A]/dt to ensure a positive rate. Also, unless a = f, -d[A]/dt and d[F]/dt are different. In general, the rate of reaction is a function of the concentrations of reactants and products, as indicated in (3).

k is the rate constant of the reaction, and [A], [B], etc., are the molar concentrations of reactants and products in (1). The exponents m,n... appearing in (3) are usually either positive or negative integers or zero.

Because (3) is a differential equation, it is called the differential rate law for (1). The goal of a kinetics study is to determine the differential rate law for the reaction (i.e., the values of the exponents m, n, s, and v) and the numerical value of the rate constant k at each of several temperatures. Suppose that appropriate kinetics experiments carried out on (1) give m = l, n = 2, s = 0, and v = -1. The differential rate law for the reaction is then

The exponents m, n, etc. are called orders. We say that the reaction is first order in A, second order in B, and inverse first order in F. It is important to realize that there is no necessary connection between the reaction orders m, n, s, and v, in (3) and the stoichiometric coefficients a, b, d, f, in (l).

The Integrated Rate Law. The most straightforward way to determine experimentally the specific form of the rate law (3) is to measure the quantity d[A]/dt as a function of each of the concentrations [A], [B], etc, and from the data deduce the reaction orders. For example, if we found that d[A]/dt quadrupled when we doubled the initial [A] while keeping the other concentrations constant, we would conclude that m = 2. In principle this approach is fine. Unfortunately, it is seldom possible to measure the quantity d[A]/dt directly. Instead what one measures is [A] at each of several times during the reaction. It is thus desirable to show directly the dependence of [A] on time. In simple cases, this can be accomplished by integration of (3). The result is called an Integrated Rate Law. For example, suppose that for a particular reaction (1), the rate law takes the very simple form in (4). This is a simple first order rate law.

We rearrange the equation to separate the time variable and the concentration variable.

We integrate from the initial conditions (the beginning of reaction) (t = 0 and [A] = [A]₀) to the conditions at some time t during the course of reaction (t = t and [A] = [A]_t)

The result is (5). This is the integrated first order rate law.

It expresses [A] as a function of time, as we wanted. If we plot the experimental [A]-t data according to this equation and obtain a straight line, we can conclude that the reaction is first order in A without ever dealing with the quantity d[A]/dt! Further, the value of the rate constant k can be obtained directly from the slope of such a linear plot (slope = -k).

For the simple second order rate law in (6),

The integrated rate law is

In this case, a plot of l/[A] versus t should be linear, with slope k.

Pseudo-Order Conditions. In the experimental determination of rate laws, it is common practice to arrange experimental conditions such that the concentration of only one of the species involved changes with time as the reaction proceeds, while the concentrations of all other species remain fixed at some pre-determined set of initial values. In this way a multi-variable differential equation such as (3) is greatly simplified. For example, if we make [B]₀, [D]₀, and [F]₀ much greater than [A]₀, then only [A] will change significantly as (1) proceeds. We say that the reaction is run under pseudo-order conditions in A. The term k[B]_oⁿ[D]_o^s[F]_o^v in equation (3) can be treated as a constant and the rate expression takes the simplified form -1/a d[A]/dt = k'[A]^m. This may be integrated to give equation (5) when m = 1, or (7) when m = 2. k', although like a rate constant, still depends on concentration, and is thus sometimes called a pseudo rate constant. The order with respect to A can be more readily determined than if the concentrations of all the species changed simultaneously. From the manner in which k' varies with [B]₀, [D]₀, and [F]₀, the entire rate law can often be deduced.

This Experiment. We will study the rate at which hydrogen peroxide, H₂O₂, reacts with iodide ion, I- , and hydrogen ion, H⁺, to give triodide ion, I₃^-, and water in aqueous solution. The equation for the reaction is (8).

By running (8) several times under pseudo-order conditions in H₂O₂ at room temperature, each time using a different [I-]₀ and/or [H⁺]₀, the rate law can be determined.

How do we keep [I^-] and [H⁺] constant and monitor [H₂O₂]? Thiosulfate, S₂O₃^2-, reacts quantitatively with I₃^- according to (9).

If we have S₂O₃^2- present in the solution while (8) is proceeding, the I₃^- produced by (8) will be converted back to I^- by (9). As long as (9) occurs very rapidly relative to (8), [I^-] will not change until the S₂O₃^2- gone. How do we signal that S₂O₃^2-is gone? I₃^-forms a blue complex with starch. So we put a little starch in the solution, too. As soon as S₂O₃^2-is used up, I₃^-will accumulate and immediately produce a blue color with the starch. If we know how much S₂O₃^2- we put in, we can calculate the amount of H₂O₂ used up in the time it took for the blue color to appear, because the combined stoichiometries of (8) and (9) tell us that 1 mole H₂O₂ is equivalent to 2 moles S₂O₃^2-.

A sketch of our procedure follows.

1. Begin a run at t = 0 with known [I^-]₀, [H⁺]₀, [S₂O₃^2-]₀, and [H₂O₂ ]₀ such that [S₂O₃^2-]₀ << [H₂O₂]₀. The subscript "0" means initial concentration. The run begins when the final reagent, H₂O₂, is added.
2. Note the time, t_l, at which the blue flash appears. At this point,
   • S₂O₃^2- is used up
   • An amount of H₂O₂ = n₀(S₂O₃^2-)/2 has been used up in the time, t_l. Here n₀ = the moles of S₂O₃^2- initially present.

