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Chemistry 2301 Conductivity Fall 2011 Determining the Dissociation Constant of Acetic Acid by a Conductimetric Method Preparatory Reading Experiment 17 in Shoemaker (1) entitled Conductance of Solutions Experiment 21 in Sime (2) entitled Conductance of Electrolyte Solutions Section 10.5 in Mortimer (3) entitled Electrical Conduction in Electrolyte Solutions Introduction The objective of this experiment is to measure the dissociation constant of acetic acid at infinite dilution o
at 25.0 C using a conductimetric method: O
O
+
OH (aq)
Acetic Acid
H+(aq)
O (aq)
Acetate Ion
Water itself is a very poor electrical conductor, however, the addition of ionic species to water increases its ability to conduct considerably. The conductivity of such a solution depends on the concentration, charges and mobilities of the ions present. We will use a VWR SympHony SB90M5 multiparameter meter to measure the conductivity of dilute solutions of the strong electrolyte potassium acetate and of the weak electrolyte acetic acid. The articles by Shedlovsky (4) and by Klotz (5) should prove to be very useful to you. You will find these in the experiment’s folder. Where appropriate in your introduction, present Kohlrausch’s law describing the effect of dilution on the molar conductivity of strong electrolytes, Kohlrausch’s law of independent ion migration and the Debye-­‐Hückel limiting law (both in general and simplified forms) and explain their importance. The conductivity meter actually measures a solution’s resistance but displays its conductivity. Explain how a set of conductivity standard solutions can be used to calibrate the conductivity meter and how the meter can then calculate conductivity, 𝜅𝜅 , values (your explanation should include the concept of a cell constant). Then define equivalent conductance, Λ, as: 𝜅𝜅
= 𝛼𝛼ℱ 𝑈𝑈 + 𝑈𝑈 Λ=
1000𝜈𝜈𝜈𝜈
Equation 1 Here, 𝜈𝜈 is the number of equivalent ions per molecule (or formula unit), 𝛼𝛼 is the fractional dissociation, 𝑈𝑈 is the ionic mobility of the charged species and 𝑐𝑐 is the concentration of the electrolyte in mol/L. Using this formula will -­‐1 2
-­‐1
2
-­‐1
yield Λ having units Ω m equiv (or S m equiv ). In this experiment we are concerned with simple one-­‐one + -­‐
electrolytes (A B ). In this case 𝜈𝜈 = 1 equivalent/mol, therefore, this is no distinction between equivalents and moles and Λ is the same as the molar conductance, Λ . For strong electrolytes 𝛼𝛼 is unity and Λ is roughly constant at all concentrations. It will however approach a finite value at infinite dilution, Λ . Onsager showed that for strong electrolytes in dilute solution Page 1 of 5 Chemistry 2301 Conductivity Fall 2011 Λ = Λ 1 − 𝛽𝛽 𝑐𝑐 Equation 2 Thus, the conductance at infinite dilution of solutions of strong electrolytes may be determined from measurements of conductance at varying concentrations. The y-­‐intercept of a graph of Λ versus 𝑐𝑐 will yield this value. For weak electrolytes, the fraction dissociated, 𝛼𝛼 , is not unity but is given by the ratio of equivalent conductance to the conductance at infinite dilution, assuming that ion mobilities are independent of concentration Λ
𝛼𝛼 = Λ
Equation 3 Λ will vary much more than it does for strong electrolytes because 𝛼𝛼 varies with concentration, however, like is the case with strong electrolytes, Λ will approach a finite value at infinite dilution. Unfortunately, it is impossible to measure the conductance of infinity dilute solutions of weak electrolytes, so another method for the determination of Λ must be employed. Show how Kohlrausch’s law of independent ion migration may be applied to give a value of the equivalent conductivity at infinite dilution for hypothetically fully ionized acetic acid, Λ , from measurable Λ values for the strong electrolytes HCl, KAc and KCl: Λ = Λ + Λ − Λ Equation 4 Now present the expression for the equilibrium constant, 𝐾𝐾 , with c expressed as a molarity: 𝛼𝛼 𝑐𝑐
𝐾𝐾 = 1 − 𝛼𝛼
Equation 5 The equilibrium constant for the dissociation of acetic acid obtained using this equation will differ from 𝐾𝐾 , the true thermodynamic value, because activity coefficients, 𝛾𝛾 , are left out of the numerator and because of the assumptions made when calculating α using equation 3. An extrapolation procedure will be used to determine 𝐾𝐾 from 𝐾𝐾 . Since 𝐾𝐾 = 𝐾𝐾 𝛾𝛾± is a good approximation, it follows that: log 𝐾𝐾 = log 𝐾𝐾 − 2 log 𝛾𝛾± Equation 6 According to Debye-­‐Hückel Theory, the mean activity coefficient at low and moderate ionic concentrations is given by: 𝐴𝐴 𝐼𝐼
log 𝛾𝛾± = − 𝑧𝑧 𝑧𝑧
1 + 𝐵𝐵 𝐼𝐼
Equation 7 The ionic strength is defined by the expression 𝐼𝐼 =
1
2
𝑚𝑚 𝑧𝑧 Equation 8 Where 𝑚𝑚 is the molality of the 𝑖𝑖th ionic species in moles per kilogram of solvent, 𝑧𝑧 is the charge on ion 𝑖𝑖 and the o
1/2
-­‐1/2
