Determination of a rate law lab report

CHM364

Experiment #1: CHEMICAL KINETICS

Methods of Initial Rates: The Iodine Clock

The homogenous reaction in aqueous solution

IO3- + 8I- + 6H+ + 3I3- + 3H2O (1)

like virtually all reactions involving more than two or three reactant molecules, takes place not in a single molecular step but in several steps. The detailed system of steps is called the reaction mechanism. It is one of the principal aims of chemical kinetics to obtain information to aid in the elucidation of reaction mechanisms, which are fundamental to our understanding of chemistry.

THEORY

The several steps in a reaction are usually consecutive and tend to proceed at different speeds. Usually, when the overall rate is slow enough to measure at all, it is because one of the steps tends to proceed so much more slowly than all the others that it effectively controls the over-all reaction rate and can be designated the rate controlling step. A steady state is quickly reached in which the concentrations of the reaction intermediates are controlled by the intrinsic speeds of the reaction steps by which they are formed and consumed. A study of the rate of the over-all reaction yields information of a certain kind regarding the nature of the rate-controlling step and closely associated steps. Usually, however, rate studies supply only part of the information needed to formulate uniquely and completely the correct reaction mechanism.

When the mechanism is such that the steady state is quickly attained, the rate law for Eq. (1) can be written in the form:

(2)

where parenthesized quantities are concentrations. In the general case, the brackets might also contain concentrations of additional substances, referred to as catalysts, whose presence influences the reaction rate but which are not produced or consumed in the over-all reaction. The determination of the rate law requires that the rate be determined at a sufficiently large number of different combinations of the concentrations of the various species present to enable an expression to be formulated which accounts for the observations and gives good promise of predicting the rate reliably over the concentration ranges of interest. The rate law can be written to correspond in form to that predicted by a theory based on a particular type of mechanism, but basically it is an empirical expression.

The most frequently encountered type of rate law is of the form [again using the reaction of Eq. (1) as an example]

(3)

where the exponents m, n, p,… are determined by the experiment. Each exponent in Eq. (3) is the order of the reaction with respect to the corresponding species; thus, the reaction is said to be the m th order with respect to IO3-, etc. The algebraic sum of the exponents m + n + p in this example, is the over-all order (or, commonly, simply the order) of the reaction. Reaction orders are usually, but not always, positive integers within experimental error.

The order of a reaction is determined by the reaction mechanism. It is related to, and is often, equal to, and is often (but not always) the number of reactant molecules in the rate-controlling step—the “molecularity” of the reaction. Consider the following proposed mechanism for the hypothetical reaction 3A + 2B = products:

a. A + 2B = 2C (fast, to equilibrium, Ka)

b. A + C = Products (slow, rate controlling,, Kb)

The rate law predicted by this mechanism is

The over-all reaction involves five reactant molecules, but it is by no means necessarily of fifth order. Indeed, the rate-controlling step in this proposed mechanism is bimolecular, and the over-all reaction order is predicted by the mechanism is 5/2. It is also important to note that this mechanism is not the only one that would predict the above 5/2-order rate law for the given over-all reactions; thus experimental verification of the predicted rate law would by no means constitute proof of the validity of the above proposed mechanism.

It occasionally, happens that the observed exponents deviate from integers or simple rational fractions by more than experimental error. A possible explanation is that two or more simultaneous mechanisms are in competition, in which case the observed order should lie between the extremes predicted by the individual mechanism. A possible alternative explanation is that no single reaction step is effectively rate-controlling.

We now turn our attention to the experimental problem of determining the exponents in the rate law. Except in first- and second-order reactions it usually inconvenient to determine the exponents merely by determining the time behavior of a reacting system in which many or all reactant concentrations are allowed to change simultaneously and comparing the observed behavior with integrated rate expressions. A procedure is desirable which permits the dependencies of the rate on the concentrations of the different reactants to be isolated from one another and determined one at a time. In one such procedure, all the species but the one to be studied are present at such high initial concentrations relative to that of the reactant studied that their concentrations may be assumed to remain approximately constant during the reaction; the apparent reaction order with respect to the species of interest is then obtained by comparing the progress of the reaction with that predicted by rate laws for first order, second order, and so on. This procedure would often have the disadvantage of placing the system outside the concentration range of interest and thus possibly complicating the reaction mechanism.

In another procedure (this experiment), which we shall call the method of initial rates, the reaction is run for a time small in comparison to the “half-life” of the reaction but large in comparison to the time required to attain a steady state, so that the actual value of the initial rate [the initial value of the derivative on the left side of Eq. 3] can be estimated approximately. Enough different combinations of initial concentrations of several reactants are employed to enable exponents to be determined separately. For example, the exponent m is determined from two experiments which differ only in the IO3- concentration.

