INTRODUCTION In analytical chemistry, we sometimes rely on the measurement of the conductivity of analyte solutions for quantitative analysis. For example, a conductivity detector is often used in conjunction with ion chromatography in the separation and detection of cations or anions in a sample solution (see Reference 1 or Reference 2). Therefore, it is important for analysts to be familiar with the concept of conductivity in order to gain an understanding of the working principle of conductivity detectors. This experiment introduces the measurement of conductivity by determining the limiting molar conductivities of strong and weak electrolytes, which will then be used to evaluate the acid dissociation constant of acetic acid. THEORY Refer to Reference 2 or Reference 3 for the general concept of conductivity. The conductivity of a solution is determined by measuring its electrical resistance. An alternating current (ca 1 kHz) is used to avoid electrolysis and polarisation at a pair of electrodes. This is possible because the charging that occurs in one half of the alternating cycle is counter balanced during the second half of the alternating current. If the electrodes in the conductivity cell are parallel to each other, of area A, and separated by a distance l (see Figure 1), the conductivity κ of the cell is related to its resistance R (ohms) by (note that 1 ohm–1 = 1 Siemen, abbreviated by S) ! = l RA ohm!1 m!1 or S m!1 ( ) Experiment 3 Conductivity of Strong and Weak Electrolytes 2 The molar conductivity Λm of a solute in aqueous solution is defined as ! “m = (# $# water) c S m2 mol % $1 & ‘ ( ) * where c is the concentration of the solute in mol m–3 (Note: a 1 mol L–1 solution is 103 mol m–3). Figure 1. The conductivity of an electrolyte solution is measured by making the cell one arm of a resistance bridge. The balance point is obtained when the resistances satisfy R1/R2=R3/R4 (or, since the current is alternating, a similar relation for the impedances). For a strong electrolyte like potassium chloride the molar conductivity is large and decreases very slowly as the solute concentration increases. It drops by about 5% as the solute concentration increases from zero to 0.1 mol L–1. Pioneering studies by Kohlrausch around 1875 showed that the molar conductivity of strong electrolytes generally vary with concentration according to a relation of the type Λm = Λo m − B c +… Equation (1) The molar conductivity ! “m o is referred to as the limiting molar conductivity of the electrolyte at infinite dilution and Kohlrausch found that the difference between the molar conductivities of the potassium and sodium salts of a particular anion is independent of the anionic species. He explained this behaviour in terms of his celebrated “law” of independent migration of ions. Each ion is assumed to make its own contribution to the molar conductivity. Thus, ! “m o = ! “+ o + ! “# o where ! “+ o and ! “# o are the molar ionic conductivities of the cation and anion, respectively, at infinite dilution. At this point, we need to introduce a parameter known as an ionic mobility. In the presence of an electric field (of strength E in V m–1), an ion will be moving towards an oppositely charged electrode at a particular velocity V (m s–1). Clearly, the stronger the electric field strength, the faster the ion will be attracted to move forward. Hence, there exists a direct l Experiment 3 Conductivity of Strong and Weak Electrolytes 3 relationship between E and V with the proportionality constant known as the ionic mobility (µ). E = µ · V The ionic mobilities, µ+ and µ–, are simply related to the corresponding ionic conductivities by ! “+ o = F µ+ and ! “# o = F µ# where F is the Faraday constant (96,485 C mol–1). Note that these two expressions indicate to us that the larger the ionic mobility is, the more conducting the electrolyte is, as expected. In order to separate the values into the ! “+ o and ! “# o contributions from the cations and anions, we make use of a property called the transport number, t, which refers to the fraction of the total current carried by each ion. Thus, if the total current, I, has components I+ carried by the cations and I– by the anions, the cation transport number t+ is given by ! t+ = I+ I = µ+ µ+ + µ” and the anion transport number is given by the corresponding expression ! t” = I” I = µ” µ+ + µ” Note that the sum of the cation and anion transport numbers is 1 by definition. Hence, if we know either, the other is readily deduced. The second part of each of these expressions comes from the fact that the ionic current caused by the application of a fixed voltage drop is proportional to the ionic mobilities (velocities per volt). Two experimental methods have been used to determine transport numbers. One method, developed by Hittorf involves measurements of ionic concentrations in the vicinity of the electrodes. The second, the moving boundary method, analyses rates of motion of boundaries between related electrolytes