Purpose

To determine the rate law and activation energy of a iodine clock reaction.

Expected Learning Outcomes

After completing this experiment, it is expected that students will be able to

• Determine the rate law and rate constant of a reaction.
• Determine the activation of a reaction in the presence and absence of a catalyst.

Textbook Reference

This experiment illustrates large parts of Chapter 14 in Tro, Chemistry: Structures and Properties, 2nd Ed.

Theoretical Background: Overview of Kinetics

In this experiment, we will study the effect of

• concentration
• temperature
• presence of a catalyst

on the rate of the iodine clock reaction

[latex]\ce{S2O}_8^{2-}(aq) + 2\ce{I-} (aq) \to 2\ce{SO}_4^{2-} (aq) + \ce{I2}(aq)[/latex]

Rate of Reaction

The rate of a reaction is related to the change in concentration (in terms of molarity) of reactant/product present per unit time. That is to say, for the reaction

[latex]\ce{A} \to \ce{B}[/latex]

the rate of reaction is given by

[latex]\displaystyle \mbox{rate} (\textrm{M}/\textrm{s}) = -\frac{\Delta [\ce{A}]}{\Delta t} = + \frac{\Delta [\ce{B}]}{\Delta t}[/latex]

Note that when you are dealing with the change in concentration of a reactant, a negative sign is placed in front. This ensures that the rate of reaction is always positive.  Also, in order to ensure that the rate of reaction has the same numerical value regardless of the reactant/product being studied, the rate of change of concentration of a species is divided by its coefficient in the expression for the rate of a reaction

Rate Laws

The concentration dependence of the reaction rate of a given reaction is summarized by its rate law.  Typically, a rate law takes the form

\begin{equation}
\mbox{rate} = k[\ce{A}]^m[\ce{B}]^n \cdots
\end{equation}

where

• k, the rate constant, is a function of the temperature of the reaction mixture.
• [latex][\ce{A}], [\ce{B}],\cdots[/latex] refer to the molarities of reactants or catalysts.^[1]
• [latex]m,n,\cdots[/latex] are the rate orders with respect to each species. The rate orders will either be integers or simple fractions (positive or negative).^[2]

Rate laws cannot be found just by reading the balanced chemical equation. The only way to find rate laws is by conducting experiments, for which there are several methods. In this experiment, you will use the method of initial rates to determine the rate law for the iodine clock reaction.

The Effect of Temperature on Reaction Rates

In accordance with collision theory, there are two reasons why reactions occur at a faster rate at higher temperatures:

• Molecules move at a faster speed, and therefore there would be more collisions per unit time
• A greater proportion of molecules have sufficient energy to react when they collide

In reality, the second effect is the more important one. From this (or empirically), it can be shown that As a result, the temperature dependence of the rate constant can be given by the Arrhenius equation:

\begin{equation}
k = A \exp\left(-\frac{E_a}{RT}\right)
\end{equation}

where A is the frequency factor, [latex]E_a[/latex] is the activation energy (in J/mol) (the minimum amount of energy required for a collision to lead to reaction), [latex]R = 8.314 \textrm{J}/\textrm{mol}\cdot \textrm{K}[/latex] is the ideal gas constant and T is the temperature in Kelvins.  Activation energies are typically between 20-250 kJ/mol.

Based on the above, there are two forms of the Arrhenius equation that are more useful for calculations.

Straight-Line Form of the Arrhenius equation

It can be shown that

\begin{equation}
\underbrace{\ln k}_{y} = \underbrace{-\frac{E_a}{R}}_{m} \times \underbrace{\frac{1}{T}}_{x} + \underbrace{\ln A}_{b}
\end{equation}

Therefore, by plotting [latex]\ln k[/latex] along the y-axis and [latex]\displaystyle \frac{1}{T}[/latex] (with temperature in Kelvins) along the x-axis, one will yield a straight line plot – the Arrhenius plot:

By comparing the Arrhenius equation above with the equation of a straight line, we can show that

\begin{equation}
E_a = -(\mbox{slope})
\end{equation}

Two-Point Form of the Arrhenius Equation

If you only have the rate constant at two different temperatures [latex]T_1[/latex] and [latex]T_2[/latex], at which the rate constants are [latex]k_1[/latex] and [latex]k_2[/latex] respectively, we can show that

\begin{equation}
\ln \left(\frac{k_1}{k_2}\right) = \frac{E_a}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right) \label{407:Arrhenius_twopoint}
\end{equation}

with which you can solve for the activation energy of the reaction.

