In this exercise, you will determine the distances to stars that appear in a pair of images taken 3 months apart. Some stars are in different positions in the two images. You will also determine the minimum distance to those stars for which there is no measurable parallax.
Take a look at the two star field images. You can assume that the patch of sky in these images is near the plane of the ecliptic. (Note that these images are actually artificial constructions to make it possible to measure many stellar parallaxes in one image. In reality, stars that are close enough to us to have measurable parallaxes wouldn’t be so close together on the sky.) The images are “negatives,” so that stars appear black on a white background. The size of a star in the images is determined not by the star’s physical dimensions, but by its brightness. The brighter stars appear bigger than faint ones.
Step 1: Compare the two star images carefully, looking for stars that appear in different locations in the two images. You may find it helpful to lay image #1 on top of image #2, and hold them up to a light. Be careful to align the two images well (most stars will line up perfectly). You can also try using a ruler to check if separations or alignments between stars have changed.
Step 2: Mark each star that has moved noticeably with an arrow on image #1 • Draw the arrows in BELOW the stars, so they point “up” at the stars. Label each star with a number, letter or name.
Step 3: For each star that moves, estimate its center by eye as best you can on image #1，and make a small dot there with a pen or pencil. Then lay image #1 on top of image #2, and look for where each star moved to in image #2. Make a small dot on image #1 at the location where the star is centered in image #2. You should now have two dots on image #1 associated with each star that moves.
Step 4: Use a ruler to measure how far each star has shifted in the three-month period between image #1 and image #2. Make the measurements in millimeters (mm), and record each measurement in the second column of Table 1 on your worksheet.
Step 5: Convert your measurements in millimeters to an angular size using the following conversion:
The resulting shift in units of arc-seconds is the known as the “parallax” of the star. Record the parallax values in the third column of Table 1.
Step 6: Compute the distances to each of the stars that moved noticeably. Use the parallax formula:
d = 1/p
Here d is the distance in parsecs (pc) and p is the parallax angle measured in arc- seconds. For example, a star with a parallax of 0.5 arcsec has a distance of 1/(0.5) = 2.0 pc. Record your results in the fourth column of Table 1.
Step 7: Compute the distances to each of the stars in light years (ly), and record your results in Table 1. Use the conversion:
Step 8: Estimate the smallest apparent shift you hypothetically could have measured.
That is, how far in mm would a star need to have shifted for you to be able to notice the shift? What does this smallest measurable shift correspond to in arc-seconds? Then compute the distance to a star that has this value of the parallax, following steps 5 and 6 above. Record your answers on the worksheet, and answer the following questions.
Q1: Look at your results from Step 6 (distance column in Table 1) above. What, if anything, can be said about the distances of stars that didn’t seem to move from image #1 to image #2? [For example, “they must be closer than.”.” or “they must be farther away than….” Fill in the blank with a number.]
Q2: Suppose you observed the same field of stars 3 months after image #2 was taken. Describe in words how you would expect the positions of stars to appear. Include a sketch if that would help explain what you would see.
Q3: Suppose you observed the field once more 9 months after image #2 was taken. Describe in words how you would expect the apparent positions of stars to compare to those observed in image #1 and/or image #2.
Q4: Put aside the images you’ve been working on for a moment. Imagine that all the stars in the galaxy have the same intrinsic brightness, like light bulbs all of the same wattage. Stars would then appear brighter or fainter depending on whether they were relatively close or relatively far away from the Earth. ]f this were the case, which stars would appear brighter as seen from Earth: those with large parallaxes, or those with small parallaxes? Explain.
Q5: Now consider the results of your analysis of the two images. Are the results consistent with the hypothesis that all stars in the Galaxy have the same intrinsic brightness? Why or why not? If not, give at least one specific example from this exercise that proves your point.
The p-chem lab manual is written by Clayton Baum at Florida Tech.