under the influence of an electric current. For weak electrolytes such as aqueous solutions of carboxylic acids or amines, the acid or base is completely dissociated at infinite dilution. However, at more realistic finite concentrations, the major species is the undissociated neutral acid or base. Thus, as we dilute a 0.1 mol L–1 solution of weak acid or base, the molar conductivity rises gradually from a low value (which depends on the degree of dissociation α). However, as we approach extreme dilution, the conductivity increases so rapidly that graphical extrapolations to infinite dilution are unreliable. For a monoprotic acid like acetic acid the degree of dissociation α can easily be measured via conductivities. At infinite dilution α = 1 and Λ = !o , while if α = 0 then Λ = 0. We assume a linear interpolation which gives α = Λ /!o . If we substitute this result into the expression for the acid dissociation constant of a weak monoprotic acid we find that 1 ( / ) ( / )( / ) 1 ( / ) 2 2 o o o o c c c c c K − Λ Λ Λ Λ = − = α α where co is the standard concentration of 1000 mol m–3. In this experiment, each student will determine the conductivity of one strong electrolyte (sodium chloride), and of one weak electrolyte (acetic acid). The conductivity of each electrolyte will be measured at different concentrations. The molar conductivity, ! “m o , of the weak electrolyte acetic acid will be determined from the ! “m o values of NaCl, NaCH3COO and HCl which are 126.45 × 10–4, 91.00 × 10–4 and 426.16 × 10–4 S m2 mol–1, respectively. Students should work in pairs with one student preparing solutions of the strong electrolyte, Experiment 3 Conductivity of Strong and Weak Electrolytes 4 the other, the weak electrolyte. Each student should measure the conductivity of the solution prepared by the student’s partner. EXPERIMENTAL 1. Stock solutions of strong electrolyte (0.100 M NaCl) and weak electrolyte (0.100 M acetic acid) are provided. Be sure to note the exact concentration of each stock solution written on the stock bottle. Using a burette, the appropriate volumetric flasks, the appropriate stock solution, distilled water and the dilutions given in the table below, prepare working solutions of both the strong and weak electrolytes. Be sure to rinse the burette with the appropriate stock solution before use. mL 0.100 M stock solution diluted to capacity of volumetric flask 25 500 mL 25 250 mL 20 100 mL 30 100 mL 50 100 mL Shake each flask several times after it is prepared. 2. It is important to understand that conductivity is a very temperature sensitive measurement parameter. For most solutions, conductivity will change roughly 2% for every 1°C change in temperature. For example, the conductivity of 0.0100 M KCl at 25°C is 1.413 mS cm–1, however at 26°C it is 1.440 mS cm–1. As such, conductivity measurements are normally performed in thermostatic baths to ensure all measurements are performed at a constant temperature. Modern conductivity meters, however, employ temperature sensors built into their conductivity sensors and once properly calibrated are able to automatically correct the conductivity measurement for a solution’s actual temperature. This automatic correction is known as Automatic Temperature Compensation (ATC). We will be making use of the ATC function of the TPS WP-84 conductivity meter in this experiment. In the lab you will be given a table containing the ATC coefficients of all the meters and for each of the two electrolytes you will be studying. When you get your meter, make note of the ID number on that meter. Make sure the number on the meter matches the number on the sensor. Identify your number of the meter in the table provided and note the value of the ATC coefficient for sodium chloride (NaCl). On your meter, press the Menu button, followed by F1:Cal then F4:ATC %. Using the ▲and▼keys, scroll to the ATC value given in the supplied table. Press F1 to store the value and then press MENU to quit. 3. You now need to calibrate your meter. For all conductance measurements, including calibration, rinse the cell and electrodes at least five times with solution to be measured. For the final filling before measurement, ensure that the electrodes are totally immersed in the solution and that there are no air bubbles trapped between them. Dislodge any bubbles by gentle finger tapping of the cell. Do not touch the Experiment 3 Conductivity of Strong and Weak Electrolytes 5 electrodes. This experiment is a good test of experimental accuracy and it should be performed with great care. Rinse (at least 5 times) and fill the measurement cell with the 0.0100M KCl standard solution. On your meter, press the Menu button, followed by F1:Cal, then F1:Conductivity. Wait 2-3 minutes for the reading to stabilise. Once stabilised, press the F1 key to calibrate. 