Catalysts

Catalysts are used to speed up a reaction by providing an alternative reaction mechanism with a lower activation energy for the reaction to occur. As the activation energy decreases, the proportion of molecules with sufficient energy to react would increase, thus increasing the rate of reaction.

The Iodine Clock Reaction

In this experiment, you will study the iodine clock reaction between [latex]\ce{S2O}_8^{2-}[/latex] and iodide ions.

\begin{equation}
\ce{S2O}_8^{2-}(aq) + 2\ce{I-} (aq) \to 2\ce{SO}_4^{2-} (aq) + \ce{I2}(aq)
\end{equation}

In the presence of thiosulfate ions ([latex]\ce{S2O}_3^{2-}[/latex]), the iodine produced in this reaction is converted back to iodide.

\begin{equation}
\ce{I2}(aq) + 2\ce{S2O}_3^{2-}(aq) \to 2\ce{I-}(aq) + \ce{S4O}_6^{2-}(aq)
\end{equation}

As this reaction occurs much faster than the main iodine clock reaction, as long as thiosulfate ions are present any iodine produced in the reaction is immediately consumed, and no free iodine is found.

In our experimental design, the number of moles of [latex]\ce{S2O}_3^{2-}[/latex] is very small compared to the original reactants. When all of the [latex]\ce{S2O}_3^{2-}[/latex] is used up, the iodine produced in the overall iodine clock reaction will no longer occur.  Therefore, the I₂ will no longer be converted back to I^–.  The starch solution in the reaction mixture would turn a dark purple, as shown in the following video from Imagination Station Toledo:

The time interval between the time of mixing and the instant when the purple starch color is observed is the time required for all of the [latex]\ce{S2O}_3^{2-}[/latex] to be used up.  From this, we can find the average rate of reaction while [latex]\ce{S2O}_3^{2-}[/latex] was present – which we approximate as the initial rate of the reaction.

For this reaction, copper(II) ions can be used as a catalyst^[3] In the last part of this reaction, we will study the effect of the catalyst on the activation energy for the catalyzed reaction.

To summarize, we will determine experimentally

• The rate law (and rate constant) at room temperature in the absence of a catalyst.
• The activation energy for this reaction with, and without, the presence of a catalyst.

Procedures

Before proceeding, please read the directions on using micropipettors.

Effect of Concentration on Reaction Rates

In this part, you will perform the reaction at different concentrations at room temperature.  So that you can time this experiment accurately, the reactants are separated into two different mixtures: Tube A and Tube B. The contents in each tube is listed in the following table.^[4]

All reagents, except starch solutions, should be measured using micropipettors. Starch solutions can be dispensed using disposable transfer pipettes.  In our calculations, we will neglect the volume of the starch solution as it is so small compared to everything else.

You will now determine how concentrations of reactants affect the rate of reaction in the absence of a catalyst, with which you will determine the rate law for this reaction.

1. Determine how you will measure the time interval.  For brevity, this is assumed to be a stopclock.^[5]
2. Mix together the volumes of all reagents for Tube A for Run 1 as listed above into a 4″ test tube.
3. Mix together the volumes of all reagents for Tube B for Run 1 as listed above into a 4″ test tube.
4. Pour the contents of one test tube into the other, and mix the solution well. Start a stopclock at the instant of mixing. When the purple color of the iodine in starch solution begins to appear, stop the stopclock and record the time required for the reaction to occur. At the same time, measure and record the temperature of the reaction mixture.
5. Repeat steps 2-4 being sure to use clean test tubes each time.  You may need to wash test tubes between trials.
6. Repeat steps 2-5 two more times, using the amounts listed for Runs 2 and 3 respectively.

Temperature Effects on Reaction Rates

For this part of the reaction, you will study the reaction rate of this reaction using the contents of Run 3, but at different temperatures.

7. Mix together all of the contents for Run 3 in Tube A as listed above in a 4″ test tube.  Place this test tube in a water bath.
8. Mix together all of the contents for Run 3 in Tube B as listed above in a 4″ test tube. Place this test tube in the same water bath as for Tube A.
9. Heat up the water bath with the test tubes prepared in it to about 45°C.
10. Pour the contents of one test tube into the other, and mix the solution well. Start the stopclock at the instant of mixing. When the purple color of the iodine in starch solution begins to appear, stop the stopclock and record the time required for the reaction to occur. At the same time, measure and record the temperature of the reaction mixture.
11. Repeat steps 7-10, except heat the reactants (in the water bath) up to 65°C instead.
12. There will be a supply of Tube A and Tube B contents (for Run 3) that have been kept in ice on the instructor’s bench. Obtain 3.00 mL of Tube A and place into one test tube, and 2.00 mL of Tube B into the other test tube. Repeat step 10 using these tubes.