References: Engel, T.; Reid, P. Thermodynamics, Statistical Thermodynamics & Kinetics, Pearson, San Francisco, 2013
(2010, 2006); Chapter 4. Selected Values of Chemical Thermodynamic Properties, National Bureau of Standards Technical Note 270-3, pp. 13, 25-27 (1968); NBS Technical Note 270-8, pp. 23-26, 64-65 (1981). (photocopy, on reserve) Purpose: Determine the molar heat of an exothermic ionic reaction involving HCl and NaOH and the endothermic solution process involving solid KNO3 when dissolved in water. Method: The heats will be measured using a constant-pressure solution calorimeter instead of the constant- volume bomb calorimeter employed in experiment 2, but in many respects the procedure will be the same. Refer to the Background in Experiment 2. You will be using a Parr Solution Calorimeter (Figure 1) with the microprocessor-based thermometer. Recall that the thermistor probe and vacuum flask (dewar) are fragile and expensive ($300) so please handle them with extreme care. Clean up any spills in the calorimeter immediately. The calorimeter automatically corrects the temperature by assuming the heat leak between the bucket and the jacket is proportional to their temperature difference. The details were given on the last page of the Experiment 2 handout.
Figure 1. Parr 1455 Calorimeter Figure 2. Parr Sample Cell This experiment is based on the relationship between the heat at constant pressure (qP) and the temperature rise (ΔT), which is analogous to equation (6) in experiment 2: qP = -Cs ΔT, where Cs is the heat capacity of the system consisting of everything inside the Dewar (1) The heat capacity of the calorimeter is obtained by measuring the temperature rise produced by the standard reaction of TRIS, tris(hydroxymethyl)aminomethane, dissolved in 0.1 M HCl. The known heat at 25oC is -58.738
2
cal/g of TRIS. Then, measurements of the temperature change associated with the reactions of interest are made to obtain the enthalpies of these reactions. Experimental Procedure: Note: Calculate the volumes of concentrated HCl (Fisher Scientific, Reagent ACS Grade) and the mass of NaOH (Fisher Scientific, Pellets) required to make the solutions before coming to the laboratory. A. Standardization with TRIS (two trials) 1. Prepare exactly 100 mL of 0.100 M HCl. (Concentrated HCl is 12.4 M.) CAUTION: Remember to add the concentrated acid to the flask partially filled with water, swirl the uncapped flask to mix the solution, and then add water to the mark.. Carefully pour this solution into the Dewar flask. 2. Weigh approximately 0.50 g of granulated (i.e., no lumps) TRIS (Sigma-Aldrich, Trisma base, 99.9%) into the teflon dish to a precision of ±0.0001 g. See Figure 2. Be careful not to drop any of the sample into the push rod socket. 3. Assemble the rotating cell; set the dish on a flat surface, grasp the glass bell, and carefully press the bell firmly onto the dish. Do not grasp or press the thin-walled glass stem during this operation since it is fragile and will break easily. Attach the cell to the stirring shaft by sliding the plastic coupling onto the shaft as far as it will go and turning the thumb screw finger tight. Do not over tighten the screw or the Teflon will crack. Place the cell in the calorimeter and attach the drive belt. 4. Turn on the Parr 6772 Calorimetric Thermometer which is attached to the 6725 Semimicro Calorimeter and the network. After 10-15 s, the touch screen Main menu will appear. The Par 6772 will determine the initial temperature (Tinit) and the corrected temperature change (T) for your samples, and send this information automatically to its web site. The Parr 6772 also will provide a real-time temperature vs. time plot. 5. Turn on the computer (user: pchem, password: chemistry) and monitor. Open Explorer and go to the Calorimetric Thermometer home page at http://163.118.205.134. Check the last few digits of the IP address by looking at the inet addr on the Parr 6772 (Main → Communication Control → Network Interface → Network Status). Sample Data on the home page contains the calorimeter reports, and LCD Image displays the Parr 6772 screen.
