Activation energy of persulfate iodide reaction

CHEMICAL KINETICS: A CLOCK REACTION

OBJECT The object of this experiment is to become familiar with experimental chemical kinetics; this will be accomplished by using acquired experimental data to determine the overall order of a reaction as well as the reaction order of the individual reacting species, propose a possible reaction mechanism, and calculate the reaction specific rate constant as well as the activation energy for the reaction. INTRODUCTION The reaction between the iodide ion, I–, and the peroxydisulfate ion, S2O82–, is shown below (RXN 1), where molecular iodine, I2, and the sulfate ion, SO42–, are the reaction products. 2 I– + S2O82– → I2 + 2 SO42– (RXN 1) iodide peroxydisulfate iodine sulfate The rate of the reaction, –Δ[S2O8]/Δt, in units of molarity per second, M/s, can be expressed by equation 1 (i.e. the rate law), where special attention is arbitrarily given to the reaction rate based on the decrease of [S2O82–], hence the negative sign. In eq. 1 k is the reaction specific rate constant, m is the reaction order of I–, and n is the reaction order of S2O82–, where concentrations are expressed in brackets (i.e. [X]) as molarity, M, and k has the appropriate units for the overall reaction order that will be determined. (eq. 1)

In this experiment the method of initial rates will be used to complete the above objectives. To accomplish this a solution of potassium iodide, a source of I–, and a solution of potassium peroxydisulfate, a source of S2O82–, will be mixed in varying concentrations and the time it takes for S2O82– to react will be recorded (i.e. Δt in eq. 1). In this reaction Δ[S2O82–] cannot be determined directly; therefore, two additional reagents will be used in the same reaction vessel for indicating and recycling purposes, which will compensate the measurement of Δ[S2O82–]. The “recycling agent” is the thiosulfate ion, S2O32–, and reacts with I2 as shown in RXN 2 below, where I– is regenerated along with the tetrathionate ion, S4O62–, as an additional product.

I2 + 2 S2O32– → 2 I– + S4O62– (RXN 2) iodine thiosulfate iodide tetrathionate At the start of RXN 1 and RXN 2, [I–]o and [S2O82–]o (i.e. the initial I– and S2O82– concentrations, respectively) are much greater than [S2O32–]o and RXN 2 is much faster than RXN 1; therefore, as I2 is produced in RXN 1 it is consumed nearly instantaneously by the recycling agent (S2O32–) shown in RXN 2. This means [I2] is nearly zero throughout the reaction; however, eventually the S2O32– will run out and I2 will build in concentration. At this point the reaction solution will turn deep blue or black as a result of I2 reacting with the added indicator, which in this reaction is a solution of starch. In the method of initial rates (i.e. the method used in this experiment) the key is to determine the instantaneous rate before the initial concentrations of reactants, in this case [S2O82–], have changed significantly, where due to the recycling agent, [I–] remains absolutely constant until all of the S2O32– is consumed. The reaction stoichiometry in RXN 1 and RXN 2

Rate = – �[S2O

2– 8 ]

�t = k[I–]m[S2O

2– 8 ]

n

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shows half as much S2O82– will be consumed as S2O32– and initially [S2O32–] is roughly 10–40 times smaller than [S2O82–]; therefore, only a small fraction of S2O82– reacts in the due course of these reactions, making the method of initial rates ideal for determining the above objectives. Several trials will be carried out in which the same concentrations of S2O32– and starch are used while varying either [I–]o or [S2O82–]o as well as varying the reaction temperature systematically. In each of these trials the volume of the reaction solution is identical (as well as [S2O32–]); therefore, the quantity Δ[S2O82–] is the same for each trial and can be instead related to the quantity Δ[S2O32–] stoichiometricly via RXN 1 and 2. For example, if it takes 10 seconds for the color change to occur in one trial and 20 seconds for the color change to occur in another trial (with the same quantity of S2O82– in both trials) then the later trial proceeded with an initial rate that was exactly half that of the former. Thus, only Δt need to be measured from the start of mixing the reagents to the time when the color of the reaction solution changes. Equation 1 can therefore be re-written as eq. 2, shown below, where [I–]o, trial 1 and [S2O82–]o, trial 1 are the initial concentrations of the iodide and peroxydisulfate ions for the conditions in trial 1 respectively, Δttrial 1 is the measured time of reaction, and the quantity Δ[S2O82–] has been replaced by its stoichiometric relationship to Δ[S2O32–]. (eq. 2) In another trial (call it trial 2 for example), the same equation can be written; however, the initial concentration of either I– or S2O82– is changed relative to trial 1. The rate constant is identical for both trials provided the temperature is the same; therefore, by dividing these two equations by each other one of the reaction orders (either m or n depending on which quantity is held constant) can be determined upon measuring Δt for both trials. Equations 3(a,b) shows this manipulation below, where in this case the [I–]o was identical in both trials. (eq. 3a) (eq. 3b) Equation 3b shows with knowledge of Δt, Δ[S2O32–], and [S2O82–]o for both trials the reaction order n can be determined. In a third trial [I–]o can be varied relative to the first and second trial while [S2O82–]o is held constant and using a similar manipulation as in eq. 3(a,b) the reaction order m can be determined. Finally, with knowledge of both reactant’s reaction orders and data from any one of the previous trials the reaction specific rate constant, k, can be determined with its appropriate units. With knowledge of a reaction’s experimentally determined reaction order it is possible to deduce qualitatively a reaction mechanism. Recall a reaction mechanism is a series of elementary, or individual, steps that must add up to give the global reaction; in this case RXN 1 above. Each elementary step’s reaction stoichiometry is identical to its reaction order and demonstrates the molecularity of the step. For example, a reaction order of 1 involves 1 molecule and is called unimolecular, a reaction order of 2 involves 2 molecules and is called bimolecular, and reactions involving more than 2 molecules are called termolecular. Generally a global

