1 KINETICS I: DETERMINATION OF A RATE LAW ADDITIONAL READING The concepts in this experiment are also discussed in sections 13.2 and 13.3 of Principles of Chemistry – A Molecular Approach, by Tro. ABSTRACT In this experiment you will qualitatively measure the rate of reaction using the initial rate method. This method involves measuring the rate of reaction before any of the reactant concentrations have decreased significantly or, in this case, measuring the amount of product formed before it increases significantly. Hydrogen peroxide is a relatively unstable liquid and will decompose quickly in the presence of many different catalysts. In this experiment we will use potassium iodide, KI, to catalyze the decomposition, where the iodide ion, I– (aq), acts as the catalyst. Catalysts remain unchanged (or are regenerated) at the end of a reaction. We can write the reaction as: 2 H2O2(aq) + I– (aq)  2 H2O() + O2(g) + I– (aq) (1) Note that the iodide ion is a reactant but it is also a product. The actual reaction is more complex than this and involves more than one step. We will investigate the kinetics of the overall reaction by systematically varying the concentration of the hydrogen peroxide while keeping concentration of the iodide fixed. The rate of reaction is to be expressed in terms of the rate of formation of oxygen gas formed whose change in pressure will be measured using a gas pressure sensor linked to a Vernier LabQuest computer interface. Also, we will vary the concentration of the iodide while keeping concentration of the hydrogen peroxide fixed. The data will be analyzed graphically to determine the order of the reaction for hydrogen peroxide and for iodide as well as the rate constant. BACKGROUND Reactions do not occur instantaneously; they take time. In this experiment we shall examine one of the many ways in which we can determine just which factors influence the speed (or rate) of a reaction. The average rate of a chemical reaction is often expressed as the change in the concentration of one of the reactants, or one of the products, divided by the time required for the change to take place. In this experiment the average rate can be defined in terms of the decrease in the concentration of hydrogen peroxide, or the decrease in concentration of iodide, or the increase in concentration of oxygen gas. Using the Greek letter delta, Δ, to signify “the change in”; square brackets, [ ], to indicate “molar concentration of…”; and Δt to represent the time needed for the given concentration change to take place (the change in time), expressions for the average reaction rate can be written: Δt Δ[O ] 1 1 Δt Δ[I ] 1 1 Δt Δ[H O ] 2 1 Rate 2 2 2        (2) Note that the term “average” is commonly omitted, although all rates are “average” unless Δt is infinitely small. Since [H2O2] and [I – ] decrease as the reaction proceeds, Δ[H2O2] and Δ[I – ] are negative quantities (Δ[H2O2] = [H2O2]final – [H2O2]initial); the rate of a reaction should be positive, so the terms containing Δ[H2O2] and Δ[I – ] are 2 preceded by minus signs. Since from the balanced equation two moles of H2O2 disappear for every one mole of I – that disappears, and since one mole of O2 is formed for every two moles of H2O2 that disappears, the term containing Δ[H2O2] is multiplied by 1/2, and those for Δ[I – ] and Δ[O2] are multiplied by 1. (See Tro, page 478). For the reaction of hydrogen peroxide with iodide, the term “Rate” in a rate law can signify any one of these changes with time. It should be remembered that the term “Rate” when used in a rate law refers not to the average rate, but to the instantaneous rate. The instantaneous rate is analogous to the reading on a car’s speedometer at any given instant; the average rate would be analogous to the value obtained by dividing the total distance driven by the total amount of time needed to make the trip. As a reaction proceeds, and the reactants diminish in concentration, it is reasonable to expect that the rate of the reaction will slow down. Fewer and fewer reactant molecules are available, making it less and less likely that those remaining will react successfully. The rate of reaction, then, should depend upon the concentrations of the reactants: Rate = k[H2O2] p [I – ] q (3) The proportionality constant, k, in the equation above is called the rate constant. The value of k, as well as the values of the exponents p and q, can only be obtained by experiment. Note that the order with respect to each reactant is usually not the same as the stoichiometric coefficient from