6. Test the stirring assembly before each trial by starting and then stopping the motor (Main→Calorimeter Operation → Stirrer). Do not start the motor unless there is liquid in the dewar. 7. Set up the Data Logger (Main → Diagnostics → Data Logger) before each trial. The interval should be 12 s, the destination should be Logfile Only in Data Format. Delete Data Log File to clear the Data Logger and make certain the Data Logger is on. 8. In Main → Calorimeter Operation, press the Start button to begin the preperiod. This activates the stirring motor and prompts for your sample ID number. Enter a unique name that includes your group initials and sample number (e.g., run #1 for group C on Tuesday afternoon could be TUPMC1). The calorimeter will allow 7- 8 minutes for the system to equilibrate before signaling the operator to initiate the reaction. The run may be aborted at any time by pressing Abort button. Press the Temperature Graph button to see a real time plot of temperature vs. time. Press the Escape button to return to the Calorimeter Operation menu. 9. When the “Mix Reactants” dialog box appears, combine the reactants by pressing the push rod downward to drop the sample out of the rotating cell. This should be done without undue friction from the finger. Push the rod down as far as it will go. Then immediately press the <Continue> button to begin the postperiod phase. It is important that this phase is synchronized with the initial mixing to obtain the correct temperature rise. The temperature of the calorimeter should change within 30 seconds after mixing.
3
10. At the end of the postperiod, the Parr 6772 will turn off the stirring motor and prepare a calorimeter report indicating the initial temperature and the temperature rise, fully corrected for all systematic heat leaks. 11. Immediately return to the Temperature Graph screen on the Par 6772, enter Setup to expand the temperature scale (Bucket Min Value and Bucket Max Value), and use LCD Image on the computer to print out the graph. (After several minutes the temperature change will be lost.) 12. With the report on the Par 6772 screen (Report → Select from List → Display), go to LCD Image on the computer web page and print out the screen. If the Report does not contain the initial temperature and the temperature rise, copy the data from the Data Logger file on the computer under Data Log to Notepad. This data consists of the date, time, Bucket temperature, and Jacket temperature in comma delimited format. This can be imported into Excel and the Bucket temperature versus time can be plotted.
13. Rinse out the cell and dewar when the run is finished. B. Exothermic heat of neutralization 1. Prepare 100 mL of 0.25 M HCl using concentrated (12.4 M) HCl. See the CAUTION in step 1 of Part A. Carefully pour exactly 90 mL of the 0.25 M HCl solution into the Dewar flask. 2. Prepare 50 mL of 2.5 M NaOH from solid NaOH. NaOH is corrosive so immediately clean up any NaOH powder spilled on the balance or the bench. Dissolve the solid in a 50-mL beaker with 30-40 mL of water and pour this solution into the 50-mL volumetric flask, adding water to the mark. Using a volumetric pipet, introduce 10 mL of the 2.5 M NaOH solution through the glass stem into the assembled cell. Carefully attach the cell to the stirring shaft as in step A.3.
3. Carry out the determination runs by following steps A.6-A.13 above.
C. Endothermic heat of solution 1. Pour exactly 100 mL of distilled water into the Dewar flask. 2. Weigh approximately 0.70 g of granulated solid potassium nitrate (Fisher Scientific, Certified ACS, > 99.0%) into the teflon dish to an accuracy of 0.1 mg.
3. Carry out the determination runs by following steps A.6-A.13 above. Adjust the scale, if necessary to accommodate a temperature decrease. Cautiously neutralize the remaining acid and base solutions with one another before pouring them down the drain.
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Calculations and Discussion: 1. Verify the temperature rise for each trial by comparing it with the T estimated from the corresponding plot.
