Determining the Rate Law for a Chemical Reaction

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1 Determining the Rate Law for a Chemical Reaction Purpose: To determine the reaction orders, rate law, and rate constant for the reaction between persulfate ions, SO8 -, and iodide ions, I - Introduction Chemical kinetics is the study of rates and mechanisms of chemical reactions. Reaction rate refers to the change in concentration of a chemical species with time. A reaction mechanism is an exact sequence of steps by which an overall chemical change takes place. Reaction rate can often be determined by monitoring the disappearance of a reactant with time, or the appearance of a product with time. The rate of a reaction depends on the concentrations of the reactants in the reaction. In general, the lower the reactant concentrations are, the slower will be the rate, and the higher the concentrations, the faster the rate. The exact way in which the reaction rate varies with reactant concentrations is described fully by the rate law, which expresses mathematically the rate of reaction in terms of reactant concentrations raised to certain powers, called reaction orders. For the hypothetical equation aa + bb cc + dd (eq. ) in which a, b, c, and d are the stoichiometric coefficients, we can state that Rate [A m [B n (eq. ) where m and n are the order of reaction with respect to a given reactant. In order to eliminate the proportionality sign and replace it with an equality, we simply add a proportionality constant k, called the rate constant. Rate = k[a m [B n (eq. 3) This is the rate law for the reaction given in equation. We say that m is the order of reaction with respect to A, and n is the reaction order with respect to B. It is important to recognize that the reaction orders are not necessarily equal to the coefficients a and b. The reaction orders must be determined experimentally, they can NOT be determined any other way. In the rate law, the rate constant k is constant for a given reaction at a given temperature, but does change when the temperature changes. More on that next week The purpose of this week s experiment, then, is to determine reaction rates with various starting concentrations of reactants, and from that determine the orders of reaction with respect to all reactants and then calculate the rate constant for the reaction. This information will then provide the complete rate law for the reaction studied.

2 The Reaction The reaction you will examine in this experiment is that between persulfate ions, SO8 -, and iodide ions, I -, in aqueous solution. The net ionic equation for the primary reaction is SO8 - (aq) + 3 I - (aq) SO4 - (aq) + I3 - (aq) (eq. 4) The source of reactant ions in this case will be ammonium persulfate, (NH4)SO8, and potassium iodide, KI. Both are soluble salts, so the ammonium ions (NH4 + ) and potassium ions (K + ) are spectator ions and do not participate in the reaction. The difficulty with determining the rate of this reaction is that all species are colorless in solution, so it would normally be impossible to monitor concentration changes effectively and thus determine when the reactants were completely consumed. To eliminate this problem, you will add starch solutions to each of the reaction mixtures. As soon as the triiodide ion, I3 - (produced in equation 4), reaches an appreciable concentration, it will react with any starch present to form a deep blue colored complex. To prevent the solutions from immediately turning blue, thiosulfate ions, SO3 -, will be added to react with the triiodide ions, I3 - produced in equation 4 and thus prevent the triiodide from reacting with the starch to form the blue colored complex until all the thiosulfate ions are consumed. SO3 - (aq) + I3 - (aq) S4O6 - (aq) + 3 I - (aq) (eq. 5) In this way, the thiosulfate ion, SO3 -, acts as a sort of chemical stopwatch since the blue color cannot form until all the thiosulfate is consumed and the triiodide ion concentration can then build up very quickly, reacting with starch to form a dark blue color. As long as thiosulfate is present the blue color cannot form, but as soon as the thiosulfate is consumed completely the blue color forms immediately. In this experiment, the amount of thiosulfate ion, SO3 -, will be constant for each determination that is performed, so the faster the reaction rate the more quickly the thiosulfate will be consumed and the sooner the blue color forms. You will thus monitor the reaction time as the time required for the appearance of the blue complex signaling the disappearance of thiosulfate ion. Reaction Rate Determination The rate of reaction can be expressed as the change in concentration of a reactant in the principal reaction (eq. 4) such as persulfate, SO8 -, divided by the change in time in which that concentration change occurred; Rate = - - change in SO 8 concentration elapsed time (eq. 6)

3 3 Rate = - - Δ[SO 8 Δt (eq. 7) Notice the negative sign in the rate expression in equations 6 and 7, indicating the disappearance of a reactant and thus a decrease in concentration. In order to get the change in persulfate ion concentration [SO8 - in eq. 7 we will need to start with the knowledge of the amount of thiosulfate ion, SO3 -, consumed, and use stoichiometry to convert that to the amount of persulfate consumed. Since the volume and concentration of thiosulfate added will be constant for all determinations (.00 ml of. x 0 - M NaSO3), so will the number of moles of thiosulfate be constant for ALL trials; moles SO3 - = (.0 x 0-3 L)(. x 0 - M) =.4 x 0-5 moles SO3 - for ALL trials. Thus the number of moles of persulfate consumed is constant for all trials also; mole I moles S O 8 =.4 x 0 moles S O 3 x moles S O - 3 x mole S O - 8 =. x 0-5 moles S - mole I - O 8 3 conversion factor from eq. 5 conversion factor from eq. 4 Since the total volume of the reaction mixture will be 9.0 ml for all determinations, the change in the persulfate concentration for all determinations is; [SO8 - = -. x 0-5 moles = -6.3 x 0-4 M SO8 - (eq. 8) L Note that the change in concentration is negative since persulfate is a reactant whose concentration diminishes with time. Therefore the rate may be calculated as; Rate = - Δ[SO 8 - = Δt (-6.3 x 0 M SO 8 ) Δt for ALL trials Rate = x 0 M t (eq. 9) where t = elapsed time from mixing of reactants to appearance of blue color. Equation 9 is thus used to calculate the reaction rate for all determinations performed in this experiment.

