Lab 11 - Chemical Kinetics

Purpose

To determine the rate law for the reaction

2 I⁻ + S₂O₈²⁻ → I₂ + 2 SO₄²⁻

Goals

1
To relate changes in reactant concentrations to changes in reaction rate.
2
To calculate a rate constant from experimental data.

Introduction

Chemical kinetics deals with the speed, or rate, of a reaction and the mechanism by which the reaction occurs. We can think of the rate as the number of events per unit time. The rate at which you drive (your speed) is the number of miles you drive in an hour (mi/hr). For a chemical reaction the rate is the number of moles that react in a second. In practice, we usually monitor how much the concentration (the number of moles in a liter) changes in a second. Reaction rates are usually expressed in units of moles per liter per second, or molarity per second (M/s).

Reaction Rates

The reaction to be studied in this experiment is a redox reaction between iodide ions and persulfate anions:

( 1 )

2 I⁻ + S₂O₈²⁻ → I₂ + 2 SO₄²⁻

Our definition of reaction rate is the change in concentration with time, but the concentration of which chemical species? The answer is, any of them. For example, we could measure the rate at which I₂ is formed. Then the rate would be:

( 2 )

Rate =

Δ[I₂]

Δt

This equation states that the rate is equal to the change in I₂ concentration divided by the change in time. The units are M/s. We could also measure the rate at which S₂O₈^2- is used up. Then the rate would be:

( 3 )

Rate = −

Δ[S₂O₈²⁻]

Δt

Note the negative sign in equation 3. Reaction rates are always given positive values, but the S₂O₈^2- concentration is decreasing as the reaction proceeds.

( 4 )

Δ[S₂O₈²⁻] = [S₂O₈²⁻]_final − [S₂O₈²⁻]_initial < 0

Hence, there is a negative sign to make the reaction rate positive. We could also measure the disappearance of I^-. In the chemical equation, two iodide ions react with each S₂O₈^2- ion. Therefore, I^- disappears twice as fast as S₂O₈^2-. The reaction rate based on disappearance of I^- would be expressed as:

( 5 )

Rate = −

Δ[I⁻ ]

2 Δt

The Chemical System Being Studied

The three reactions of importance in this experiment are:

( 6 )

2 I⁻ + S₂O₈²⁻ → I₂ + SO₄²⁻

( 7 )

I₂ + 2 S₂O₃²⁻ → 2 I⁻ + S₄O₆²⁻

( 8 )

I₂ + starch indicator → blue-black product

The purpose of the experiment is to measure the rate of Reaction 6. A product of this redox reaction between iodide ions and persulfate ions (S₂O₈^2-) is elemental iodine. Iodine, in the presence of thiosulfate ions (S₂O₃^2-) will reform iodide ions (Reaction 7). Iodine can also, in the presence of starch, form a blue-black product (Reaction 8). Reaction 7 is faster than Reaction 8, and occurs preferentially if S₂O₃^2- is present. However, if no S₂O₃^2- is present, or if it is used up, Reaction 8 occurs and the dark color of the indicator appears.

Method of Initial Rates

The change in concentration of a chemical species usually depends on the concentration of that species when the reaction begins. At the beginning of the reaction, its concentration is high, and a substantial amount of reactant will disappear in a second. Near the end of the reaction, its concentration is low, and a much smaller amount of reactant will disappear in a second. A standard way to compare reaction rates under different conditions is to measure the time it takes for the first small percentage of reaction to occur. This gives the initial rate. In this experiment, you will find the time it takes for the first small percentage of Reaction 6 to occur, but in an indirect way. The time it takes for Reaction 7 to occur will actually be measured. The experiment will be set up such that the amount of thiosulfate (S₂O₃^2-) is only about one percent of the amounts of iodide and persulfate (S₂O₈^2-) ions. During the first percent or so of Reaction 6, the elemental iodine produced is consumed by thiosulfate in Reaction 7. No iodine is left to react with the starch indicator. When the S₂O₃^2- is used up, Reaction 6 is still going (it still has about 99% to go!), but the iodine produced then begins to react with the starch, giving a color change. Thus, the color change indicates the total consumption of thiosulfate, S₂O₃^2-. Knowing the amount of thiosulfate that reacted and measuring the time that it takes to react gives Δ[S₂O₃^2- ]/Δt. This is related to the rate of Reaction 6 (what we want!) by the stoichiometry of the reactions,