2. Standardization. Calculate the heat capacity of the calorimeter using the TRIS standard. a. The value of qp (in cal) used for the reaction involving m grams of TRIS is given by
qP = -m[58.738 + 0.3433(25 – T.63)] where T.63 = 0.63T + Tinit. The term 0.3433(25 – T.63) adjusts the heat of reaction to any temperature above or below the 25oC reference temperature. b. Use equation (1) along with the value of qP in the previous step and the temperature rise to obtain the value of Cs for the calorimeter. Calculate the average Cs for the two trials. Note that the value of Cs is for 100 mL of aqueous solution in the calorimeter so that this volume must be maintained for the samples. 3. Determination of H for the neutralization reaction. Use equation (1) along with the value of Cs from above and the temperature rise to calculate qp in cal. Determine n, the number of moles of limiting reactant, from the balanced stoichiometric equation and the volumes and concentrations of each reactant. Finally, calculate qp (kcal/mol) for the neutralization reaction. 4. Determination of H for the KNO3 solution. Use equation (1) along with the value of Cs from above and the temperature rise to calculate qp in cal. Calculate qp (kcal/mol) from the mass of the salt used in this experiment. 5. Compare your heats of reaction (kcal/mol) to the values obtained using the literature data for the heats of formation. Include the uncertainties for your values. (The uncertainty in your ΔH value can be estimated by comparing the ΔH value calculated using your average Cs with the ΔH value calculated using the Cs value for one of your trials.) The NBS Technical Notes concentrations are expressed in # mols solvent/1 mol solute. Choose the values closest to your concentrations expressed in molarity. For example, a 1.0 M solution could be expressed as 55.6 mols H2O/1 mol solute, assuming 1 liter of solvent. The state “c” represents crystalline solid. 6. For the neutralization reaction, calculate the differences between the ΔH values for the concentrations used in this experiment and the values that would apply at infinite dilution. Are these differences within the qualitative estimate of the experimental uncertainty in measuring the ΔH values?
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done in the text (and we reviewed it in class) so it should be easy but I thought it was so important that I’d like you to put what they say into your own words.
c) Now, I’d like you to generalize the expression for the specific heat Cv to be
appropriate to a polyatomic molecule, specifically H2O(g). Assume that we’ll be working in the temperature range from 300 – 800 K where we can consider ourselves to be way above the rotational temperature Θrot so you can just approximate the rotational contribution to specific heat to be 3R/2 per mole corresponding to R/2 for each of the three rotational degrees of freedom. The main modification you need to make is to consider that there are 4 degrees of vibrational freedom for water (asymmetric stretch ħω1 = 3756 cm-‐1, symmetric stretch ħω2 = 3652 cm-‐1, bending mode ħω3 = 1595 cm-‐1 and another bending mode ħω4 = 1595 cm-‐1).
d) Use your expression from c) to plot Cv versus temperature over the
temperature range specified above (calculating a point every 100 K should be enough). Compare your result to experimental values from the literature.
e) As is evident from Figure 4.7, there is excellent agreement of calculated and
measured specific heats. The text notes (page 160) that the agreement can be improved still further if we refine the harmonic oscillator model to consider anharmonicity – i.e. the fact that the potential is not really harmonic. (For reference, see problem 1-‐27 and 1-‐31 of the text on page 34). Given that accounting for anharmonicity decreases the spacings between energy levels relative to what they would have been in a completely harmonic system, reason as to whether making a correction for anharmonicity would increase or decrease the values of your calculated specific heat. Explain your reasoning.
like virtually all reactions involving more than two or three reactant molecules, takes place not in a single molecular step but in several steps. The detailed system of steps is called the reaction mechanism. It is one of the principal aims of chemical kinetics to obtain information to aid in the elucidation of reaction mechanisms, which are fundamental to our understanding of chemistry.
THEORY
The several steps in a reaction are usually consecutive and tend to proceed at different speeds. Usually, when the overall rate is slow enough to measure at all, it is because one of the steps tends to proceed so much more slowly than all the others that it effectively controls the over-all reaction rate and can be designated the rate controlling step. A steady state is quickly reached in which the concentrations of the reaction intermediates are controlled by the intrinsic speeds of the reaction steps by which they are formed and consumed. A study of the rate of the over-all reaction yields information of a certain kind regarding the nature of the rate-controlling step and closely associated steps. Usually, however, rate studies supply only part of the information needed to formulate uniquely and completely the correct reaction mechanism.