Rate trial 1 = – �[S

2

O2– 8

]

�t trial 1

= – �[S

2

O2– 3

]

2�t trial 1

= k[I–]m o, trial 1

[S 2

O2– 8

]n o, trial 1

Rate trial 1 = – �[S

2

O2– 3

]

2�t trial 1

= k[I–]m o, trial 1

[S 2

O2– 8

]n o, trial 1

Rate trial 2 = – �[S

2

O2– 3

]

2�t trial 2

= k[I–]m o, trial 2

[S 2

O2– 8

]n o, trial 2

Rate trial 1

Rate trial 2 =

–�[S 2

O2– 3

]/2�t trial 1

–�[S 2

O2– 3

]/2�t trial 2

=

✓ [S

2

O2– 8

] o, trial 1

[S 2

O2– 8

] o, trial 2

◆n

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reaction might have many elementary steps; however, only 1 of those steps can be the rate- determining step. The rate-determining step is, by definition, the slowest step and thus is the rate at which the global reaction proceeds and mirrors the experimentally determined reaction order. Using the method of initial rates as outlined above and chemical reasoning; a reaction mechanism for RXN 1 can be determined. The last object is to determine the activation energy, Ea, of RXN 1 and explore the use of a catalyst. The activation energy is a threshold energy that must be overcome to produce a chemical reaction and is typically reported in units of kJ/mol. This threshold can be overcome by the conversion of kinetic energy to potential energy via molecular collisions. Recall kinetic molecular theory (KMT) predicts an increase in temperature results in higher molecular velocities and an increase in the frequency of collisions, meaning that most reactions will speed up (i.e. the rate constant, k, becomes larger) at higher temperatures due to their heightened ability to overcome the activation energy barrier. Equation 4(a,b) shows the Arrhenius equation, where A is the frequency factor, T is the reaction temperature, and R is the ideal gas constant (8.314 J/mol·K). Note that eq. 4b is most useful in this exercise as it resembles the equation of a line (y = mx + b), (eq. 4a) (eq. 4 b) with the slope, m, being the quantity –Ea/R, the x-axis being 1/T, the y-axis being the natural log (ln) of k, and the y-intercept, b, being the natural log (ln) of A. Thus repeating RXN 1 with the same concentrations but different temperatures and plotting the results as ln(k) vs. 1/T will yield a straight line and the best fit slope and y-intercept will give the activation energy and frequency factor, respectively. Increasing the temperature of RXN 1 is not the only way to increase the reaction’s rate constant. Catalysts, defined as a molecular or atomic species that speeds up a reaction while not being consumed itself, lower the activation energy of a reaction for the same given temperature by intimately becoming a part of the reaction mechanism. Copper(II) sulfate, a known catalyst for RXN 1, will be tested in a separate trial at the same temperature and concentration as a previous trial to verify its role as a catalyst in RXN 1. PROCEDURE Work in pairs. Each pair obtains from the stockroom 1 stopwatch, and 3 10-mL graduated pipets Each pair obtain from the side counter the following five stock solutions in five separate beakers that are labeled, clean but not dry, and pre-rinsed two or three times with small portions of the appropriate stock solution: (1.) about 75 mL of a 0.200 M KI stock solution, (2.) about 75 mL of a 0.100 M K2S2O8 stock solution, (3.) about 15 mL of a 0.200 M KCl stock solution, (4.) about 25 mL of a 0.100 M K2SO4 stock solution, and (5.) about 50 mL of a 0.0050 M Na2S2O3 stock solution. Rinse one labeled, clean, graduated pipet two or three times with small portions of KI stock solution from the beaker. Rinse a second labeled, clean, graduated pipet similarly with the K2S2O8 stock solution from that beaker. Rinse the third labeled, clean, graduated pipet similarly with the Na2S2O3 stock solution from that beaker. After rinsing everything, support each pipet upright in the burette clamp, which each pipet positioned just above each respective stock solution beaker (i.e. KI, K2S2O8, and Na2S2O3).