   Calculate [H₂O₂] in the solution at time t_l. As soon as the blue flash appears and the time is noted,

3. Quickly add another small, known amount of S₂O₃^2-.
4. Again note the time, t₂, at which blue appears.
   • From the amount of S₂O₃^2- added at time t₁, calculate [H₂O₂] in the solution at time t₂.
5. Continue 3 and 4 to obtain [H₂O₂] remaining at each of several times during reaction.

The above procedure requires calculation of concentrations in the reaction mixtures. Each reaction mixture will be prepared by mixing aliquots of stock solutions of I^- and S₂O₃^2- with buffer solution and water to give a total volume of 19.0 mL. Reaction is then initiated by adding 1.0 mL of H₂O₂ stock solution, to give a final total volume of 20.0 mL. If [A]_stock symbolizes the concentration of the stock solution of reagent A, V_A the volume of the aliquot of that stock solution used, and V_T the total volume of reaction mixture, the concentrations of reagents in the reaction mixture can be calculated using the following equations.

In these equations,

Nine 0.1-mL aliquots of S₂O₃^2- stock solution will be added to the reaction mixture as reaction proceeds, the total volume, V_T, in (10) and (11) will change from 20.0 to 20.9 mL. Therefore, [I-] will not be strictly constant during the run, and H₂O₂ will be diluted somewhat as reaction proceeds. To minimize the effect of dilution, we replace V_T with V_T,avg (the average volume during a run) in (10) and (11).

(10) and (11) are modified as follows:

Finally,

Focus Questions

1. For each kinetics run, construct a table giving
   • The value of [I-]₀ (see Background section for method of calculation).
   • Values of t (including t = 0, there should be 11 values for each run).
   • The value of [H₂O₂] for each t (see Background Section for method of calculation).
2. For each run, make appropriate plots to determine the order of reaction with respect to H₂O₂.
3. Extract observed pseudo-order rate constants from your plots.
4. Make an appropriate plot of these rate constants to determine the order of the reaction with respect to I^-.

• 6 small beakers (100 or 150 mL)
• 6 5-cm watch glasses
• graduated cylinders (5 and 25-mL)
• 4 50-mL Erlenmeyer flasks
• thermometer
• 3 2-mL graduated pipets
• 1 5-mL graduated pipet
• small syringe pipet pump
• large syringe pipet pump
• 100-microliter pipettor
• stopwatch (optional)
• 22.5 mL 0.200 M KI
• 30.0 mL buffer solution
• 5.0 mL 0.2% starch solution
• 7.5 mL standard Na₂S₂O₃ ( 0.2 M)
• 6.0 mL 0.4 M H₂O₂

Note to instructor: Click here for recipes for preparation of solutions.

Record all data in your notebook. Obtain a Labkit and additional required glassware, a stopwatch, and a 100-microliter autopipettor. Clean the glassware thoroughly using brushes and Alconox detergent (pipets cannot be cleaned this way, but can be rinsed). Remove all soap with tap water, then rinse with distilled water and dry thoroughly.

Preliminary Activities

1. Label clean dry beakers, one for each required solution: (I^-, buffer, starch solution, S₂O₃^2-, distilled water, H₂O₂, (Table 1)).
2. Obtain appropriate amounts of the solutions (Table 1) and cover the supply beakers.
3. Record the exact concentrations of the I^-, Na₂S₂O₃, and peroxide solutions.

Kinetics Runs

Four kinetic runs will be carried out using the volumes of stock solutions in Table 1. The procedure for carrying out Run 1 will be outlined in detail. The others are carried out in a similar manner.

Run 1:

1. To a clean, dry 50-mL Erlenmeyer flask, add the quantities of reagents 1-5 indicated under run 1 in Table 1, and mix.
2. With a graduated pipet, add 1.0-mL of H₂O₂ stock solution to the flask, swirl, and simultaneously begin timing.
3. At the blue flash
   • record the elapsed time to the nearest second (t = t_l). NOTE: Do not stop the timer, which should run continuously throughout the experiment. You should note the total time elapsed as each successive blue flash appears. (If using a stopwatch, you can use the lap time button to mark time elapsed at the blue flash. This button will not affect the continuously running total elapsed time.)
   • add exactly 0.10 mL of S₂O₃^2- solution using the pipettor, and swirl the flask.

     NOTE: At t₁ you are adding the second increment of S₂O₃^2- while recording the time required for the first increment to react.

4. Continue as in 3). At each blue flash,
   • Record the total elapsed time to that point;
   • Add a 0.1 mL increment of S₂O₃^2-, until you have added a total of 1.00 mL of S₂O₃^2- (including the 0.1 mL present initially)
5. Record the temperature.
6. IMMEDIATELY discard the reaction solution down the drain and rinse the reaction flask with tap water. If you allow the solution to remain in the flask, a lot of I₂ will form, making the flask difficult to clean.

Carry out Runs 2-4 in similar fashion.

If time allows, design a procedure to determine the order in H⁺.

If time allows, design a procedure to determine the temperature dependence of the rate.

Clean-up. When you have finished all of your work:

• Dispose of left over solutions and reaction mixtures as indicated below.
• Clean Pasteur pipets, graduated pipets, vials, and other glassware by recommended procedures, shake off excess water, and place in the drying oven.
• Clean and return all borrowed equipment to the instructor before leaving lab.
• Clean up your work area before leaving lab.

Disposal Methods

Discard left-over solutions in the sink; flush down the drain with water.