Effect of a Catalyst on Reaction Rates and Activation Energies

13. Repeat steps 2-5, using the amounts of solutions listed in Run 3, except add one drop of the Cu²⁺ solution provided into Tube A before everything is mixed together.
14. Repeat step 12 using the amounts of solutions listed in Run 3, except add one drop of the Cu²⁺ solution provided into Tube A before everything is mixed together.

Waste Disposal

All chemicals (except unused starch solution) in this experiment must be disposed of in the designated waste beaker.

Data Analysis

Determining the Rate of Reaction and Concentrations in the Reacting Mixture

Remember that we’re studying the iodine clock reaction.  Based on our understanding of how stoichiometry relates to the definition of reaction rates, the rate of this reaction is given by

\begin{equation}
\mbox{rate} = \frac{\Delta [\ce{I2}]}{\Delta t} \label{407:rate_def_application}
\end{equation}

In this experiment, the time interval [latex]\Delta t[/latex] is the time elapsed between the time of mixing for the reagents and the appearance of iodine (purple color).  In this time, all of the [latex]\ce{S2O}_3^{2-}[/latex] would be consumed. Therefore, from the stoichiometry of the reaction between [latex]\ce{S2O}_3^{2-}[/latex] and I₂,

\begin{equation}
\Delta [\ce{I2}] = \frac{1}{2} [\ce{S2O}_3^{2-}]_{\mbox{init}} \label{407:I2_and_S2O3}
\end{equation}

and therefore the rate of the iodine clock reaction is

\begin{equation}
\mbox{rate} = \frac{1}{2} \cdot \frac{[\ce{S2O}_3^{2-}]_{\mbox{init}}}{\Delta t}
\end{equation}

The initial concentration of [latex]\ce{S2O}_3^{2-}[/latex] can be calculated by performing a dilution calculation using the equation

\begin{equation}
M_1 V_1 = M_2 V_2 \label{407:dilution}
\end{equation}

where the final volume is the total volume of everything in the reaction mixture. We can typically neglect the volumes of the starch and Cu²⁺ solutions that was added as these are small compared to the overall volume in the tube.

For each reacting mixture, the initial concentrations for each of the reactants (I^– and [latex]\ce{S2O}_8^{2-}[/latex]) can be calculated using the dilution equation as well.

Determining the Rate Law and Rate Constant

Based on the results from the three room temperature trials, you should be able to figure out using the method of initial rates the rate law of this reaction in the absence of a catalyst.  The rate law will be of the form

\begin{equation}
\mbox{rate} = k[\ce{I-}]^m [\ce{S2O}_8^{2-}]^n \label{407:ratelaw_iodineclock}
\end{equation}

where $m$ and $n$ are the rate orders with respect to [latex][\ce{I-}][/latex] and [latex][\ce{S2O}_8^{2-}][/latex] respectively.  You will need to figure out m and n to determine the rate law.

Use the data for each trial to obtain the rate constant for each trial.  The rate constant should be concentration-independent.

Determining the Activation Energy with No Catalyst

Given the reaction data at different temperatures, you should be able to determine the rate constant at different temperatures using the rate law you determined in the previous part. For room temperature, you should take the average of the rate constants for both trials of Run 3, using the average temperature for the two runs for Run 3 (taken from the concentration-rate part of the experiment).^[6]

We can make an Arrhenius plot using this data with [latex]\ln k[/latex] along the y-axis plotted against [latex]1/T[/latex] (with temperature in Kelvins) along the x-axis. From this plot, one can obtain the slope of the plot, which can be used to solve for the activation energy as described above.

Determining the Activation Energy with a Catalyst

Given that we do not know the rate law for this reaction now (since the rate law depends on the mechanism for the reaction, which would involve the catalyst), we cannot find the rate constant in each case. However, given that the concentration terms would cancel out if the same concentrations are used, we can rewrite the two-point form of the Arrhenius equation as

\begin{equation}
\ln \left(\frac{\mbox{rate}_2}{\mbox{rate}_1}\right) = -\frac{E_a}{R} \left(\frac{1}{T_2} – \frac{1}{T_1}\right) \label{407:two_point_Arrhenius_rate}
\end{equation}

By substituting the relevant data into this equation, the activation energy with a catalyst can be found from the two data points available.