4. Next measure the conductivity of distilled water after rinsing the cell at least seven times with the distilled water. As with calibration, wait at least 2-3 minutes for the reading to stabilise before you record it. 5. Measure the conductivities of the strong electrolyte solutions you prepared, starting with the most dilute. Again, wait at least 2-3 minutes for the reading to stabilise before you record it. 6. Before you can measure the conductivities of the weak electrolyte, you need to again adjust the ATC coefficient. Identify the number of your meter in the table provided and note the value of the ATC coefficient for acetic acid. On your meter, press the Menu button, followed by F1:Cal then F4:ATC %. Using the ▲and▼keys, scroll to the ATC value given in the supplied table. Press F1 to store the value and then press MENU to quit. 7. Measure the conductivities of the weak electrolyte solutions you prepared, starting with the most dilute and waiting at least 2-3 minutes for the reading to stabilise before you record it. 8. Process your results as detailed in 3(a) and 3(b) below. RESULTS AND DISCUSSION Please check the list of dos and don’ts before preparing the laboratory report! 1. Introduction – no more than one typed page. 2. Experimental – approximately half a typed page. 3. Results and Discussion (you are to present results in the Results section, followed by a discussion and/or comments on the results in the Discussion section). a. Present your results for the strong electrolyte in a table with the following headings: Concentration c / mol m-3 Conductivity κ / S m-1 Difference conductivity (κ- κwater) / S m-1 Molar conductivity Λm / S m2 mol-1 c / mol 1 2 m- 3 2 Experiment 3 Conductivity of Strong and Weak Electrolytes 6 Using the CBMS208/CBMS608 linear regression spreadsheet on iLearn, plot Λm against ! c . Decide if the plot is linear (1) by testing if the correlation coefficient is statistically significant, (2) by performing the Wald-Wolfowitz runs test on the residuals, and (3) by performing ANOVA. If you are convinced that it is a linear plot, report the corresponding equation and the associated standard deviation and 95% confidence interval for both the slope and intercept of your plot. Based on the relationship given by Equation (1) on page 2, deduce ! “m o , the limiting molar conductivity at infinite dilution. b. For the weak acid use the headings above and add to your table the headings α (the degree of dissociation), Kc (the equilibrium constant for dissociation of the weak acid based on conductivity), log10 Kc and ! c “# where: !” = ” “# ! ” # # $ % & & ‘$ (%(‘) and (CH COOH) 3 o α = Λm Λm . Plot log10(Kc) against ! c “# and report the standard deviation and the 95% confidence interval for both the slope and intercept of your plot. Based on the relationship log Kc = log Ka + B ! c “# , deduce the pKa (and hence Ka) of acetic acid. Note that the limiting molar conductivity of acetic acid is given by ! “m o (CH3COOH) = “m o (HCl) + “m o (NaCH3COO) # “m o (NaCl) c. Compare your experimental results to literature values and comment on your results. Do not simply report that your results are higher/lower than the literature values! State the sources from which you have obtained the literature values. d. List all possible errors (not mistakes!) encountered in this experiment. If it is possible to quantify a source of error (such as those from glassware, balances, etc), then make sure you do so. 4. Conclusion. – no more than half a typed page. ADDITIONAL EXERCISES 1. The specific conductivity of a 0.25 mol L-1 solution of ethanoic acid at 18°C is 4.4 × 10-4 S cm-1. The molar conductivity of the hydrogen and ethnoate ions at the same temperature are 310 and 77 S cm2 mol-1, respectively. Calculate the dissociation constant of ethanoic acid. 2. The molar conductivity of a 0.1 mol L-1 solution of sodium fluoride is 83.5 S cm2 cm-1. The salt may be taken as 92% dissociated. If the transport number of the sodium ion is 0.45, what are the mobilities of the sodium and fluoride ions? 3. It was mentioned on page 2 that the moving boundary method is used to determine the transport numbers of ions. (a) Give a brief description of the principles behind this method in order to show how transport numbers can be determined from the experimental results obtained using Experiment 3 Conductivity of Strong and Weak Electrolytes 7 the moving boundary method. [Give the reference(s) from which you have located the information.] (b) In a moving boundary experiment on KCl, the apparatus consisted of a tube of internal diameter 4.146 mm, and it contained aqueous KCl at a concentration of 0.021 mol L-1. A steady current of 18.2 mA was passed, and the boundary advanced as follows: Δt /s 200 400 600 800 1000 x / mm 64 128 192 254 318 Find the transport number of K+, its mobility and its ionic conductivity. REFERENCES 1. P.W.Atkins, “The Elements of Physical Chemistry”, Oxford University Press, 2001, page 188 – 192. 2. R.A.Alberty, R.J.Silbey, “Physical Chemistry”, John Wiley & Sons, Inc., 5th Edition, 1997, page 716 – 719. 3. P.W.Atkins, “Physical Chemistry”, Oxford University Press, 6th Edition, 1998, page 736 – 745.