Kinetics (Determining Rate Law) Handout PDF

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EXPERIMENT 5 Kinetics: Determining the Rate Law

CHGN122

CONTEXT You have already tapped into the topic of kinetics – the study of reaction rates - in lecture. The connection between kinetics and engineering leaps off the page...an engineer can design an incredibly creative, spectacular system only to find that the rate at which the system operates is far too slow…or maybe even too fast. We must understand and incorporate the impact of rate in all areas of engineering and science to be able to optimize the fundamental time piece of any efficiently operating system. Kinetics is the context for the next two weeks in lab. This week, you will experimentally determine the rate law for a given reaction – that is, how the reaction rate depends on reactant concentration. Next week, you will experimentally determine the activation energy of a reaction by examining how the available thermal energy (temperature) determines the rate. PURPOSE AND MOTIVATION This week, you will have the opportunity to carry out the method of initial rates from beginning to end. In lecture, you were provided with initial rate data, from which you determined the rate law and rate constant, k. In lab, you will generate your own initial rate data, from which the rate law (specifically the individual orders of each reactant). Once the rate law is sorted out, you then have all the information needed to calculate the relative rate constant. After determining the rate law and relative rate constant, you will measure and calculate the activation energy for the same reaction. You will do this by measuring the rates of a reaction at various temperatures to calculate the activation energy of the reaction. The activation energy will be determined by graphing your data using the Arrhenius Equation you encountered in lecture. PRE-LAB ASSIGNMENT – See Canvas for details INTRODUCTION For this experiment, you will study rate properties (chemical kinetics). The rate law (including the order of reactants and the rate constant) will be experimentally determined for the reaction between iodide ion and bromate ion under acidic conditions. In other words, you will determine the rate law for Eq. 1, shown below. In this experiment you will evaluate the rate constant, k, and reaction orders for each reactant in the reaction: 6 I-1(aq) + BrO3-1(aq) + 6 H+1(aq) → 3 I2(aq) + Br-1(aq) + 3 H2O(l)

(Eq. 1)

This reaction proceeds reasonably slowly at room temperature. Its rate depends on concentrations of the I-1, BrO3-1 and H+ ions according to the rate law: Rate = k [I-1]m [BrO3-1]n [H+1]p

(Eq. 2)

where m, n and p are the reaction order with respect to each reactant.

Revised 2018.01.21 © 2017 Department of Chemistry and Geochemistry, Colorado School of Mines

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Our method for measuring the rate of the reaction involves what is frequently called a clock reaction. The clock reaction provides a simple method by which we can “time” the reaction through cues that are visible to our eyes. To create the clock reaction, a secondary reaction (Eq 3) is coupled to the reaction of interest (Eq 1). I2(aq) + 2 S2O3-2(aq) → 2 I-1(aq) + S4O6-2(aq) (Eq. 3) These two reactions (Eq’s 1 and 3) will take place simultaneously in the reaction flask. As compared with the first reaction, the reaction in Eq. 3 is instantaneous. The I2 produced in Eq. 1 reacts completely with the thiosulfate ion, S2O3-2, present in the solution (of Eq. 3) so that the concentration of I2 remains effectively zero, until the entire amount of thiosulfate ion has reacted. As soon as the S2O3-2 is gone from the system, the I2 produced in the first reaction remains in the solution and its concentration begins to increase. The presence of I2 is made apparent by a starch indicator that is added to the mixture. I2, even in small amounts, reacts with starch to produce a blue/black color (the initial reaction mixture is clear in color). By carrying out the first reaction in the presence of S2O3-2 and a starch indicator, we introduce a “clock” into the system. Our clock tells us when a given amount of BrO3-1 ion has reacted (1/6 mole BrO3-1 per mole of S2O3-2) which is just what we need to know, since the rate of reaction can be expressed in terms of the time it takes for a particular amount of BrO3-1 to be used up. For this experiment, we will carry out the reaction between BrO3-1, I-1 and H+1 ions under different concentration conditions. Measured amounts of each of these ions in solution will be mixed in the presence of a constant small amount of S2O3-2. The time it takes for each mixture to turn blue/black will be measured. The time obtained for each reaction will be inversely proportional to its rate. By changing the concentration of one reactant at a time while keeping the others constant, we can investigate how the rate of the reaction varies with the concentration of each reactant, which will allow us to calculate the rate order for each reactant. Once we know the order for each reactant, we can determine the rate constant for the overall reaction. EXPERIMENTAL PROCEDURE

WORK IN PAIRS

The table on the next page gives the reagent volumes (mL) to be used in carrying out the reactions for this experiment.