When the mechanism is such that the steady state is quickly attained, the rate law for Eq. (1) can be written in the form:
(2)
where parenthesized quantities are concentrations. In the general case, the brackets might also contain concentrations of additional substances, referred to as catalysts, whose presence influences the reaction rate but which are not produced or consumed in the over-all reaction. The determination of the rate law requires that the rate be determined at a sufficiently large number of different combinations of the concentrations of the various species present to enable an expression to be formulated which accounts for the observations and gives good promise of predicting the rate reliably over the concentration ranges of interest. The rate law can be written to correspond in form to that predicted by a theory based on a particular type of mechanism, but basically it is an empirical expression.
The most frequently encountered type of rate law is of the form [again using the reaction of Eq. (1) as an example]
(3)
where the exponents m, n, p,… are determined by the experiment. Each exponent in Eq. (3) is the order of the reaction with respect to the corresponding species; thus, the reaction is said to be the mth order with respect to IO3-, etc. The algebraic sum of the exponents m + n + p in this example, is the over-all order (or, commonly, simply the order) of the reaction. Reaction orders are usually, but not always, positive integers within experimental error.
The order of a reaction is determined by the reaction mechanism. It is related to, and is often, equal to, and is often (but not always) the number of reactant molecules in the rate-controlling step—the “molecularity” of the reaction. Consider the following proposed mechanism for the hypothetical reaction 3A + 2B = products:
a. A + 2B = 2C (fast, to equilibrium, Ka)
b. A + C = Products (slow, rate controlling,, Kb)
The rate law predicted by this mechanism is
The over-all reaction involves five reactant molecules, but it is by no means necessarily of fifth order. Indeed, the rate-controlling step in this proposed mechanism is bimolecular, and the over-all reaction order is predicted by the mechanism is 5/2. It is also important to note that this mechanism is not the only one that would predict the above 5/2-order rate law for the given over-all reactions; thus experimental verification of the predicted rate law would by no means constitute proof of the validity of the above proposed mechanism.
It occasionally, happens that the observed exponents deviate from integers or simple rational fractions by more than experimental error. A possible explanation is that two or more simultaneous mechanisms are in competition, in which case the observed order should lie between the extremes predicted by the individual mechanism. A possible alternative explanation is that no single reaction step is effectively rate-controlling.
We now turn our attention to the experimental problem of determining the exponents in the rate law. Except in first- and second-order reactions it usually inconvenient to determine the exponents merely by determining the time behavior of a reacting system in which many or all reactant concentrations are allowed to change simultaneously and comparing the observed behavior with integrated rate expressions. A procedure is desirable which permits the dependencies of the rate on the concentrations of the different reactants to be isolated from one another and determined one at a time. In one such procedure, all the species but the one to be studied are present at such high initial concentrations relative to that of the reactant studied that their concentrations may be assumed to remain approximately constant during the reaction; the apparent reaction order with respect to the species of interest is then obtained by comparing the progress of the reaction with that predicted by rate laws for first order, second order, and so on. This procedure would often have the disadvantage of placing the system outside the concentration range of interest and thus possibly complicating the reaction mechanism.
In another procedure (this experiment), which we shall call the method of initial rates, the reaction is run for a time small in comparison to the “half-life” of the reaction but large in comparison to the time required to attain a steady state, so that the actual value of the initial rate [the initial value of the derivative on the left side of Eq. 3] can be estimated approximately. Enough different combinations of initial concentrations of several reactants are employed to enable exponents to be determined separately. For example, the exponent m is determined from two experiments which differ only in the IO3- concentration.
In the present experiment the rate law for the reaction shown in Eq. (1) will be studied by the initial rate method, at 25 0C, and at a pH of about 5. The initial concentrations of iodate ion, iodide ion, and hydrogen ion will be varied independently in separate experiments, and the time required for the consumption of a definite small amount of the iodate will be measured.
