we might also expect the reaction rate to be influenced by ph. In fact, the rate has been reported to follow the rate law:

Transcription

1 KINETICS Objective: The objective of this lab is to measure the rate of iron oxidation, to determine the order of the reaction, and thereby to gain familiarity with rate laws in both the differential and integrated forms. Background You have been exposed to the standard rate laws (zero order, first order, second order) many times. Hopefully, you are already familiar with the differential and integrated forms of these rate laws. Perhaps you have wondered how it is that all the myriad reactions that occur really follow such simple mathematical formulations. In reality, they often do not. In this lab, we will study the oxidation of Fe(+) by oxygen in aqueous solution at circumneutral ph. The two half-reactions involved are: Fe Fe + + e - ¼O + H + + e - ½ H O Electron transfer reactions occur either directly between the oxidant and reductant (inner sphere reactions), or at most between redox partners coordinated in an outersphere complex. The first step, therefore, is for Fe and O to come together in solution. Because Fe exists primarily as the free aquo ion at near-neutral (i.e., circumneutral) ph, the oxygen molecule must displace a water molecule in the solvation shell. A single Fe atom can only transfer one electron to the dioxygen molecule; this forms superoxide anion (the pk a is.88) in which the oxygen atoms are bound by only a single pair of electrons, one oxygen atom has one unpaired electron, and the other has all paired electrons and a net negative charge (see figure below). Superoxide must then separate from the Fe + atom which, because of its high charge density now pulls the water molecules in the solvation shell closer and causes some of them to deprotonate (Fe(OH) + is the dominant species at circumneutral ph). The superoxide must find another Fe atom, enter the solvation shell, gain a second electron, break away and grab a proton from the solvated water molecules to form H O (hydrogen peroxide). Some of the hydrogen peroxide will disproportionate to form H O and O, and some will react further with more Fe atoms to ultimately form H O. As more Fe(+) forms, some will begin to precipitate as Fe(OH) (s). The only point that you should learn from this is that the oxidation of Fe by dissolved oxygen is not a simple reaction. How then might we hope to express the rate of Fe(+) oxidation as a simple rate law? The discussion above indicated that at circumneutral ph the net reaction ends up being: Fe(H O) O Fe(H O) (OH) (s) + H O + 8H + If the initial reaction between O and Fe is rate limiting (i.e., it is the slowest step in the multi-step sequence of reactions), then we might expect the overall rate of reaction to be proportional to the concentrations of Fe(+) and dissolved oxygen. (The low concentrations of the intermediate oxidation states of oxygen such as peroxide and superoxide attest to their reactivity; it is reasonable to expect that they will react more quickly than dioxygen with Fe.) Because of all of the hydrolysis reactions that occur,

2 we might also expect the reaction rate to be influenced by ph. In fact, the rate has been reported to follow the rate law: b a = k [ Fe ] [ O ][ OH ] In this laboratory experiment, you will determine if the rate is first order with respect to iron, and also determine the order with respect to [OH - ]. Note that we could just as well have written: b + a = k'[ Fe ][ O ][ H ] As long as ph and O concentration do not change, the rate law could be written: = k'' [ Fe ] b where k is equal to k[o ][OH - ] a. If b is equal to one, the rate law may be integrated to yield: [ Fe ] t ln k'' t = [ Fe ] t= 0 This is the equation of a straight line (ln[fe ] vs. t); the slope of that line would be different at different values of ph or of dissolved oxygen. If b is greater than one, however, we would need to use an alternate expression. Consequently, we will determine b before determining the rate constant or the value of a. In this lab, we are going to maintain O concentration constant but change ph and Fe concentration to find values for k and a. The particular reaction with which you will work has more than esoteric interest for environmental engineers. Reduced iron must be oxidized and removed from many ground waters in water treatment plants; the size of the mixing basin and flow rates must be designed to account for the oxidation rate. Similarly, reduced iron is sometimes added as a flocculent; the rate of oxidation and the rate law must be considered in designing facilities for such a treatment. Procedures Overview Four groups will find on their lab bench a flask of buffered water that is being aerated. These four groups will first prepare containers into which they can put their Fe samples. Then the four groups will add concentrated Fe(+) solution to the bubbling buffer solution and start a stop watch; at specified time intervals, you will collect a sample from the bubbling broth and add it to your pre-prepared flasks. Once all samples have been collected you will measure the absorbance of each Fe sample, and, using the calibration curve prepared by the fifth group, you will calculate the concentration of Fe in each sample. Each of the four groups will also calibrate their ph meter and measure the ph of the aerated buffer solution. The fifth group, in addition to making the calibration curve for Fe, will also measure the concentration of the stock Fe solution. Specific procedures for four groups. Make certain that you have all of the necessary equipment at your work bench including: 0-mL volumetric flasks