the balanced reaction, i.e., we cannot assume that p = 2. There is no way to predict on the basis of the balanced chemical equation alone what the values will be. In this experiment we will use the initial rate method to determine values for the rate constant, k, and the two exponent’s p and q. We will carry out two sets of experiments, one set varying [H2O2] while holding [I – ] constant, and the other varying [I – ] while holding [H2O2] constant. The exponent p will be determined in the first set of runs, since holding the I – (aq) concentration constant focuses attention on the effect of [H2O2]. The situation will be reversed in the second set of experiments, leading to the determination of the exponent q. The initial rate (which we shall now refer to as the rate) will be determined by measuring the change in pressure of the oxygen gas that is formed over a five minute period. Using a gas pressure sensor and the Vernier system, you will obtain data similar to the following: Figure 1 Since the change in partial pressure of the oxygen, ∆PO2, is proportional to its change in concentration, ∆[O2], then we can write the reaction rate can be expressed as: 3 Rate = Δt ΔPO2 (4) The slope of the linear part of the curve between 50 and 100 seconds in Figure 1 is, to a good approximation, the rate of the reaction. Combining equation 3 and 4, we can write the rate law as: Rate = Δt ΔPO2 = k[H2O2] p [I – ] q (5) The effect of a reactant’s concentration on the reaction rate can be found by varying its concentration in several repetitions of the reaction. In the first set of experiments, we will use varying initial concentrations of H2O2, but the use same amount of I – for each determination, thus keeping [I – ] constant. Since the reaction order with respect to iodide, q, is a constant, [I – ] q will be constant for this set of reactions. This allows us to simplify Equation 5 even further: Rate = k’ [H2O2] p (where k’ = k [I – ] q ) (6) It is useful to take the natural logarithm of both sides of Equation 6, to give: ln(Rate) = p ln[H2O2] + lnk’ (7) Equation 7 has the form of the equation of a straight line, y = m x + b. A plot of ln(Rate) on the y-axis versus ln[H2O2] on the x-axis will yield a straight line of slope p, which is the order of the reaction with respect to hydrogen peroxide. Using the same type of procedure with constant [H2O2], we can obtain the same type of information for [I – ] and q. The equations that would apply are: Rate = k” [I – ] q (where k” = k [H2O2] p ) (8) ln(Rate) = q ln[I – ] + lnk” (9) For these experiments, a plot of ln(Rate) versus ln[I – ] should give a line having a slope equal to the order of the reaction with respect to iodide, namely q. SAFETY/HYGIENE/WASTE DISPOSAL 1. As always wear your goggles! 2. Caution: concentrated acids are corrosive. You should wear gloves and be sure your skin is not exposed. Discard the gloves after use, and wash your hands. Acid exposure may result in an itchy sensation. If you have any sensation of itching, burning, or tingling, thoroughlyflush the area with water. Inform your lab instructor while flushing the area should you experience any of the symptoms listed. Don’t wait until several minutes have passed. 3. Never raise containers of solution, especially corrosive solutions, to eye level or above. In particular, avoid this when filling a buret. 4 4. Never weigh chemicals directly on a balance pan. Use weighing paper, glassware, or other secondary container. 5. Waste solutions from this experiment should be disposed of in a designated container. PROCEDURE Your lab instructor will divide the class into pairs. Equipment and Chemicals Provided in Lab:  Vernier Lab Quest computer interface  gas pressure sensor  black stopper assembly  plastic tubing with one connector  125-mL Erlenmeyer flask  small beakers  graduated cylinder  thermometer  ring stand and utility clamp  stirrer/hot plate  stir bar magnet  burets filled with 0.880 M H2O2(aq) (prepared by diluting 90.0 mL of 30% H2O2 to 1 L)  burets filled with 0.500 M KI(aq) (prepared by dissolving 83.00 g of KI in 1 L of DI water) 1. Connect the gas pressure sensor to Channel 1 of the Vernier LabQuest computer interface (which will now be referred to as LabQuest). The pressure (kPa) should be displayed in a box on the LabQuest screen. The value will fluctuate a little. If you do not see a pressure reading displayed, consult your lab instructor. 2. Check the following settings (in upper right of the screen): Mode: Time Based Rate: 5.0 samples/s Length: 300.0 s If you need to change the settings, follow the procedure that you used in previous experiments. 