4: Chemical Kinetics - The Iodine Clock Reaction (Experiment)

Pre-lab Questions

1. Why do you rinse the burets and graduated cylinder with the solution you will be using prior to filling each apparatus?
2. What factors affect the rate constant? Why and how do these factors affect the rate constant?

Introduction

Rate law for the oxidation of iodide ion by peroxodisulfate ion: method of initial rates.

Chemical reactions do not occur instantaneously. An appreciation for the time-dependent (kinetics) nature of a chemical reaction will be gained by studying the initial rates of oxidation of iodide ion (\( \ce{I-} \)) by peroxodisulfate ion (\( \ce{S2O8^{2-}} \)).

\[ \ce{3I^{-}_{(aq)} + S2O8^{2-}_{(aq)} -> I3^{-}_{(aq)} + 2SO4^{2-}_{(aq)}} \]

The effects of concentration, temperature, and a catalyst on the reaction rate will be addressed. We must have a way to follow the reaction. In the past, indicators such as phenolphthalein have been used; here, a starch complex will be used. This is not a redox or pH indicator, but the color changes in response to the presence of iodine. Aqueous starch suspensions turn blue in the presence of a small quantity of tri-iodide ion (\( \ce{I3^{-}} \)), allowing for convenient means of detecting one of the reaction products. The reaction is carried out in the presence of thiosulfate ion (\( \ce{S2O3^{2-}} \)) to measure the time necessary for a fixed quantity of \( \ce{I3^{-}} \) to be formed. The thiosulfate ion reacts rapidly with tri-iodide ion according to Reaction \(\PageIndex{2}\).

\[ \ce{I3^{-}_{(aq)} + 2S2O3^{2-}_{(aq)} -> 3I^{-}_{(aq)} + S4O6^{2-}_{(aq)}} \]

Consequently, no blue color is formed with the indicator until all of the thiosulfates are used up and an appreciable concentration of tri-iodide ion builds up in the solution. When the thiosulfate has completely reacted, the solution suddenly turns blue due to the formation of the \( \ce{I3^{-}} \) starch complex.

The initial amounts suggested for the reaction are 20.0 mL of 0.20 M \( \ce{KI} \), 20.0 mL of 0.10M \( \ce{(NH4)2S2O8} \), 10.0 mL of 0.0050 M \( \ce{Na2S2O3} \), and 5 drops of starch indicator (see Table \(\PageIndex{1}\) for a list of the volumes to be used). This provides 4.0 mmol of \( \ce{I-} \), 2.0 mmol of \( \ce{S2O8^{2-}} \), and only 0.05 mmol of \( \ce{S2O3^{2-}} \). The \( \ce{I-} \) and the \( \ce{S2O8^{2-}} \), thus, are present in large excess, and the concentration does not change appreciably during the time interval of the measured reaction. For studies at lower concentrations, we shall dilute a smaller volume of \( \ce{KI} \) solution with 0.20 M \( \ce{KCl} \), or a smaller volume of \( \ce{(NH4)2S2O8} \) solution with 0.10 M \( \ce{(NH4)2SO4} \), to restore the total volumes to 20.0 mL each. In this way, we can vary only one concentration at a time and study the effect of this on the rate. We make the dilutions with these similar-type of salt solutions instead of with water to keep the total ionic strength of the mixtures approximately constant; otherwise, the rate would be affected by the change of total ionic concentration.

Experimental

Students will work together on this experiment sharing data for all parts of this experiment. Student A will mix the solutions while student B times the reaction (to the nearest second). A table should be prepared with five columns to record for each mixture the elapsed time and the volumes of 0.20 M \( \ce{KI} \), 0.20 M \( \ce{KCl} \), 0.10 M \( \ce{(NH4)2S2O8} \), and 0.10 M \( \ce{(NH4)2SO4} \) used for the solutions you prepared.

Quantitative Precautions

Rinse the burets  and 10 mL ml grad cylinder thoroughly with small portions of the solution to be measured before filling each. Rinse the beakers that are used to contain your reaction mixtures with deionized water, and shake out any excess(but do not dry them) before and after each run.