3 Squirt bottle with Milli-Q water ph meter stirring plate magnetic stirrer and retrieval rod plastic syringe or glass pipet Spectrophotometer that is turned on Aerating solution of buffer Designated sampling time intervals Instructions for spec usage Instructions for calibration of ph meter. To each of the 0-mL volumetric flasks add 0 ml of ortho-phenanthroline solution and ml of acetate buffer; label the flasks -;. While step is being done, other group members can calibrate the ph meter at their site (instruction page is on the desk top);. After the ph meter has been calibrated, measure the ph of the aerating buffer solution;. Using a glass pipet, add ml of Fe(II) stock solution to the beaker of bubbling buffer (00 ml) and start the stop watch immediately as you start the addition; 6. At the designated time intervals, withdraw ml of the Buffer + Fe solution and add it (quickly) to a pre-prepared volumetric flask; be sure to fill the numbered flasks in the correct sequence; shake the flask vigorously immediately after adding the Fe, fill the flask to the line with Milli-Q water using your squirt bottle;. When all samples have been taken, shake all of the flasks to be certain they are well mixed. 8. Measure the absorbance of each sample at 0 nm by pouring sample into a cuvet, wiping the cuvet with a Kimwipe, inserting the cuvet into the spectrophotometer, and recording the absorbance (specific instructions on spec usage is on your work bench); Group : Preparation of calibration curve You are to prepare standards (plus one blank) of known Fe concentration by diluting the stock solution.. Label 9 0-mL volumetric flasks -8 and blank ;. In each flask place 0 ml of orthophenanthroline solution and ml of acetate buffer;. Fill the blank flask to the line with Milli-Q water and shake;. To the remaining flasks, add the following amounts of Fe stock solution: Flask 00 μl Flask 0 μl Flask 00 μl Flask 0 μl Flask.0 ml Flask 6. ml Flask.0 ml Flask 8.0 ml

4 After the additional to each flask, shake the flask vigorously, fill it to the line with Milli-Q water and then shake it well again.. Following the instructions for the spectrophotometer, set the wavelength to 0 nm, and zero the spec using Milli-Q water; 6. Read the absorbance of each standard going from lowest to highest concentration; be certain to wipe the cuvet with a Kimwipe before placing it in the spectrophotometer; also be sure to rinse the cuvet with the standard before filling it for absorbance measurement. Measurement of Initial Fe concentration You also have a beaker containing buffer solution on your work bench. You will follow the same procedure as the other groups in adding Fe stock solution to this buffer, and you will measure the resultant Fe concentration. Because your buffer solution will be at low ph, no oxidation of the Fe(+) will occur, and all groups will use your measured concentration as the time-zero concentration.. Prepare 0-mL volumetric flasks by adding 0 ml of ortho-phenanthroline solution and ml of acetate buffer;. Using a glass pipet, add ml of Fe(II) stock solution to the beaker of buffer; mix thoroughly;. Using a glass pipet or syringe, withdraw ml of the buffer + Fe solution and add it to one of the pre-prepared volumetric flasks; vigorously shake the flask immediately after adding the Fe, then fill to the mark with Milli-Q water and shake well again;. Repeat step for the remaining volumetric flasks;. Record the absorbance of all four flasks just as was done for the standards above; Data Analysis. The first step is to plot the calibration curve. Look at the curve, determine if any outliers should be omitted from the regression, and decide how to treat the blank (i.e., do you force the regression through zero, do you subtract the blank from all samples, do you subtract the blank from the standards before you do the regression). At that point, perform the regression analysis, and use the results to calculate the concentrations of Fe in all samples. Remember that the samples are diluted 0-fold before you measure them (i.e., you add ml of sample to ml of water and reagent); you must calculate the concentration of Fe in the undiluted sample.. First, you need to determine the order of the reaction with respect to Fe (i.e., the value of the exponent, b. The rate law is: b a Rate = = k [ Fe ] [ O ][ OH ] We could rewrite this as: a log ( Rate) = log ( k[ O ][ OH ] ) + b log[ Fe ] The slope of a plot of log(rate) vs. log[fe ] should equal the order of the reaction with respect to Fe concentration. You can calculate the rate as Δ[Fe ]/Δt

5 between any two sampling points. The dilemma is then what to use as the concentration of Fe when that rate applies. One approach to solve this dilemma is to plot the rate vs. time, fit the points to a smooth curve, and use the equation of this curve to calculate the value of the rate at each sampling time. This will then give you a rate (mole/l-minute) at times for which you have measured the Fe concentration. You can then plot log(rate) vs. log[fe ] and determine the order of the reaction with respect to iron concentration.. If the reaction is first order with respect to iron, proceed with step ; if not, proceed to step. If the reaction is first order with respect to iron, then a plot of ln[fe ] vs. time should be linear, but because each group worked at a different ph, the slope should be different for each group. Tabulate the slope and ph for all four groups, and determine the value of a in the expression: k'' = k[ O ][ OH ] a where k is the slope of each group s results (ln[fe ] vs. time). The value of a tells you the order of the reaction with respect to [OH - ] (and [H + ]).. If you found b to be an integer >, you must write the appropriate rate law and integrate it to find the correct expression to use to derive the value of a. For instance, if b =, then the rate law would be: = k'' [ Fe ] The integrated form of this rate law is: = + k" t [ Fe ] t [ Fe ] t= 0 To obtain k, one would plot /[Fe ] vs. time. You would then proceed to tabulate the value of k and ph for all four groups and to determine the value of a (order of reaction with respect to OH - ) in the expression: k'' = k[ O ][ OH ] a. Use your rate law to calculate the expected range of half-lives for Fe(+) in natural waters. Use the range of ph values observed in your natural samples (ph 6. to 8.) and assume a dissolved oxygen concentration of 9. mg/l (0. mm). Lab report This report can be short; the main objectives are to give you some experience making kinetics measurements and working with rate laws. In addition, you see first hand how fast iron is oxidized. In the results section you should include items - above. In the discussion you should state what the rate law is based on your results. You can also discuss item.

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7 CE0 Fe Oxidation Kinetics Lab Data Collection Before you leave the lab, be certain that this sheet is completely filled out. You will need all of these results to do the data analyses. I. Calibration curve Group: Concentration of Fe Stock solution (obtain value from TA) Flask Vol. Stock Solution (ml) Blank Conc. Fe (μm) II. Initial Fe concentration Replicate Replicate Replicate Replicate III. Kinetics measurements Group ph Flask # Time of sample 6

8 Group ph Flask # Time of sample 6 Group ph Flask # Time of sample 6 Group ph Flask # Time of sample 6 8