3. Assemble the apparatus as shown in Figure 2 below. Use the clear tubing to connect the black rubber stopper to the gas pressure sensor; about one half turn of the fittings will secure the tubing tightly. Twist the black stopper snugly into the neck of the Erlenmeyer flask (which should be clean) so as to avoid losing any of the oxygen gas that will be produced. The flask should not contain any solutions at this stage, only the bar magnet. 5 4. Using the volumes shown in the table below for Run 1, dispense the required amount of H2O2 and KI solutions from the burets into separate small, dry beakers. Measure the volume of DI water required using a graduated cylinder. Let the solutions sit for a few minutes so that they will come to the same temperature. Since the solution were prepared in advance there temperatures should had a chance to equilibrate, that is the temperatures difference should be within 1 C of each other. It is advisable to construct a table in your lab notebook similar to that shown below and with an additional column for rate (see Data Sheet). Run Volume H2O2(aq), (mL) Volume KI(aq), mL Volume water, mL 1 10.00 5.00 45.0 2 15.00 5.00 40.0 3 20.00 5.00 35.0 4 5.00 10.00 45.0 5 5.00 15.00 40.0 6 5.00 20.00 35.0 7* 10.00 5.00 45.0 *For Run 7, add a small amount (tip of the spatula) of iron(III) chloride hexahydrate (FeCl3•6H2O) to the water. 5. Remove the black stopper from the flask and add the water. Adjust the dial so that the bar magnet stirs at a moderate speed. 6. Add the H2O2 solution followed by the KI solution and replace the stopper securely in the flask. Why do you think the solution turns a yellow color? Start collecting pressure data by tapping the green arrow on the lower left of the screen with the stylus. The pressure may fall slightly before it starts to increase. If the pressure exceeds about 120 kPa the stopper may pop off (which can be prevented by holding down the stopper). This is OK as long as the curve has a linear portion and data has been collected for at least 200 seconds. 7. After Run 1 has finished you have to determine the rate of the reaction. The screen may look something like this. If your graph is not scaled like this, choose the Graph Option in the menu bar and tap on Autoscale Once. Note that in this case the pressure suddenly dropped because the pressure approached 120 kPa and the stopper popped off! Place the stylus on the screen at the lower end of the linear portion and then drag to the upper end, then release (this is similar to using a mouse to highlight text or a figure on a computer). Then tap the Analyze menu and select Curve Fit and tap the box next to Pressure. From the Choose Fit Equation menu, select Linear. The equation of the straight line, y = mx + b, should appear followed by the values of m and b. Record the value of the slope (m) in your lab notebook. This value is equal to the rate of the reaction. 6 8. Remove the black stopper from the flask and empty the solution into the appropriate waster container. 9. Repeat steps 4 – 8 for Runs 2 – 7. Before starting a new Run, you should tap the file cabinet icon (next to the box that reads Run 1) with the stylus. This will create a new graph for the new Run. Note that Run 7 is the same as Run 1 with a small amount (tip of the spatula) of iron(III) chloride hexahydrate, FeCl3•6H2O, added to the water. 10. Rinse out all of the glassware and return it to the bench. Disconnect the tubing from the black stopper and the gas pressure sensor. 11. Delete any stored data from the computer interface by tapping the “File” menu with the stylus and selecting “New”. The LabQuest should be left turned on for the next lab section. If the lab is scheduled to end at 4:50 PM or 8:20 PM then the LabQuest should be turned off by pressing the silver button on the top left of the device. 12. Hand in a copy of your data (recorded in your lab notebook) to your lab instructor. 