sum is taken over all ionic species in the solution. In equation 7, for dilute solutions at 25 C, 𝐴𝐴 = 0.509 kg mol Page 2 of 5 Chemistry 2301 Conductivity Fall 2011 and the quantity 𝐵𝐵 is nearly unity for many electrolytes. In addition, it is valid to approximate molality by molarity (mol/L). For the very dilute solutions of acetic acid used in this experiment, the 𝐼𝐼 = 𝛼𝛼𝛼𝛼 is very small and equation 7 is well approximated by log 𝐾𝐾 = log 𝐾𝐾 + 2 0.509 𝛼𝛼𝛼𝛼 Equation 9 Hence, if 𝐾𝐾 has been determined at many dilute concentrations, a plot of log 𝐾𝐾 versus 𝛼𝛼𝛼𝛼 will give a straight line. Extrapolation to 𝑐𝑐 = 0 (the y-­‐intercept) can be made to yield log 𝐾𝐾 from which 𝐾𝐾 can be easily calculated. Experimental Safety Issues This is a relatively safe experiment. There are no major safety concerns associated with its performance. MSDS sheets for all chemicals used can be found in the experiment’s folder placed near experimental setup in C-­‐3041. Please wear appropriate eye protection while performing this experiment. If you wish, you may also wear a lab coat. Disposable gloves are not required but are available if you wish to use them. Temperature control is very important when making conductivity measurements as small fluctuations in o
temperature can cause significant changes in conductivity. We wish to measure the conductivity at 25.00 C. This is possible by placing the vessel containing the sample solution in a stable, thermostated water bath. The large bath provided for your use has a large heat capacity and excellent temperature control is provided by an external o
circulating water bath controlled at 24.5 C and a proportional temperature controller with a small quartz heater. o
The external water bath circulates water through a large coil immersed in the 25.00 C bath. The proportional o
controller is set so that its quartz heater provides just enough heat to bring the bath’s temperature to 25.00 C. o
You will notice that the thermometer in the bath reads slightly more than 25.00 C. This is correct because this o
o
thermometer has been calibrated and displays 25.04 C when the true temperature is 25.00 C. A circulator mounted towards the rear of the bath stirs the water so that a uniform temperature is achieved throughout. The water used during the course of this experiment should have a low conductivity. We do not want ions present in the water to cause our conductivity measurements to be artificially high. Usually, dissolved CO 2 (producing carbonic acid) is the source of these unwanted ions. The water distilled in this lab has been checked many times and was found to have a suitably low conductivity. Solution Preparation You will be measuring the conductivity of solutions of the strong electrolyte, potassium acetate, KAc, and of the weak electrolyte, acetic acid. The conductivity must be measured at various dilute concentration. Stock solutions, A, of KAc and acetic acid will be provided with concentrations 𝑐𝑐 ≅ 0.02 M and 𝑐𝑐 = 0.05000 M respectively. You will first dilute these solutions to appropriate concentrations (i.e. 𝑐𝑐 /4, 𝑐𝑐 /16, and 𝑐𝑐 /64). It is extremely important that you perform the following work very carefully. The quality of your results depends on accurate dilutions and scrupulous care in avoiding contamination of the dilute solutions by stray electrolytes. Begin with the KAc solution. Transfer about 30 – 35 mL of this solution into a 50 mL clean, dry beaker. Using a clean, dry 25.00 mL pipette, transfer this volume of solution into a 100.00 mL volumetric flask, make up to the mark with distilled water, cap and invert 25 times. Call this first diluted solution B. Page 3 of 5 Chemistry 2301 Conductivity Fall 2011 Rinse the pipette with acetone and dry with nitrogen gas. Repeat the procedure with solution B and a clean 100.00 mL volumetric flask to make solution C and again with solution C to make solution D. Repeat the entire procedure for the acetic acid solution. When finished you should have six 100.00 mL volumetric flasks, 3 containing dilute KAc and three containing dilute acetic acid. Conductivity Measurements Before beginning conductivity measurements we must calibrate the conductivity meter with standard solutions (solutions of known conductivity). An instructor will guide you through a 3-­‐point calibration of the meter. When complete, strictly follow the procedure below to measure the conductivity of the stock solutions (A) and each of the diluted solutions (B, C and D): 1. Ensure a large test tube is clean and dry. If it is not rinse with acetone and dry with nitrogen gas. 2. Drop a small magnetic stir bar into the test tube and pour in ~40 mL of the solution to be measured. It will be helpful to mark the level of the solution on the test tube so this volume can be easily added for all subsequent measurements. 3. Clamp the test tube into the bath, using the larger clamp provided, so that its bottom is almost touching the small magnetic stirrer submerged in the bath. Turn on the stirrer (it can be left on throughout the entire measurement procedure). 4. Ensure the conductivity probe is clean and DRY (if not, wipe with a Kimwipe). Remove the conductivity probe from its holder and lower it into the test tube so that it’s sensor is below the solution level but not so low as to touch the rotating stir bar. Hold it in place with the small adjustable clamp. 5. Allow the probe to sit in the stirring solution for approximately 60 seconds them press the measurement key on the meter. When the units after the conductivity value stop flashing the meter has stabilized. o