Solution Preparation

Make the following solutions. \( \ce{KI} \) and \( \ce{(NH4)2S2O8} \) are solids, so you will need to calculate the mass required to make these solutions:

• 250mL of 0.20 M \( \ce{KI} \)
• 250mL of 0.10 M \( \ce{(NH4)2S2O8} \)

To avoid contamination with other chemicals, rinse your wash bottle 3x with deionized water before refilling. Make the solution in a 250ml volumetric flask then store it in a labeled 250 or 300 ml Erlenmeyer flask. Stock solutions of the other reagents needed for this experiment are available by the sink or weighing area.

Before beginning any measurements, practice the art of transferring quickly, 20 mL of deionized water contained in each of two 50 mL beakers, into a 250 mL beaker.

Simultaneously, gently rotate the beaker to mix the solutions and start the timer as nearly as possible at the instant of mixing.

(1) Determination of the order of the reaction

Fill two burets, one with 0.20 M KI and the other with 0.10 M \( \ce{(NH4)2S2O8} \). For Mixture 1, carefully measure 20.0 mL of each solution separately into different 50 mL beakers, labeled A and B, which have been rinsed with deionized water and drained. Rinse and drain a 250 mL beaker to be used as the reaction vessel, then measure exactly 10.0 mL of 0.0050 M \( \ce{Na2S2O3} \) (sodium thiosulfate) into this beaker, add 10 drops of starch indicator, and swirl the solution gently to promote mixing.

Start the reaction by quickly transferring the solutions from the 50 mL beakers to the 250 mL beaker as you practiced, gently rotate the beaker to mix the solutions, and start the timer. Time the reaction from the moment of mixing to the instant the solution begins to turn blue. For this first experiment, repeat the rate measurement with a second set of samples, which should be consistent with the first result to within about 1 second.

Carry out similar rate measurements with mixtures 2-7, measuring \( \ce{KI} \) and \( \ce{(NH4)2S2O8} \) from the burets. The \( \ce{KCl} \) and \( \ce {(NH4)2SO4} \) are less critical, and may be measured carefully with a 10 mL graduated cylinder. For each run, measure exactly 10.0 mL of 0.0050 M \( \ce{Na2S2O3} \) into the rinsed reaction beaker, add 5 drops of starch solution, then add the contents of beakers A and B simultaneously with mixing, and time the reaction. Run duplicate trials on each mixture and repeat runs where there is an appreciable difference (> 10%) between results for the same mixture. During one pair of runs, measure the temperature of the reacting mixture with a thermometer, and record the result—Mixture #6 will be a good choice.

 

Mixture	Beaker A	Beaker B
1	\( \text {20.0 mL KI} \)	\( \text{20.0 mL } \ce {(NH4)2S2O8} \)
2	\( \text {10.0 mL KI} \) \( \text {10.0 mL KCl} \)	\( \text{20.0 mL } \ce {(NH4)2S2O8} \)
3	\( \text {5.0 mL KI} \) \( \text {15.0 mL KCl} \)	\( \text{20.0 mL } \ce {(NH4)2S2O8} \)
4	\( \text {20.0 mL KI} \)	\( \text{10.0 mL } \ce {(NH4)2S2O8} \) \( \text{10.0 mL } \ce {(NH4)2SO4} \)
5	\( \text {20.0 mL KI} \)	\( \text{5.0 mL } \ce {(NH4)2S2O8} \) \( \text{15.0 mL } \ce {(NH4)2SO4} \)
6	\( \text {10.0 mL KI} \) \( \text {10.0 mL KCl} \)	\( \text{10.0 mL } \ce {(NH4)2S2O8} \) \( \text{10.0 mL } \ce {(NH4)2SO4} \)
7	\( \text {5.0 mL KI} \) \( \text {15.0 mL KCl} \)	\( \text{5.0 mL } \ce {(NH4)2S2O8} \) \( \text{15.0 mL } \ce {(NH4)2SO4} \)

Table \(\PageIndex{1}\). Summary of the volumes to be used for the determination of the order

(2) The effect of temperature on the reaction rate

Carry out a rate measurement at an appreciably lower temperature as follows. Use the same conditions that were used for Mixture 6, except cool the solutions in beakers A and B in an ice bath for 15 minutes (with occasional swirling) before mixing. Cool the reaction beaker as well. Mix the solutions and record the time necessary to complete the reaction. While the mixture is reacting, measure its temperature with a thermometer and record the result. Repeat this part of the experiment except warm the solutions on a hot plate.