4 4 Determining Reaction Orders You will use the method of initial rates to determine reaction orders for the reactants in this experiment. The assumption is that the amounts of reactants consumed in the timed interval are small compared to the total concentration of those reactants present in the reaction mixture, and therefore the reaction rate is constant during that time. So it is the initial rate of reaction that is being measured. The rate law for this reaction is of the form Rate = - Δ[SO 8 - Δt = k[so8 - x [I - y (eq. 0) Using subscripts to denote determination number yields Rate = k[so8 - x [I - y for determination, and Rate = k[so8 - x [I - y for determination Dividing the first equation by the second gives Rate = k [S O [I Rate = k [S O [I - x - y 8 - x - y 8 (eq. ) If the experiment is designed such that the concentration of iodide ion is the same for determinations and (as they are in this experiment), these concentration terms will cancel, as will the rate constants, since rate constant is constant for a given reaction at a given temperature; Rate = k Rate = k [S O [I - x - y 8 - x - y [SO 8 [I (eq. ) which reduces to Rate = [S O Rate = [S O - x 8 - x 8 (eq. 3) - x - Rate [SO 8 [SO 8 = - x = - Rate [SO 8 [SO 8 x (eq. 4) Or more simply, - Rate [SO 8 = - Rate [SO 8 x (eq. 5)

5 5 Since both concentrations can be calculated from molarity and volume used, and both rates will be calculated using equation 9, the only unknown in equation 5 is x, the order of reaction with respect to persulfate ion. A similar calculation using determinations in which the persulfate concentration remains constant as the iodide ion concentration is varied (e.g. determinations 3 and 4) will allow derivation of the analogous equation for calculating y, the order of reaction with respect to iodide; Rate [I Rate [I = y (eq. 6) Mathematical note: In order to solve an equation like eq. 5 or eq. 6, you must use logarithms to solve for x. Remember that log a m = m log a. This identity allows isolation of the unknown m (or x in eq. 5, or y in eq. 6), which is the exponent that corresponds to the reaction order. You will need to use this relationship in calculating reaction orders in this experiment, as well as in the post-lab questions. Determining the Rate Constant If the reaction rates, reactant concentrations, and reaction orders are all known, then it is a simple matter of solving equation 0 for the rate constant, k, using data from any of the determinations that you have done. Rate = k[so8 - x [I - y (eq. 7) Theoretically, all determinations should give the same value for k, but experimental variations will produce some slight differences. However, all determinations should have rate constants that are fairly close to one another. Procedure SAFETY NOTE!! The reagents used in this experiment are irritants. Avoid contact with your skin, eyes, and clothing. If you do spill some on yourself, wash immediately with cold water. Notify your instructor.

6 6. You will need four burets, a ml pipet and a ml pipet to measure the solutions to be used in this experiment. See Tables and for the solutions and amounts to be used. It is imperative that you clearly label each of the burets with the contents so as not to combine the solutions incorrectly. After labeling each buret, rinse the buret several times with small (~-3 ml) portions of the solution with which you will fill the buret. Be sure you rinse through the buret tip, too. Then add enough solution to the buret to carry out all four determinations. That will vary depending on the solution. Make sure there are no air bubbles in the buret tip before starting the titration. Make sure all your buret readings are read to the nearest 0.0 ml; that is, to two digits to the right of the decimal point. Use the blue pipet pumps to deliver the starch and sodium thiosulfate solutions to flask A.. Prepare two 50 ml Erlenmeyer flasks, labeled Flask A and Flask B, with the solutions indicated in Table for determination. Once both flasks are prepared, record in Data Table 4 the room temperature and you are ready to perform determination. Be sure to use precisely the volumes specified in Tables and. 3. This step requires teamwork. One of you will operate a stopwatch while the other mixes the contents of Flasks A and B. As the person mixing begins to pour the contents of one flask into the other, the person doing the timing watches carefully, and starts the stopwatch when about half the liquid in the first flask has been transferred to the second flask. Once all the liquid from both flasks has been combined into one flask, the person mixing pours all the liquid back into the first flask, then pours it all back into the second flask in order to completely mix the solutions. After three such pourings, the reaction flask can be set down and watched carefully. The person timing should stop the stopwatch as soon as the color of the reaction mixture changes from colorless to deep blue. Record the reaction time on Data Table. NOTE: Be very careful in reading the stopwatch. The stopwatch gives you a time in minutes and seconds; thus a time of :7 is NOT.7 minutes, but rather it is minute and 7 seconds, or 87 seconds. 4. Repeat determination until two successive trials give reaction times within 0% of each other. For example, if the reaction time was 80 seconds, 0% of 80 is 8 seconds, so the times should be 80 ± 8 seconds. So in that example, the range of allowed times for the second trial would be from 7 to 88 seconds. Record all times on Data Table. 5. Repeat step 3 for determinations and 3. (NOTE that determinations and 4 are identical; just transcribe data for determination into the spaces for determination 4 on the table.) Do at least two trials of each determination such that the times are within 0% of each other. Record all data on Data Table. 6. Before cleaning your burets, show your data to your instructor to confirm that the results are satisfactory. If yours is not the last section of the lab this week, cover the tops of the burets with parafilm and leave the solutions in them for the next class. If yours is the last section of the lab this week, rinse your burets thoroughly (including the