PROCEDURE/METHOD
The time required for a definite small amount of iodate to be consumed will here be measured by determining the time required for the iodine produced by the reaction (as I3-)to oxidize a definite amount of a reducing agent, arsenious acid, added at the beginning of the experiment. Under the conditions of the experiment arsenious acid does not react directly with the iodate at a significant rate but reacts with iodine as quickly as it is formed. When the arsenious acid has been completely consumed, free iodine is liberated which produces a blue color with a small amount of soluble starch which is present. Since the blue color appears rather suddenly after a reproducible period of time, this series of reactions is commonly known as the “iodine clock reaction.”
The reaction involving arsenious acid may be written, at a pH of about 5,
H3AsO3 + I3- + H2O HAsO4 + 3I- + 4H+ (4)
The over-all reaction, up to the time the starch end point, can be written, from equations (1) and (4),
IO3- + 3H3AsO3 I- + 3HAsO4 + 6H+ (5)
Since with ordinary concentrations of the other reactants hydrogen ions are evidently produced in quantities large in comparison to those corresponding to pH 5, it is evident that buffers must be used to maintain constant hydrogen-ion concentration. As is apparent from the method used, the rate law will be determined under conditions of essentially zero concentration of I3-; the dependence of the rate on triiodide, which is fact has been shown to be very small,[footnoteRef:1] will not be measured. Under these conditions, Eq. (3) is an appropriate expression for the rate. [1: Dushman et al. ]
A constant initial concentration of H3AsO3 is used in a series of reacting mixtures having varying concentrations of IO3-, I- and H+. Since the amount of arsenious acid is the same in each run, the amount of iodate consumed up to the color change is constant, and related to the amount of arsenious acid by the stoichiometry of Eq. (5). The initial reaction rate in mole liter-1 sec-1 is thus approximately the amount consumed (per liter) divided by the time required for the blue end point to appear. From the initial rates of two reactions in which the initial concentration of only one reactant is varied and all the other concentrations kept the same, it is possible to infer the exponent in the rate expression associated with the reactant which is varied. This is most conveniently done by taking logarithms of both sides of Eq. (3) and subtracting the expressions for the two runs.
EXPERIMENTAL PROCEDURE
Solutions. Two acetate buffers, with hydrogen-ion concentrations differing by a factor of 2, will be prepared. Use will be made of the fact that at a given ionic strength the hydrogen-ion concentration is proportional to the ratio of acetic acid concentration to an acetate ion concentration:
(6)
Where at 25 0C, k = 1.753 x 10-6 mole liter-1. The experiments will all be carried out at about the same ionic strength (0.16 +/- 0.01), and accordingly the activity coefficient is approximately the same in all experiments, by the Debye-Hückel theory. It will also be seen that within wide limits the amount of buffer solution employed in a given total volume is inconsequential, provided the ionic strength of the resultant solution is always kept about the same. (Note success of this experiment is closely tied to the accuracy with which the required reagent quantities are calculated, measured or weighed). Use appropriately sized graduated cylinders for larger volumes and pipettes for for smaller volumes (See Table 1). The solutions required are as follows:
Starch solution: 1.0 %. Heat to a boil 100 mL of water. In another beaker, place 1.0 g of starch and add a small amount of hot water to it, begin by mixing the two until a paste forms. Then add the rest of the hot water, which will dissolve the remaining starch. The solution should appear thick with a blue tint.
Buffer A: Prepared from100 mL of 0.75 M NaAc (sodium acetate) solution, 100 mL of 0.22 M HAc (acetic acid) solution, and about 20 mL of 1.0% soluble starch solution into a 500 mL volumetric flask. Make up to the 500 mL mark with distilled water. This should afford a H+ ion concentration of about 1 × 10-5 M.
Buffer B: Prepared from 50 mL of 0.75 M NaAc (sodium acetate) solution, 100 mL of 0.22 M HAc (acetic acid) solution, and about 10 mL of 1.0% soluble starch solution into a 250 mL volumetric flask. Make up to the 500 mL mark with distilled water. This should afford a H+ ion concentration of about 2 × 10-5 M.