Clean up

• All solutions need to go to the appropriate waste container
• Rinsings can go down the drain

Method of Analyzing the Experimental Data

We assume that the rate law for Reaction \(\PageIndex{1}\) takes the usual form

\[ \text{rate} \ce {= \frac {d[I3]^{-}}{dt = k[I^{-}]^{m}}[S2O8^{2-}]^{n} } \]

Our objective is to determine the reaction order of [\( \ce{I^{-}} \)] and [\( \ce{S2O8^{2-}} \)], m and n.

If the extent of the reaction is sufficiently small, then [\( \ce{I^{-}} \)] and [\( \ce{S2O8^{2-}} \)] are approximately constant (and equal to their initial concentrations when the reaction begins) during each run; therefore, the rate is approximately constant. (We achieve a small extent of reaction by using an amount of \( \ce{S2O8^{2-}} \) that is small compared to the amounts of \( \ce{I^{-}} \) and \( \ce{S2O8^{2-}} \).)

\[ \text{initial rate } \ce {= \frac {\Delta [I3]}{\Delta t} = k[I^{-}]_{o}^{m}[S2O8^{2-}]_{o}^{n} } \]

where \(\Delta t\) is our measured time interval between mixing and appearance of the blue color.

For every mole of [\( \ce{I3^{-}} \)] produced in reaction (1), two moles of \( \ce{S2O3^{2-}} \) will be consumed in reaction (2). Therefore,

\[ \ce {\Delta[I3^{-}] = - \frac{1}{2} \Delta [S2O3^{2-}] = \frac {1}{2} [S2O3^{2-}]_{o}} \]

combining these equations, we obtain

\[ \ce{ \frac{ \frac{1}{2}[S2O3^{2-}]_{o} }{\Delta t} = k[I^{-}]_{o}^{m}[S2O8^{2-}]_{o}^{n}} \]

We now have three unknowns: k, m, and n. To simplify matters, suppose that we use the same initial concentration of \( \ce{S2O3^{2-}} \) in two experiments, a and b. Also suppose that the experiments were done at the same temperature so that k is constant.

Then,

\[ \ce{ \frac{ \Delta t_{a}}{\Delta t_{b}} = \frac { k_{b}[I^{-}]_{o}^{m}[S2O8^{2-}]_{o}^{n} }{ k_{a}[I^{-}]_{o}^{m}[S2O8^{2-}]_{o}^{n} }} \]

From this general form, derive the equation that applies to

(a) two experiments with the same initial concentration of \( \ce{I^{-}} \),

(b) two experiments with the same initial concentration of \( \ce{S2O8^{2-}} \).

From (a), derive an explicit formula for n.

From (b), derive an explicit formula for m.

Data Analysis

(1) Include the explicit formulas for m and n and derivations for the determination of m and n. Also include the equations for the initial concentrations of \( \ce{I^{-}} \) and \( \ce{S2O8^{2-}} \). Show your work!

(2)

(a) Determine m and n for all possible combinations (HINT: there are 5 possible combinations for m and 5 for n). Your results for m and n should be close to integers. Assume that any differences from integers are caused by experimental errors, and use the nearest integer when calculating k.

(b) A better way to determine m and n is with a least-square fit. Plot log(rate) versus log([\( \ce{I^{-}} \)]) for trails where [\( \ce{S2O8^{2-}} \)] remains constant. Plot log(rate) versus [\( \ce{S2O8^{2-}} \)] for trials where [\( \ce{I^{-}} \)] remains constant. Determine m and n and their associated standard deviations. Compare these results to the results obtained from part a above.

(3)

(a) Calculate the rate constant for all trials, include the units of the rate constant.

7 at room temperature

1 at low temperature

1 at high temperature

(b) Calculate the average rate constant at room temperature along with the standard deviation, relative standard deviation, and 95% confidence limit.

(c) The Arrhenius Equation can be used to analyze temperature-dependent kinetics data to extract the Activation Energy got a reaction. One form of the Arrhenius Equation is:

\( \ce{ k = Ae^{-E_{a}/RT }} \)

where \(E_{a}\) is the activation energy, \(R\) is the ideal gas constant, \(T\) is the temperature in Kelvin and \(A\) is a pre-exponential factor with units equal to those of the rate constant. Using your high, low, and room temperature rate constant and associated temperatures, plot the natural logarithm of the rate constant versus the inverse temperature, determine the Activation Energy of the reaction, including units and standard deviation

(4) In your discussion/conclusion, be sure to compare the various values you calculated, especially for the rate constant under the various conditions.