7 7 tip) with lots of water and store them in the buret stands upside down with the stopcocks open. All waste from this experiment can be poured down the drain along with lots of water. determination number Table - Determining the Effect of SO8 - Concentration on Reaction Rate FLASK A FLASK B starch,.x0 - M ml NaSO3, 0.0 M 0.0 M 0.0 M (use ml (NH4)SO8, KI, ml KNO3, ml ml (use ml ml pipet) pipet) 0.0 M (NH4)SO4, ml determination number Table - Determining the Effect of I - Concentration on Reaction Rate FLASK A FLASK B starch,.x0 - M ml NaSO3, 0.0 M 0.0 M 0.0 M (use ml (NH4)SO8, KI, ml KNO3, ml ml (use ml ml pipet) pipet) 0.0 M (NH4)SO4, ml Calculations. Calculate the initial concentration of iodide ions for each determination, and record them on Data Table. Initial here means at the moment the solutions are mixed but before any reaction has taken place. So this is, in effect, a dilution calculation. For example, in determination, you have taken 4.00 ml of 0.0 M KI and diluted it to a total volume of 9.00 ml. (Note that the total volume for all six determinations is 9.00 ml.) You can use the dilution formula MV = MV (eq. 8) to calculate the initial concentration M at the moment of mixing, where M and M are the undiluted and diluted molarities, and V and V are the undiluted and diluted volumes, respectively.

8 8. Calculate the initial concentration of persulfate ions for each determination using volumes and concentrations of (NH4)SO8 along with equation 8. Record these initial concentrations on Data Table. 3. Calculate the average reaction time for each of the four determinations, and record on both Data Table and Data Table. 4. Calculate the reaction rate for each determination using equation 9. Use your average reaction times for t in equation 9. Record the rates on Data Table, including correct units with your rates. 5. Using your data for determinations and, calculate the reaction order with respect to persulfate ion by solving for x in equation 5. Calculate x to two digits to the right of the decimal point by taking the logarithm of both sides (see mathematical note on page 3. Record the results on Data Table Using your data for determinations 3 and 4, calculate the reaction order with respect to iodide ion by solving for y in equation 6. Calculate y to two digits to the right of the decimal point. Record the results on Data Table Using equation 7, calculate the rate constant, k, for each of the four determinations. Record your results on Data Table 4. Be sure to include correct units with your rate constants. 8. On the bottom line of Data Table 4, write the complete rate law for the reaction you studied in this experiment. Include the average of your calculated values for the rate constant, k, and your reaction orders rounded off to an integer.

9 9 Determining the Rate Law for a Chemical Reaction Data Table Reaction Times (s) determination trial trial trial 3 average time (s) 3 4 Data Table determination initial [SO8 - initial [I average time (s) rate (include correct units)

10 0 Determining the Rate Law for a Chemical Reaction Data Table 3 Reaction Orders (x is order for SO8 -, y is order for I - ) determinations used x determinations used y and 3 and 4 Data Table 4 determination 3 4 Rate Law: rate constant, k (include correct units) at o C

11 Determining the Rate Law for a Chemical Reaction Post-lab Questions. Using the method of initial rates for determining reaction orders, a student finds that 0.76 =.73 x 0.4 where x represents the reaction order with respect to a given reactant. Calculate the value of the reaction order x to two decimal places. Show your calculations.. For the reaction X + Y + Z Products, the following data were obtained. (HINT: Reaction times are inversely proportional to reaction rates.) exp. no. [Xo [Yo [Zo reaction time (s) Determine the rate law, including reaction orders with respect to all reactants, and show how you obtained the reaction orders.

12 Determining the Rate Law for a Chemical Reaction Pre-laboratory Assignment. For the reaction A + B + C Products, the following data were obtained; exp. no. [Ao [Bo [Co initial rate (Ms - ) a) Show work to calculate or explain the reaction orders with respect to all reactants b) Show calculations to determine the rate constant k, including units.. Provide the name and formula for the two reactants in this experiment. Reactant Reactant chemical compound name ion formulas stock solution [M a) Do Calculations and explained on page 7. Record the initial concentration values in the appropriate spaces in Data Table. b) Show calculations for the initial concentration of potassium iodide in Det. 3. Last revised 8//07 DN c) Show calculations for the initial concentration of ammonium persulfate in Det..

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