Trial 1 2 3 4 5

Table 1. Amounts (mL) of each reactant for each Trial Reaction Flask 1 Reaction Flask 2 0.010 M KI 0.0010 M Na2S2O3 H2O 0.040 M KBrO3 0.10 M HCl 10 10 10 10 10 20 10 0 10 10 10 10 0 20 10 10 10 0 10 20 8 10 12 5 15

1. For Trial 1, use graduated cylinders to measure out 10 mL of 0.010 M KI solution, 10 mL of 0.0010 M Na2S2O3 solution and 10 mL H2O into a 200 or 250 mL flask (Reaction Flask 1). Swirl to mix. 2. Measure out 10 mL of 0.040 M KBrO3 solution and 10 mL of 0.10 M HCl solution into a second 200 or 250 mL flask (Reaction Flask 2). Make sure to clean grad. cylinders between each new reagent. 3. To Reaction Flask 2, add a pea-size amount of solid starch indicator. Swirl to mix. 4. Note the time and pour contents of Reaction Flask 2 into Reaction Flask 1. Swirl to mix and start timing! Page 2 of 7

5. Record the time it takes for the solution to turn blue. Record the temperature of the final solution. Note that it takes a while for the full color change to occur, but you should note the time as soon as you observe a very faint light blue color appear! It is important that you consistently note the time at the first hint of blue for each trial. 6. All solutions should be disposed in proper waste containers. The reaction flasks should be rinsed well with DI water before proceeding to the next trial. 7. Repeat the procedure with the different concentrations of reactants listed for each trial (2-5 in Table 1). Don’t forget to add the starch indicator! Make sure all glassware is clean before starting a new trial. 8. Repeat any trials that don’t proceed as expected (way too long or way too short of time). DELIVERABLES AND EXPECTATIONS You need to write a formal lab report for this experiment. For your lab report, you need to have a title page and the following sections:        

Abstract Introduction Methods/Experimental Results Discussion Conclusion References Appendices (ask your TA if this is required)

Refer to Canvas for help on writing a cohesive lab report. Your report should be no more than five pages (excluding figures, graphs, title page, and references). Aside from the general report criteria, you need to include the following tables and calculations in your report:  

Table 1 and 2 Calculations shown in variable form first o Concentration values for Table 2 o Reaction orders for each reactant o Rate constant for trials 1 to 4 o Trial 5 prediction o Percent error for trial 5 (experimental vs. calculated)

Note: If time permits, complete the following calculations before you leave lab. CALCULATIONS AND QUESTIONS From your data, determine the orders of reaction for the three reactants (I -1, BrO3-1, H+1) and use these to determine the rate constant. In the reaction, the color change occurs when a constant pre-determined number of moles of BrO3-1 is used up. Our “color clock” allows us to measure the time required for the fixed number of moles of BrO3-1 to react making the results visible. The rate of reaction is determined by the time, t, required for the color to change; the relative rate of reaction is inversely proportional to the time, t. Since we are

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concerned with relative rates (each trial compared to another) rather than absolute rates (each trial co mpared to known values), we will take all relative rates as being equal to 1000/t. 1) Calculate relative rates and concentrations of reactants after mixing. Recreate Table 2 (below) in your report using the data from your experiment. NOTE: The reactant concentrations in the various trials are NOT those of the stock solutions added. These reagents were diluted by the other solutions when you mixed them. The final volume of the reaction mixture is 50 mL in all cases. Use the M1V1 = M2V2 equation to find the final concentrations for each reagent in each trial.

Trial 1 2 3 4 5

Time (t) (sec)

Table 2: Data and calculations from each trial. 1000/t Reactant Concentration after mixing (M) -1 (relative rate) I BrO3-1 H+1

Temp. (oC)

2) Determine the reaction order for each reactant. Using the data in your table, find the order for each reactant. Do this by using the rate constant equation and the relative rates for each trial. Remember, this is a relative rate, not an absolute rate, so we can compare them. Designate the relative rate constant as k’. This value is the same for each trial as long as the reactants don’t change (changing their concentrations only affects the rate, not the rate constant). Use the final concentrations for each reactant in specific trials to determine the order for each reactant. In the below equation, the superscripts after each reactant signify what power or order they are. The order for each (i.e. the superscript) is what you are trying to determine. The different reactants are given different letters for their order only to signify that they may or may not be the same value. Orders for the reactants can be 0th order (superscript = 0), 1st order (superscript = 1), 2nd order (superscript = 2) or 3rd order (superscript = 3). Relative rate = k’ [I-1]m [ BrO3-1]n [H+1]p Notice that each of Trials 2 - 4 differ from Trial 1 in the concentration of only one reagent (see Table 1). From the ratio of the relative rates of Trial 1 and any of Trials 2-4, find the order for the reactant whose concentration changed. This ratio (relative rate 1/relative rate 2-4) is equal to the order for the reactant that changed concentration. Below is an example for Trial 1 vs Trial 2 (use your own data for your report). In the example, the equation is filled in with sample data for Trial 1 and Trial 2. The relative rate equations for Trials 1 and 2 are divided and all terms that are equal are cancelled.