( 9 )

Rate = −

Δ[S₂O₈²⁻]

Δt

= −

Δ[S₂O₃²⁻]

Δt

The one half in the formula arises from the 1:2 stoichiometry between S₂O₈^2- and S₂O₃^2- ions. The term Δ[S₂O₃^2- ] is negative (the concentration decreases as the reaction proceeds), but the negative sign in the formula again gives a positive value for the rate.

Rate Constants and Reaction Orders

A simple question about reaction rates is this: does the rate you measure depend on the amount of reactants you start with? It seems as if it should, but this is not always the case. The answer to the question depends on the mechanism of the reaction. A reaction mechanism is the series of steps that the reaction follows. The slowest step determines the measured reaction rate, and is called the rate-determining step. Look again at the reaction whose rate is to be measured:

( 10 )

2 I⁻ + S₂O₈²⁻ → I₂ + 2 SO₄²⁻

You might guess that this reaction occurs when two iodide and one persulfate ion collide together in solution. However, a collision between three species such that they meet in the correct orientations to react is very rare. Most likely, the reaction proceeds in simpler steps. Some reasonable mechanisms are these:

1
The rate-determining step has two iodide ions coming together. In this case, the rate depends only on the initial concentration of iodide.
2
The rate-determining step involves a persulfate ion decomposing. In this case, the rate depends only on the initial concentration of persulfate.
3
The rate-determining step has an iodide ion and a persulfate ion coming together. In this case, the rate depends on the concentrations of both ions.

All of the mechanisms are plausible. The only way to distinguish among them is by experiment. The concentration dependencies are summarized by the rate law. For our reaction, the rate law can be written:

( 11 )

Rate = k[I⁻ ]^x[S₂O₈²⁻]^y

Here, k is called the rate constant, which is unique to the reaction. (Do not confuse k, the rate constant, with K, the equilibrium constant!) The exponents x and y must be determined by experiment. We do this by measuring the reaction rate at different initial concentrations of iodide and persulfate. For example, if we double the initial [I^-] and the rate does not change, then x must be equal to zero, and the reaction is said to be zero order in iodide ions. If the rate doubles when [I^- ] is doubled, x must be one, and the reaction is first order in iodide ions. If the rate goes up by a factor of four when [I^- ] is doubled, x must be two, and the reaction is second order in iodide ions. Doing other experiments and varying [S₂O₈^2-] will then allow one to determine y, the reaction order for persulfate ion. Your CH 201 textbook gives an algebraic method for determining x and y, which is needed for more complicated reaction orders. Once the reaction order for each reactant is determined, we can substitute the values for reactant concentration, order, and rate (change in concentration per unit time) for a given run of the reaction into the rate law and solve for the rate constant, k. The units of k will vary with the overall reaction order, which is the sum of the individual exponents. Reaction order is an indication of the total number of species involved in the rate-determining step of the reaction mechanism. You will carry out five runs of the reaction to be studied, Reaction 6. These runs will enable you to determine the reaction order in each of the reactants, and calculate the rate constant. You will then determine the rate law for the reaction between iodide and persulfate ions.

Equipment

2
50 mL burets
2
50 mL graduated cylinders
4
100 mL beakers
4
50 mL beakers
1
magnetic stir plate
1
magnetic stir bar
1
10.00 mL volumetric pipet
1
pipet bulb
1
ring stand with buret clamp
1
deionized water squirt bottle

Reagents

~90 mL
0.200 M KI
~90 mL
0.100 M (NH₄)₂S₂O₈
~60 mL
0.0050 M Na₂S₂O₃
~30 mL
0.200 M KCl
~30 mL
0.100 M (NH₄)₂SO₄
~30 drops
3% starch solution

Safety

Ammonium persulfate, (NH₄)₂S₂O₈, is an oxidizing agent. Oxidizing agents can supply their own source of oxygen and may react violently with organic liquids or other reducing agents. The dilute persulfate solutions used in this experiment may be handled safely with other aqueous solutions. The chemicals used in this experiment are very dilute so gloves will not be available. Remember to wash your hands with soap and water when the experiment is completed.