7 CALCULATIONS AND RESULTS When working with reactions that occur in solution, the concentration of the stock solution is defined as the initial concentration before mixing (BM), upon mixing the initial concentration will change because of dilutions. The concentration after mixing depends on the volume of the reaction mixture. In Run 1 the [H2O2]BM = 0.880 M, and the initial volume is 10.00 mL. When all the chemicals are mixed the final volume of the reaction mixture will be 60.0 mL. What we need to determine in this experiment are the initial concentrations of the reaction components after mixing, [H2O2]AM. To determine the concentration after mixing we will use the dilution equation, M1V1 = M2V2, where 1 is the initial values before mixing and 2 are the initial values after mixing. The concentration of hydrogen peroxide after mixing is calculated in the following way: M1V1 = M2V2 [H2O2]BM V1 = [H2O2]AM V2 (0.880 M) x (10.00 mL) = [H2O2]AM x (60.0 mL) [H2O2]AM = 0.147 M For each run you will have to calculate the concentrations of H2O2(aq) and I (aq) after mixing using the method described above. You will estimate the values for p and q using the data in your rate table. At home you will use Excel to plot your data and verify the values of p and q which were estimated in lab. The orders of the reaction, p and q, are found by plotting graphs of ln(Rate) on the y-axis versus the natural log of the concentration of one of the reactants (after mixing) on the x-axis. The slope of the straight line will be the order of the reaction with respect to that reactant. Runs 1 – 3 will yield the value of the order in hydrogen peroxide (p), since the concentration of the iodide was held constant. Runs 4 – 6 will yield the value of the order in iodide (q), since the concentration of the hydrogen peroxide was held constant. Calculating the rate constant, k, is straightforward. Once you have the values for p and q, and the concentrations of both reactants after mixing for Runs 1 – 6, substitute them into Equation 5. The values of k should be about the same for each run, and an average value should be calculated. You should think carefully about the units for k. In Run 7, a small amount of an additional catalyst, FeCl3•6H2O, was used. You should be able to calculate k for Run 7 and compare it with the average value for Runs 1 – 6. You should be able to conclude something about how this catalyst affects the rate of the reaction. 8 DATA SHEET Complete the following table: Run [H2O2]AM, mol/L [I  ]AM, mol/L ln[H2O2]AM ln[I  ]AM Rate, kPa/s ln(Rate) 1 2 3 4 5 6 7 Show how you calculated [H2O2]AM and [I  ]AM for Run 2: Using your rate table you now will approximately determine the values for p and q. Each member within the group will do one set of calculation shown in the table below. You will then compare your values for p and q to determine if your runs are consistent. The table below indicates which pairs of run can be used to determine the values of p and q. Runs Runs Runs p 1 & 2 1 & 3 2 & 3 q 4 & 5 4 & 6 5 & 6 To determine the order for H2O2, the value for p, using run 1 and 2 To determine the order for [I ], the value for q, using run 4 and 5 Order in hydrogen peroxide _____ Order in iodide _____ (value of p to nearest whole number) (value of q to nearest whole number) To verify your values for p and q calculated above, you will plot two graph, using Excel. The first graph will be a plot of ln(Rate) vs. ln[H2O2]AM using data from runs 1 through 3 in which the iodide concentration was held constant. The second graph will be a plot of ln(Rate) vs. ln[I  ]AM using data from runs 4 through 6 in which the hydrogen peroxide concentration was held constant. Use the “Add Trendline” feature to draw the best straight line through the data points for each graph. The equation of the line as well as the R2 value should appear on your graph. Based on the discussion on page 3 the slope of the best fit line represents the order of reaction for each component ([H2O2]2/[H2O2]1)p = R2/R1 n p = m p = ln(m)/ln(n) ([I ]5/[I ]4) q = R5/R4 n q = m q = ln(m)/ln(n) 9 POST-LAB EXERCISES 1. Calculate the value of the rate constant, k for Runs 1 – 6. Show a sample calculation for Run 2. Determine the average value of k. What are the units of k? Run k 1 2 3 4 5 6 Ave. 2. Compare the rate of Run 1 with that of Run 7. How much faster does the reaction occur when a small amount of iron(III) chloride hexahydrate is present compared to the reaction without this compound? What is the role of the iron(III) chloride hexahydrate, i.e., why does it affect the rate of the reaction? 3. Suppose we were able to measure the amount of oxygen gas formed in units of moles/L, and the rate of formation of oxygen was found to be 0.0125 M/s. a. Using the rate law for this reaction and the units associated with each variable, show what the derived units for the rate law constant would be. (b) What would be the rate of decomposition of the hydrogen peroxide? Explain your answer. Name: _________________________ Lab Day: M T W R F Instructor: __________________ Room: 103 109 117 125 Lab Time: __________________