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Example Calculation (USE YOUR OWN DATA FOR YOUR REPORT): Relative rate 1 = k’(0.0020)m(0.020)n(0.0080)p Relative rate 2 = k’(0.0040)m(0.020)n(0.0080)p Thus, when all the same terms are cancelled: Relative rate 1 = (0.0020)m Relative rate 2 = (0.0040)m Relative rate 1/Relative rate 2 = (0.50)m The “relative rate 1” and “relative rate 2” will be the values from Table 2 (1000/t). If you do this properly, you will have an equation involving only one superscript (‘m’ in this example) as the unknown. Solve this equation for the order of the reaction (to the nearest whole number). For Trials 1 and 2 this “m” value will give you the order of the reaction with respect to the I-1 ion. Example Calculation (USE YOUR OWN DATA FOR YOUR REPORT): Relative rate 1 = 11.8 = k’(0.0020)m(0.020)n(0.0080)p Relative rate 2 = 22 = k’(0.0040)m(0.020)n(0.0080)p 11.8/22 = (0.0020/0.0040)m 0.536 = (0.50)m m ≈ 1 (to the nearest whole number) Apply the same approach to Trials 1 and 3 to find the value of “n” (the order with respect to BrO3-1) and Trials 1 and 4 to find the value of “p” (the order with respect to H+1). Report these values to the nearest whole number in a table. Show ALL calculations for m, n, and p determinations. 3) Calculate the value of the relative rate constant, k’. Having found m, n and p, the relative rate constant (k’) can now be calculated by plugging these values and the relative rates found for each reaction, along with the reactant concentrations for Trials 1-4, into the relative rate equation: Relative rate = k’(I-1)m(BrO3-1)n(H+)p Determine the four k’ values (one for each of trials 1-4). Calculate an average k’ for your reaction. Report all k’ values and the average k’ value. SHOW ALL CALCULATIONS! Using k’ave, predict the relative rate (1000/t) and time (t) for Trial 5 (i.e. solve the rate equation for relative rate then convert this to t). Report both the calculated t and the observed (i.e. experimental) t. Calculate the percent error between these two times (use the calculated t as the true value). Give reasons for any differences found between the observed and the calculated. Page 5 of 7

Although you worked in pairs, each person must submit their own unique lab report. See the Lab Handbook for details on what should be included in a Formal Lab Report. Refer to the rubric below for a point break down of the report. This report is due two weeks after the lab was performed (week of March 9).

Experiment 5 Rubric Pre-Lab

10 points

Notebook Pages  Purpose  Method/Experimental  Observations  Conclusions

10 points

Formal Lab Report

80 points

Abstract 10 points  States relevant background information and explains the motivation behind the experiment  Clearly describes the experimental method with enough detail for the reader to understand  States the results of the experiment and if applicable, include statistics about the result’s accuracy and precision  Conclusions describe the implications of the results. The importance of the findings or results are clear  Section is written using 250 words or less Introduction 15 points  Describe what the experiment is about and what scientific concepts are being studied  Explain the purpose and objective(s) of the experiment (what you’re doing and why)  If necessary, offer a hypothesis regarding the outcome of the experiment and the scientific reasoning behind the hypothesis

Methods  Written in narrative form (not a bulleted list)  Verbs written in past tense  Written clearly, easy to follow, and contain enough detail to be repeated

10 points

Results 10 points  Provide a few sentences about the experiment’s overall findings  Contain only results, observations and calculations  Experimental findings are organized and displayed using a combination of visuals (graphs, tables, figures) and text o Graphs, tables and figures are labeled and accompanied by a few sentences describing the overall findings and key details

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Discussion 15 points  Provide meaningful interpretation of experimental findings  Discuss results expectations o State whether findings allow you to accept/reject hypothesis o Provide specific evidence as to why findings allow you to accept/reject hypothesis o Reject your hypothesis – explain why initial reasoning is incorrect  State source of errors and explained how these errors affects your experimental results Conclusion  Re-state the purpose of the experiment  Highlight the main findings and/or state the final results  If necessary, accept/reject hypothesis/hypotheses and provide evidence  State sources of errors that impacted your experimental results  Offer suggestions on how to minimize experimental error References  Correct format (IEEE or ACS style)  Use at least 5 references Writing  Formal, technical language; no first person  Grammar  Appropriate use of past and present tense  Neat formatting  Organization

Total for Experiment 5

5 points

5 points

10 points

100 points

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