6. Ensure that the temperature on the top line of the display reads 25.0 C. If so record the conductivity o
value in your notebook. If not, perform the measurement again until the temperature reads 25.0 C. 7. Remove the probe and hang it back in its special holder. Remove the test tube from the bath, retrieve the magnet and dispose of the solution. Dry the electrode well with Kimwipes. The procedure needs to be repeated for each solution to be measured. In total, there are 8 measurements to be taken. Clean up 1. Turn off the conductivity meter by holding the power button. 2. Rinse the probe with distilled water and dry with a Kimwipe. Leave it hanging in its holder. 3. Discard all prepared solutions in a sink and rinse the 100 mL flasks with distilled water. Place them in the oven to dry. 4. Rinse the pipette with distilled water then acetone. Leave it by the experiment. 5. Rinse the large test tubes with distilled water then acetone. Leave them by the experiment. Page 4 of 5 Chemistry 2301 Conductivity Fall 2011 Results Perform the following calculations in a spreadsheet: 1. Use the dilution formula you learned in first-­‐year to calculate the concentrations, c, of each of the 3
prepared solutions in mol/L (note that 1 L = 1 dm ). You should try to use SI units throughout these calculations. Tabulate the stock and prepared solutions concentrations in Excel. 2. In a new column, record the conductivities of each solution. Note the conductivities displayed by the meter have the units µS/cm or mS/cm. Since you should use SI units, convert the conductivities so that the units are S/m. 3. Calculate the equivalent conductance, Λ, of each solution using equation 1. 4. For the strong electrolyte only, calculate 𝑐𝑐. Plot a graph of Λ versus 𝑐𝑐. Perform a linear regression analysis on the plot and report the conductance at infinite dilution, Λ , using equation 2. 5. Use your Λ value for KAc and the literature values of Λ for HCl and KCl to calculate Λ for acetic acid using equation 4. 2
-­‐1
Λ , = 0.04262 S m equiv 2
-­‐1
Λ , = 0.014986 S m equiv 6. For each dilution of acetic acid, calculate 𝛼𝛼 using equation 3, then 𝐾𝐾 from equation 5 and, finally, 𝛼𝛼𝛼𝛼. 7. Plot log 𝐾𝐾 versus 𝛼𝛼𝛼𝛼 and perform a linear regression analysis on the data. If the slope is positive (as it should be), calculate 𝐾𝐾 from the y-­‐intercept and equation 9. If the slope is negative or the data cannot be fit well with a line, simply report an average value of 𝐾𝐾 . When reporting 𝐾𝐾 (or 𝐾𝐾 ) you must always include the temperature at which the measurements were made as equilibrium constants vary with temperature. Discussion o
Obtain the literature value of 𝐾𝐾 at 25 C for acetic acid and compare your experimental value to it. In terms of the assumptions made, explain why your experimental value might differ from the literature value. Using the literature value of 𝐾𝐾 and equation 9, draw a dashed literature/theory line on your plot (i.e. the line that you would have obtained had your experimental value of 𝐾𝐾 matched the literature). Are the deviations from this line reasonable in view of the experimental errors expected in this work? Would you expect there to be more deviation from the literature/theory line at high or low values of 𝛼𝛼𝛼𝛼? Why? Some factors that affect conductivity were mentioned in the introduction. The conductivity of 0.2000 M HCl is greater than that of 0.2000 M KCl even though both HCl and KCl are strong electrolytes. Why is this the case? Works Cited 1. Shoemaker, David P., Garland, Carl W. and Nibler, Joseph W. Experiments in Physical Chemistry. 8th. New York : McGraw Hill Higher Education, 2009. ISBN 978-­‐0-­‐07-­‐282842-­‐9. 2. Sime, Rodney J. Physical Chemistry -­‐ Methods, Techniques, and Experiments. Philadelphia : Saunders College Pubulishing, 1990. ISBN 03-­‐0-­‐009499-­‐2. 3. Mortimer, Robert G. Physical Chemistry. 3rd. Boston : Elsevier Academic Press, 2008. ISBN-­‐13: 978-­‐1-­‐12-­‐
370617-­‐1. 4. The Determination of the Ionization Constant of Acetic Acid at 25°, From Conductance Measurements. MacInnes, Duncan A. and Shedlovsky, Theodore. 1932, Journal of the American Chemical Society, Vol. 54, pp. 1429-­‐1438. ISSN: 0002-­‐7863. 5. Klotz, Irving M. and Rosenburg, Robert M. Chemical Thermodynamics; basic theory and methods. Menlo Park : W. A. Benjamin, Inc., 1972. Page 5 of 5