k = Ae–Ea/RT

ln(k) = –Ea R

✓ 1

T

◆ + ln(A)

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Rinse a labeled, clean 10-mL graduate cylinder two or three times with small portions of the KCl stock solution. Rinse a second labeled, clean 10-mL graduated cylinder two or three times with small portions of the K2SO4 stock solution. After rinsing, position both graduated cylinders next to their respective stock solution beakers (i.e. KCl and K2SO4). PART 1: CONSTANT TEMPERATURE AND VARIABLE CONCENTRATION In Part 1 the reaction orders, m and n, as well as the rate constant, k, from eq. 1 will be determined.

TABLE 1: VOLUMES OF SOLUTIONS TO BE USED IN PART 1

Trial Beaker 1 Contents and Volumes Beaker 2 Contents and Volumes

0.200 M KI

0.200 M KCl

0.0050 M Na2S2O3

0.100 M K2S2O8

0.100 M K2SO4

Starch

1 10.0 mL none 5.0 mL 10.0 mL none 2 drops 2 10.0 mL none 5.0 mL 5.0 mL 5.0 mL 2 drops 3 5.0 mL 5.0 mL 5.0 mL 10.0 mL none 2 drops 4 10.0 mL None 5.0 mL 2.5 mL 7.5 mL 2 drops

For each trial clean 2 30-mL beakers and label them 1 and 2 respectively. Drain each vessel well but not dry it. Additionally, clean a 125-mL Erlenmeyer flask and drain it well but do not dry it. For each trial pipette the specified volume (see Table 1) of 0.200 M KI into beaker 1. If the volume of the KI solution in the flask is less than 10.0 mL, add 0.200 M KCl using the appropriate graduated cylinder to bring the total solution volume up to 10.0 mL. Next, pipette 5.0 mL of 0.0050 M Na2S2O3 into the beaker with the KI/KCl solution. Mix the contents of the flask well by swirling for a few seconds. For each trial pipette the specified volume (see Table 1) of 0.100 M K2S2O8 into beaker 2. If the volume of K2S2O8 is less than 10.0 mL, add 0.100 M K2SO4 using the appropriate graduate cylinder to bring the total solution volume up to 10.0 mL. Next, add 2 drops of a starch solution to the beaker. Mix the contents of the beaker well by swirling for a few seconds. Have a thermometer and stopwatch on hand. Test the stopwatch to be sure it works and learn how to use it. Set the stopwatch back to zero. Dump the contents of beaker 1 into the Erlenmeyer flask, then dump the contents of beaker 2 into the Erlenmeyer flask and immediately mix thoroughly by swirling for a few seconds; start timing at the instant of dumping beaker 2. It is not necessary to continue swirling the beaker after the initial thorough mixing. Record to the nearest second the time required for the blue or black color to appear. Pay attention to the timing, the color change will occur between 30 and 500 seconds; therefore, even a few seconds can be significant for the faster trials. Insert a thermometer into the reaction vessel after the color change and record the temperature to the nearest degree Celsius. You may have to tilt the flask slightly to avoid touching the tip of the thermometer to the bottom or side of the flask.

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After each trial discard the contents of the flask and rinse and drain each beaker and flask before beginning the next trial. Repeat any trial that for any reason did not appear to proceed properly or was not within 1–2 oC from the mean temperature of the other trials. PART 2: VARIABLE TEMPERATURE AND CONSTANT CONCENTRATION In Part 2 the activation energy, Ea, and frequency factor, A, from eq. 4(a,b) will be determined.

TABLE 2: VOLUMES OF SOLUTIONS AND TEMPERATURES TO BE USED IN PART 2

Trial Beaker 1 Contents and Volumes Beaker 2 Contents and Volumes

Temp. Bath Procedure 0.200 M KI

0.200 M KCl

0.0050 M Na2S2O3

0.100 M K2S2O8

0.100 M K2SO4

Starch

1 10.0 mL none 5.0 mL 10.0 mL none 2 drops room temp no bath needed

5 10.0 mL none 5.0 mL 10.0 mL none 2 drops 38–42 oC

use the hottest tap water you can get to fill the bath

6 10.0 mL none 5.0 mL 10.0 mL None 2 drops 9–12 oC

use some ice to cool the cold tap water for the bath

7 10.0 mL None 5.0 mL 10.0 mL none 2 drops 0 oC or

lower

Start with a bath almost full of ice and add enough cold water to yield a slush

Repeat the general procedure from Part 1 using the conditions found in Table 2. Note, all concentrations in this part will be identical; however, you will change the temperature of the reaction systematically. Use a trough for the water/ice bath and follow the indicated procedure in Table 2. A few inches of water/ice is all that is needed for the bath; do not over fill. Place both Beaker 1 and 2 with their respective mixtures in the trough as well as the empty Erlenmeyer flask and allow the contents to come to about the same temperature before dumping and timing (about 2–3 minutes).