In the present experiment the rate law for the reaction shown in Eq. (1) will be studied by the initial rate method, at 25 0C, and at a pH of about 5. The initial concentrations of iodate ion, iodide ion, and hydrogen ion will be varied independently in separate experiments, and the time required for the consumption of a definite small amount of the iodate will be measured.

PROCEDURE/METHOD

The time required for a definite small amount of iodate to be consumed will here be measured by determining the time required for the iodine produced by the reaction (as I3-)to oxidize a definite amount of a reducing agent, arsenious acid, added at the beginning of the experiment. Under the conditions of the experiment arsenious acid does not react directly with the iodate at a significant rate but reacts with iodine as quickly as it is formed. When the arsenious acid has been completely consumed, free iodine is liberated which produces a blue color with a small amount of soluble starch which is present. Since the blue color appears rather suddenly after a reproducible period of time, this series of reactions is commonly known as the “iodine clock reaction.”

The reaction involving arsenious acid may be written, at a pH of about 5,

H3AsO3 + I3- + H2O HAsO4 + 3I- + 4H+ (4)

The over-all reaction, up to the time the starch end point, can be written, from equations (1) and (4),

IO3- + 3H3AsO3 I- + 3HAsO4 + 6H+ (5)

Since with ordinary concentrations of the other reactants hydrogen ions are evidently produced in quantities large in comparison to those corresponding to pH 5, it is evident that buffers must be used to maintain constant hydrogen-ion concentration. As is apparent from the method used, the rate law will be determined under conditions of essentially zero concentration of I3-; the dependence of the rate on triiodide, which is fact has been shown to be very small,[footnoteRef:1] will not be measured. Under these conditions, Eq. (3) is an appropriate expression for the rate. [1: Dushman et al. ]

A constant initial concentration of H3AsO3 is used in a series of reacting mixtures having varying concentrations of IO3-, I- and H+. Since the amount of arsenious acid is the same in each run, the amount of iodate consumed up to the color change is constant, and related to the amount of arsenious acid by the stoichiometry of Eq. (5). The initial reaction rate in mole liter-1 sec-1 is thus approximately the amount consumed (per liter) divided by the time required for the blue end point to appear. From the initial rates of two reactions in which the initial concentration of only one reactant is varied and all the other concentrations kept the same, it is possible to infer the exponent in the rate expression associated with the reactant which is varied. This is most conveniently done by taking logarithms of both sides of Eq. (3) and subtracting the expressions for the two runs.

EXPERIMENTAL PROCEDURE

Solutions . Two acetate buffers, with hydrogen-ion concentrations differing by a factor of 2, will be prepared. Use will be made of the fact that at a given ionic strength the hydrogen-ion concentration is proportional to the ratio of acetic acid concentration to an acetate ion concentration:

(6)

Where at 25 0C, k = 1.753 x 10-6 mole liter-1. The experiments will all be carried out at about the same ionic strength (0.16 +/- 0.01), and accordingly the activity coefficient is approximately the same in all experiments, by the Debye-Hückel theory. It will also be seen that within wide limits the amount of buffer solution employed in a given total volume is inconsequential, provided the ionic strength of the resultant solution is always kept about the same. (Note success of this experiment is closely tied to the accuracy with which the required reagent quantities are calculated, measured or weighed). Use appropriately sized graduated cylinders for larger volumes and pipettes for for smaller volumes (See Table 1). The solutions required are as follows:

Starch solution: 1.0 %. Heat to a boil 100 mL of water. In another beaker, place 1.0 g of starch and add a small amount of hot water to it, begin by mixing the two until a paste forms. Then add the rest of the hot water, which will dissolve the remaining starch. The solution should appear thick with a blue tint.

Buffer A : Prepared from100 mL of 0.75 M NaAc (sodium acetate) solution, 100 mL of 0.22 M HAc (acetic acid) solution, and about 20 mL of 1.0% soluble starch solution into a 500 mL volumetric flask. Make up to the 500 mL mark with distilled water. This should afford a H+ ion concentration of about 1 × 10-5 M.

Buffer B : Prepared from 50 mL of 0.75 M NaAc (sodium acetate) solution, 100 mL of 0.22 M HAc (acetic acid) solution, and about 10 mL of 1.0% soluble starch solution into a 250 mL volumetric flask. Make up to the 500 mL mark with distilled water. This should afford a H+ ion concentration of about 2 × 10-5 M.

