# THE DETERMINATION OF THE RATE EQUATION FOR A REACTION

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1 THE DETERMINATION OF THE RATE EQUATION FOR A REACTION In this experiment you will study the reaction of Hydrogen Peroxide and Iodide ion given by the following equation: 2 I H 1+ + H 2 O 2 I H 2 O Eqn. 1. If the above equation is a correct and complete expression for the reaction, then we must experimentally determine if the rate of the reaction depends on the concentration of either iodide ion or peroxide or both. Assume the rate does not depend on the hydrogen ion concentration. If we write an expression for the rate equation for this reaction as follows: the objective is to determine: Rate = k [H 2 O 2 ] a [I 1- ] b a. if both peroxide and iodide ion are needed in this rate reaction. b. the value of the exponents a. and b. in the reaction equation. In order for this experiment to be successful, various conditions must be fulfilled: 1. The acidity must remain constant. We do this by using a Sodium Acetate-Acetic Acid buffer. This is the reason hydrogen ion does not appear in the expression for the rate equation. It remains essentially constant during the reaction. 2. The reverse reaction must be suppressed. To do this we add Sodium Thiosulfate which reacts with the Iodine formed as shown by the following reaction: I S 2 O I 1- + S 4 O 6 2- Eqn. 2 As long as excess thiosulfate ion is present, no free iodine can accumulate and the reaction can not go in the reverse direction. 3. We must be able to accurately measure the rate. The mechanism of the reaction is as follows: a. Iodide ion reacts with peroxide to form Iodine (I 2 ). b. The iodine so produced reacts with thiosulfate to form Iodide ion, and the solution remains colorless. c. Eventually all the thiosulfate is used and free Iodine accumulates. d. The free Iodine now reacts with the starch to give the solution a blue-black color which is easily detected. Page 1

3 PROCEDURE Students are to work in pairs using 2 beakers 250 ml or larger. CLEANLINESS IS VERY IMPORTANT. MANY SUBSTANCES CATALYZE THE DECOMPOSITION OF HYDROGEN PEROXIDE: The following solutions are prepared in a 250 ml beaker: Water Buffer 0.3 M KI starch M Na 2 S 2 O M H 2 O ml 5 ml 1.5 ml 10 drops 5 ml 5 ml ml 5 ml 3.0 ml 10 drops 5 ml 5 ml ml 5 ml 5.0 ml 10 drops 5 ml 5 ml ml 5 ml 5.0 ml 10 drops 5 ml 10 ml ml 5 ml 5.0 ml 10 drops 5 ml 20 ml Mix the first five reagents in a 250 ml beaker measuring the KI and thiosulfate with the pipettes provided for their dispensing. Measure from the pipette directly into your 250 ml beaker. Place the beaker on a piece of white paper. Pour 100 ml of the peroxide solution into a beaker and take it to your bench. Add the peroxide solution to the solution prepared in the 250 ml beaker, record the starting time*, and stir the solution thoroughly. Do not remove the stirring rod. It is not necessary to stir the solution after this point. Watch for the appearance of the first blue color to the solution. Record the time of the color appearance. Since several minutes will be required for Solution #1 to react, proceed immediately to Solution #5. This solution will react fairly rapidly and will permit you to observe the color change. After a reaction goes to completion, discard the solution, rinse the beaker with tap, then distilled water and shake dry. Do not wipe with towels or use air. With the clean beaker, not dry, move on to Solution #4. Do the remaining solutions in reverse order. This will permit you to have one beaker free at all times to prepare a new solution. The only data obtained in this experiment is the total time required to observe color changes. Measure this as accurately as possible, to the nearest second. *Use the pipette provided for the addition of the peroxide. Start timing as soon as the first drop of peroxide enters the solution. Page 3