H3AsO3: 0.03 M. Should be made up from NaAsO2 and brought to a pH of about 5 by the addition of HAc (acetic acid).
3NaAsO2 + 3HAc + 3H2O 3H3AsO3 + 3NaAc (7)
KIO3: 0.1 M
KI: 0.2 M
Suggested sets of initial volumes of the four reactant solutions, based on a final total volume of 100 mL, are given in the table below.
Table 1: Initial volumes of reactant solutions in mL and suitable pipette sizes
Solution
Pipettesizes
Initial volumes of reactant solutions in mL
I
II
III
IV
H3AsO3
5
5
5
5
5
IO3-
5
5
10
5
5
Buffer A
20 , 25
65
60
40
0
Buffer B
20, 25
0
0
0
65
I-
25
25
25
50
25
Two or three runs should be made on each of the four sets. The instructor may modify that requirement in the interest of time. Inquire as to whether any modifications are in effect. Two or more runs should also be made on a set with proportions chosen by the student in which the initial compositions of two reacting species differ from those in set I. In each case, the amount of buffer required is that needed to obtain a final volume of 100 ml.
It is convenient to use each pipette only for a single solution, in so far as possible, to minimize time spent rinsing. The pipettes should be marked to avoid mistakes.
To make a run, pipette all of the solutions except theKI solution into one of the vessels and the KI solution into another. Remove both vessels from the bath, and begin the reaction by pouring iodide rapidly but quantitatively into the other vessel containing the other reagents, simultaneously starting the stopwatch. Pour the solution back and forth once or twice to complete the mixing, and place the vessel containing the final solution back into the bath.2 Stop the watch at the appearance of the first faint but definite blue color.
Note that as a practical matter, most students find it most convenient to set up the four reactions simultaneously on a white background. The appropriate quantity of the KI solution is then added to the matching reaction vessel and the timing of the reaction to the endpoint (color change) is begun while the vessel is carefully swirled to ensure mixing.
CALCULATIONS
1. The student should construct a table giving the actual initial concentrations of the reactants IO3-, I-, and H+.
2. The H+ concentrations should be calculated from the actual concentrations of NaAc (sodium acetate) and HAc (acetic acid) in the stock solutions employed, with an activity coefficient calculated by use of the Debye-Hückel theory for the ionic strength (= 0.16) of the reacting mixtures.
3. Using the known initial concentrations of H3AsO3, calculate the initial rate for each run.
4. From appropriate combinations of sets I, II, III, and IV, calculate the exponents in the rate expression Eq. (3).
5. Calculate a value of the rate constant k from each run, and obtain an average value of k from all runs (if performed in duplicate or triplicate). Compared the experimentally determined value of k to the literature value of (1.753 x 10-6 mole liter-1).
6. Write the rate expression, with the numerical values of the rate constant k and the experimentally obtained values of the exponents. Beside it write the temperature (assume room temperature is 25 °C) and ionic strength at which this expression was obtained.
7. Write another rate expressions, in which those exponents which appear to be reasonably close (within experimental error) to integers are replaced by the integral values. Use this expression to calculate values for the initial rates of all sets studied and compare them with the observed initial rates.
DISCUSSION
The kinetics of this reaction have been the subject of much study, and the mechanism is not yet completely elucidated with certainty. following is an incomplete list of the mechanisms that have been proposed:
As part of the lab report, the student should discuss the above mechanisms in connections with his experimentally determined rate law.
MISCELLANEOUS
The oxidation of iodide by chlorate ion ClO3- has also been studied. Although the reaction appears to be attended by complications which make it difficult to study, under certain conditions it can be carried out as an “iodine clock” experiment. For the interested student, suggested concentration ranges for 20 to 25 °C are ClO3-, 0.05 to 0.01 M; I-, 0.025 to 0.10 M. A sulfate-bisulfate buffer may be used. The resulting rate law is not identical with that for the reaction with iodate, but appears to be compatible with mechanisms analogous to several of those given above.