H3AsO3: 0.03 M . Should be made up from NaAsO2 and brought to a pH of about 5 by the addition of HAc (acetic acid).

3NaAsO2 + 3HAc + 3H2O 3H3AsO3 + 3NaAc (7)

KIO3: 0.1 M

KI: 0.2 M

Suggested sets of initial volumes of the four reactant solutions, based on a final total volume of 100 mL, are given in the table below.

Table 1: Initial volumes of reactant solutions in mL and suitable pipette sizes

Solution

Pipette

sizes

Initial volumes of reactant solutions in mL

I

II

III

IV

H3AsO3

5

5

5

5

5

IO3-

5

5

10

5

5

Buffer A

20 , 25

65

60

40

0

Buffer B

20, 25

0

0

0

65

I-

25

25

25

50

25

Two or three runs should be made on each of the four sets. The instructor may modify that requirement in the interest of time. Inquire as to whether any modifications are in effect. Two or more runs should also be made on a set with proportions chosen by the student in which the initial compositions of two reacting species differ from those in set I. In each case, the amount of buffer required is that needed to obtain a final volume of 100 ml.

It is convenient to use each pipette only for a single solution, in so far as possible, to minimize time spent rinsing. The pipettes should be marked to avoid mistakes.

The buffer solutions and the iodide solution should be equilibrated to 25 °C by clamping flasks containing them in a thermostat bath set at the temperature.[footnoteRef:2] Two vessels of convenient size (ca. 250 mL) and shape (beakers or Erlenmeyer flasks); rinsed and drained essentially dry, should also be clamped in the bath. One of them (the reaction vessel) should have a white painted bottom surface (or have a piece of white cloth taped under the bottom) to aid in observing the blue end point unless other means are available to obtain a light (white contrasting) background. The easiest improvisation is to place the Erlenmeyer flask on strips of white paper towels. [2: For our purposes allowing the reaction vessels to sit on the bench top at room temperature is a sufficient approximation of 25 °C.]

To make a run, pipette all of the solutions except the KI solution into one of the vessels and the KI solution into another. Remove both vessels from the bath, and begin the reaction by pouring iodide rapidly but quantitatively into the other vessel containing the other reagents, simultaneously starting the stopwatch. Pour the solution back and forth once or twice to complete the mixing, and place the vessel containing the final solution back into the bath.2 Stop the watch at the appearance of the first faint but definite blue color.

Note that as a practical matter, most students find it most convenient to set up the four reactions simultaneously on a white background. The appropriate quantity of the KI solution is then added to the matching reaction vessel and the timing of the reaction to the endpoint (color change) is begun while the vessel is carefully swirled to ensure mixing.

CALCULATIONS

1. The student should construct a table giving the actual initial concentrations of the reactants IO3-, I-, and H+.

2. The H+ concentrations should be calculated from the actual concentrations of NaAc (sodium acetate) and HAc (acetic acid) in the stock solutions employed, with an activity coefficient calculated by use of the Debye-Hückel theory for the ionic strength (= 0.16) of the reacting mixtures.

3. Using the known initial concentrations of H3AsO3, calculate the initial rate for each run.

4. From appropriate combinations of sets I, II, III, and IV, calculate the exponents in the rate expression Eq. (3).

5. Calculate a value of the rate constant k from each run, and obtain an average value of k from all runs (if performed in duplicate or triplicate). Compared the experimentally determined value of k to the literature value of (1.753 x 10-6 mole liter-1).

6. Write the rate expression, with the numerical values of the rate constant k and the experimentally obtained values of the exponents. Beside it write the temperature (assume room temperature is 25 °C) and ionic strength at which this expression was obtained.

7. Write another rate expressions, in which those exponents which appear to be reasonably close (within experimental error) to integers are replaced by the integral values. Use this expression to calculate values for the initial rates of all sets studied and compare them with the observed initial rates.

DISCUSSION

The kinetics of this reaction have been the subject of much study, and the mechanism is not yet completely elucidated with certainty. following is an incomplete list of the mechanisms that have been proposed:

As part of the lab report, the student should discuss the above mechanisms in connections with his experimentally determined rate law.

MISCELLANEOUS

The oxidation of iodide by chlorate ion ClO3- has also been studied. Although the reaction appears to be attended by complications which make it difficult to study, under certain conditions it can be carried out as an “iodine clock” experiment. For the interested student, suggested concentration ranges for 20 to 25 °C are ClO3-, 0.05 to 0.01 M; I-, 0.025 to 0.10 M. A sulfate-bisulfate buffer may be used. The resulting rate law is not identical with that for the reaction with iodate, but appears to be compatible with mechanisms analogous to several of those given above.