Waste Disposal

All of the solutions can be disposed of down the sink drain followed by flushing with plenty of water.

Prior to Class

Please read the following sections of Lab Safety and Practices:

Please review the following videos under Instructional Videos:

Please complete WebAssign prelab assignment. Check your WebAssign Account for due dates. Students who do not complete the WebAssign prelab are required to bring and hand in the prelab worksheet.

Lab Procedure

Please print the worksheet for this lab. You will need this sheet to record your data.

Five different solutions with similar names are used in this experiment. Clearly label your glassware so you will not mix things up. For example,

50 mL buret for KI
100 mL beaker for obtaining KI
50 mL beaker for KI dispensed from buret
50 mL buret for (NH₄)₂S₂O₈
100 mL beaker for obtaining (NH₄)₂S₂O₈
50 mL beaker for (NH₄)₂S₂O₈ dispensed from buret
10.00 mL pipet for Na₂S₂O₃
graduated cylinder for KCl
graduated cylinder for (NH₄)₂SO₄
100 mL beaker in which to run the reaction

Although you are using burets and pipets to measure volumes, you will be dispensing the liquids into beakers, and pouring them from the beakers as you conduct the reactions. Some loss of liquid will occur in these transfers. Therefore, it is not necessary to read the buret to 0.01 mL as you would in a titration. Read to the nearest 0.1 mL (small gradation).

The following procedure of steps a through g applies for each run. Make sure the reaction beaker is rinsed and dried between each run.

a
Use your KI buret to measure the appropriate amount of 0.200 M KI into the labeled beaker.
b
Use your (NH₄)₂S₂O₈ buret to measure the appropriate amount of 0.100 M (NH₄)₂S₂O₈ into the labeled beaker.
c
Use a pipet to measure 10.00 mL of Na₂S₂O₃ into the reaction beaker. Add 3 or 4 drops of starch solution.
d
Use a graduated cylinder to add KCl or (NH₄)₂SO₄ solution to the reaction beaker if it is required for the run. These solutions are added to maintain a constant concentration of ions in all the runs.
e
Add the magnetic stir bar to the reaction beaker and mix the contents of the reaction beaker.
f
This step needs to be carefully coordinated. While the contents of the reaction beaker are being stirred, simultaneously add both the KI and (NH₄)₂S₂O₈ solutions to the reaction beaker. This is the initial time for the reaction.
g
Watch the reaction and note the time at which the blue-black color of the starch-iodine complex appears. Record the elapsed time in Data Table A.

Table A: Determination of Rate Law:

2 I⁻ + S₂O₈²⁻ → I₂ + 2SO₄²⁻

Question 1: What are the initial concentrations of iodide, persulfate, and thiosulfate in the first run? Account for dilution and show your work.

Question 2: What is Δ[S₂O₃^2- ] at the time of the color change in the first run?

Question 3: What is the rate of the reaction in the first run? Show your work.

Record the values from these calculations in Data Table B. Repeat the calculations for the other four runs.

Table B: Calculations for Determination of Rate Law

Question 4: Inspect the data in Data Table B. What is the order of the reaction with respect to iodide ions? Explain how you arrived at your answer.

Question 5: Inspect the data in Data Table B. What is the order of the reaction with respect to persulfate ions? Explain how you arrived at your answer.

Question 6: Write the rate law for this reaction, showing the proper exponents.

Question 7: Calculate the rate constant for the first run. Include units. Show your work, and record the result in Data Table B.

Calculate the rate constants for the other four runs and record the rate constants in Data Table B.

When you are finished, rinse all of your glassware with water, dry it and return it to the set-up area where you found it.

Before leaving, enter your results in the InLab assignment. If all results are scored as correct, log out. If not all results are correct, try to find the error or consult with your teaching assistant. When all results are correct, note them and log out of WebAssign. The InLab assignment must be completed by the end of the lab period. If additional time is required, please consult with your teaching assistant.