4 DATA Solution Number Start Time Finish Time Elapsed Time No. 1 - Trial 1 No. 1 - Trial 2 No. 2 - Trial 1 * No. 2 - Trial 2 * No. 3 - Trial 1 No. 3 - Trial 2 No. 4 - Trial 1 No. 4 - Trial 2 No. 5 - Trial 1 No. 5 - Trial 2 *Use your thermometer as a stirring rod in this set and record the temperature of the solutions. (For this set of reactions only.) Page 4

5 Determination of the Energy of Activation for this reaction I. Effect of a Catalyst on the reaction rate PROCEDURE Prepare a reaction mixture equivalent to one of the solutions prepared above. Add 2 drops of 0.10 M Cu(NO 3 ) 2 solution, a catalyst, and then add the peroxide solution. Record the time of the peroxide addition and the time upon blue color formation. Compare the elapsed time for this reaction with the time necessary for the uncatalyzed reaction. This reaction is to be run at room temperature. Start Time Finish Time Elapsed Time Elapsed Time for Uncatalyzed Reaction II. Effect of Temperature on the Reaction Rate In general, the rate of a reaction doubles for every ten degree rise in temperature. We are going to examine this statement, and from the results, calculate the Energy of Activation for the reaction under consideration. PROCEDURE Prepare a reaction mixture equivalent to the solution prepared in reaction (2) on the previous experiment. Do not add the peroxide at this time. Using your hot plate, heat the reaction solution, minus the peroxide*, to a temperature approximately 10 degrees above the temperature previously measured. When a constant temperature has been obtained add the 5 ml portion of peroxide, stir briefly with your thermometer and record the time. Record the time for the formation of the first permanent blue color. Record the temperature of the reaction. Start Time Finish Time Elapsed Time Temperature *Heat the peroxide solution separately from the reaction solution. Page 5

6 CALCULATIONS Note: Use Excel to complete all the calculations. All plots should be printed to the laser printer. The template containing the calculations should be saved under the name PEROX. Excel functions should be used to determine the slope and the intercept of all linear plots. 1. Calculate the molarity of the KI and H 2 O 2 in each solution. The final volume is 100 ml for each solution. 2. Calculate the number of moles of Na 2 S 2 O 3 initially present in each solution. This will be constant for all solutions. 3. From Equation 2. on the first page of the experiment calculate the number of moles of free Iodine (I 2 ) with which the above amount of Na 2 S 2 O 3 will react. This will be constant for all solutions. 4. From Equation 1. on the first page of this experiment calculate the number of moles of H 2 O 2 that must be reduced to form the amount of I 2 calculated in step 3. This will be constant for all solutions. 5. Convert the elapsed time into minutes, to two decimal places, and, if more than one trial was obtained, calculate an average time. 6. Calculate the rate of the reaction for each solution in the experiment in terms of moles of H 2 O 2 consumed per minute. 7. Construct a table of your results with the following headings: Reaction Number Initial [KI] Initial [H 2 O 2 ] Rate of Reaction 8. Construct another table of results by taking the log of the above quantities: Reaction Number Log Initial [KI] Log Initial [H 2 O 2 ] Log Rate of Reaction Be neat on the above tables. These will be turned in as part of your report. 9. Using Excel to plot Log Rate along the y-axis against Log [KI] along the x-axis*. Use Excel functions to calculate the slope and the intercept of this line. The slope of this line is equal to the value of exponent "b" in the rate equation. Round the slope to the nearest integer. The intercept is equal to Log K app. Using the relationships derived on the next page, calculate a value for the rate constant k from Log K app. Use the data from reactions 1, 2 and 3 for this plot. Page 6