Once both Beaker 1 and 2 are at the same temperature place the thermometer in Beaker 1, record the temperature to the nearest degree Celsius before initiating the reaction then dump the contents of Beaker 1 into the Erlenmeyer flask followed by Beaker 2 and swirl thoroughly for a few seconds. Keep the reaction vessel immersed in the bath throughout the reaction and record the time to color change, as was done in Part 1. After the reaction as stopped record the temperature again. PART 3: EFFECT OF A CATALYST Repeat Trial 1 exactly as was done in Part 1 except add 1 drop of 0.1 M CuSO4 to Beaker 1 before dumping its contents into Beaker 2.

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WASTE DISPOSAL By the end of the lab period all solutions must end up in the waste jug. You may periodically dispose of your solutions as you go to prevent a long line from occurring.

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A CLOCK REACTION Name: ____________________________ Partner’s Name:____________________________ Section: Day ________ Hours: ________ DATA PART 1: CONSTANT TEMPERATURE AND VARIABLE CONCENTRATION

Trial Δt (seconds)

[I–]o at the instant of mixing (M)

[S2O82–]o at the instant of mixing (M)

[S2O32–]o at the instant of mixing (M)

–Δ[S2O32–] 2Δt

(M/s)

Temperature (oC)

1

2

3

4

PART 2: VARIABLE TEMPERATURE AND CONSTANT CONCENTRATION

Trial Δt (seconds)

[I–]o at the

instant of mixing (M)

[S2O82–]o at the

instant of mixing (M)

[S2O32–]o at the

instant of mixing (M)

–Δ[S2O32–] 2Δt

(M/s)

Temperature (oC)

initial final mean

5

6

7

PART 3: EFFECT OF A CATALYST

Trial Δt (seconds)

[I–]o at the instant of mixing (M)

[S2O82–]o at the instant of mixing (M)

[S2O32–]o at the instant of mixing (M)

–Δ[S2O32–] 2Δt

(M/s)

Temperature (oC)

8

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RESULTS PART 1: CONSTANT TEMPERATURE AND VARIABLE CONCENTRATION Using your data from Part 1 and the method of initial rates described in the introduction and eq. 3(a,b), determine the order of I–, m, and S2O82–, n, and report your results in the blanks below. Use the space provided to show your work. m = __________ n = __________ The overall reaction order and molecularity is: __________ Write the rate law for the reaction (with respect to S2O32–): The units for the rate constant, k, are: __________ Using the rate law you determined and the data from Trials 1–4, calculate the rate constant, k, and report your results where indicated. Show your work for 1 Trial and use the correct units. Trial 1 k = Trial 2 k = Trial 3 k = Trial 4 k = Calculate the mean (average) value for the rate constant of these four trials at room temperature and the average deviation as a percent of the mean value. Mean = ____________________ Percent Average Deviation = ____________________

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PART 2: VARIABLE TEMPERATURE AND CONSTANT CONCENTRATION Calculate the value of the rate constant as you did above for Trials 5–7. Trial 5 k = Trial 6 k = Trial 7 k = Fill out the table below using your calculated rate constants from Trials 1, and 5–7

Trial k ln (k) mean T (oC) Mean T (K) 1/T (K–1)

1

5

6

7

Using a software package such as Microsoft Excel, plot your data with ln (k) on the y-axis and 1/T (K–1) on the x-axis (See Appendix 7, Using Excel to Make Plots). Fit the data with a best-fit line and report your results below (see eq. 4b). Make sure to label both axes appropriately and include a title. You must print your graph with the best-fit line results and attach it to the end of this report for full credit. Write the best-fit line equation from your results and report the R2 value: Activation Energy, Ea, in units of kJ/mol = ___________________ Frequency Factor, A, (include the correct units) = _______________ PART 3: EFFECT OF A CATALYST Calculate the value of the rate constant as you did above for Trial 8. Trial 8 k =

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QUESTIONS 1. Suggest a reasonable 2-step reaction mechanism for the reaction between I– and S2O82–. Step 1: Step 2: Sum of the two steps: 2. Calculate the Activation Energy, Ea, of the catalyzed reaction (i.e. Trial 8) in units of kJ/mol

and show your work in the space provided. 3. Does your answer for questions 2 make sense? Why or Why not? Use no more than 3

complete sentences. 4. Briefly describe using your own words what the frequency factor, A, represents using no