7 Starting from a general statement of the rate law for this reaction: Rate = k [H 2 O 2 ] a [KI] b For solutions 1, 2, and 3, [H 2 O 2 ] is constant Therefore: Let K app = k [H 2 O 2 ] a After substituting: Rate = K app [KI] b Take the logarithm of the equation: log Rate = log K app [KI] b Separate the terms being multiplied: log Rate = log K app + log [KI]b Remove the exponentiation: log Rate = b log [KI] + log K app The general equation for a straight line is: y = mx + B Defining: y = log Rate m = b (slope) x = log [KI] B = log K app (intercept) Thus "b" and B can be determined by plotting log [KI] on the x-axis vs. log Rate on the y- axis for solutions 1, 2, and 3, and drawing the best possible straight line through the data. The exponent "b" is equal to the slope of the line, and log K app is the intercept. The rate constant k can be calculated from K app by recalling the definition of that variable. 10. Using Excel plot Log Rate along the y-axis vs Log [H 2 O 2 ] along the x-axis* Use Excel functions to calculate the slope and the intercept of this line. The slope of this line is equal to the value of "a" in the rate equation. Round the slope to the nearest integer. The intercept is equal to Log K app. Using relationships for Log K app similar to those derived above for Log K app, calculate a value for the rate constant k from Log K app. Use the data from reactions 3, 4, and 5 for this plot. A derivation similar to that done above may be performed for the determination of the exponent "a". You should derive the relationships between k, K app and "a" for yourself. Page 7

8 11. Using the values of "a" and "b" obtained above, the rate expression on the first page of the experiment and your data from the table in step 7 above, calculate a value for the rate constant k for each solution. 12. Using the results of step 11, above calculate an average value for the rate constant k and compare this value of k to the value of k obtained from the plots in steps 9 and 10 above. Note: Sometimes the values for the rate constants k obtained in steps 9, 10 and 11 do not agree as much as they should. Ideally they should all be the same! This variation can be an artifact of the rounding done in steps 9 and 10 in determining the values of "a" and "b", particularly if that round-off was large. It may be necessary to do the calculations of k in steps 9, 10 and 11 twice, once using rounded values for "a" and "b", and a second time using unrounded values of "a" and "b" to get consistent values for the rate constant k. Be sure to comment in your report on the agreement between the values of k, and whether rounded or unrounded values of "a" and "b" gave the more consistent results. 13. Write a completed expression for the rate of reaction for this reaction. For a value for k use the average of the three determinations. * In these two graphs, the x-axis must start at zero; the y-axis does not need to start at zero. 1. Table I: 2. Table II: REPORT FORM Rate of Reaction Reaction Number Initial [KI] Initial [H 2 O 2 ] Rate of Reaction Reaction Number Log Initial [KI] Log Initial [H 2 O 2 ] Log Rate of Reaction Page 8

9 3. Calculate the slope of the line plotted in calculation step 9. Round off to the nearest integer. This is the value of exponent "b" in the rate equation. 4. Calculate the slope of the line plotted in calculation step 10. Round off to the nearest integer. This is the value of exponent "a" in the rate equation, 5. Calculate the value of the specific rate constant k from the y-intercept of the line plotted in calculation step 9. The value of the y-intercept equals Log K app. The relationship between K app and k was derived earlier. 6. Calculate the value of the specific rate constant k from the y-intercept of the line plotted in calculation step 10. The value of the y-intercept equals Log K app. The relationship between K app and k was derived earlier. 7. Calculate an average value for the specific rate constant k from the 5 different values calculated in calculation step Calculate an average value of the specific rate constant k using the values calculated in steps 5, 6, and 7 of this report. 9. Write the complete rate of reaction expression for this reaction. 10. Calculate the Energy of Activation, E a, for this reaction. Using the time and temperature data obtained in the two reactions that involved measuring the solution temperature and the equation below calculate the Energy of Activation for this reaction. Given the following equation: log (time 1 /time 2 ) = (E a /2.303R)[(T 2 -T 1 )/T 1 xt 2 ] where T 2 represents the higher temperature in K, T 1 represents the lower temperature in K, time 2 is the time, in minutes, for the reaction at the higher temperature, and time 1 is the time, in minutes, for the reaction at the lower temperature, and R is the Ideal Gas Constant expressed as value 1.99 cal/ K. Page 9

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