LEC 06 Electrochemistry What you can learn about Kohlrausch s law Equivalent conductivity Temperature-dependence of conductivity Ostwald s dilution law Principle and tasks It is possible to differentiate between strong and weak electrolytes by measuring their electrical conductance. Strong electrolytes follow Kohlrausch s law, whereas weak electrolytes are described by Ostwald s dilution law. The examination of the concentration dependence of the conductivity allows the molar conductivities of infinitely diluted electrolytes to be determined, and facilitates the calculation of the degree of dissociation and the dissociation constants of weak electrolytes. What you need: Experiment P3060640 with Cobra3 Chem-Unit Experiment P3060611 with Cobra3 Basic-Unit Conductivity of a strong electrolyte as a function of the concentration. Conductivity of a weak electrolyte as a function of the concentration Wash bottle, 500 ml 33931.00 1 1 Silicon grease, 100g 31863.10 1 1 Silica gel, orange, granular, 500 g 30224.50 1 1 Acetic acid, 1 M solution, 1000 ml 48127.70 1 1 Potassium chloride, 250 g 30098.25 1 1 Water, distilled, 5 l 31246.81 1 1 Set of Precision Balance Sartorius CPA 623S and measure software 49221.88 1 1 PC, Windows XP or higher with Cobra3 P3060611/40 Cobra3 Basic-Unit, USB 12150.50 1 Cobra3 Chem-Unit 12153.00 1 Power supply, 12 VDC/2 A 12151.99 1 1 Software Cobra3 Conductivity 14508.61 1 Measuring module, Conductivity 12108.00 1 Conductivity probe K1 18151.02 1 Cobra3, sensor 20 110 C 12120.00 1 Data cable, RS232 14602.00 1 Software Cobra3 Chem-Unit 14520.61 1 Conductivity temperature probe Pt1000 13701.01 1 Magnetic stirrer, mini 47334.93 1 1 Magnetic stirring bar, l = 15 mm 46299.01 1 1 Retord stand, h = 750 mm 37694.00 1 1 Right angle clamp 37697.00 2 1 Support rod with hole 02036.01 1 Holder for 2 electrodes 45284.01 1 Spring balance holder 03065.20 1 1 Glass beaker, 150 ml, tall 36003.00 2 2 Volumetric flask, 250 ml 36550.00 4 4 Volumetric flask, 500 ml 36551.00 4 4 Volumetric flask, 1000 ml 36552.00 6 6 Funnel, glass, d = 80 mm 34459.00 1 1 Volumetric pipette, 1 ml 36575.00 2 2 Volumetric pipette, 5 ml 36577.00 4 4 Volumetric pipette, 25 ml 36580.00 4 4 Volumetric pipette, 100 ml 36582.00 1 1 Pipettor 36592.00 1 1 Pipette dish 36589.00 1 1 Pasteur pipettes, l = 145 mm 36590.00 1 1 Rubber bulbs 39275.03 1 1 Weighing dishes, 80 50 14 mm 45019.25 1 1 Spoon 33398.00 1 1 Desiccator 34126.00 1 1 Porcelain plate for desiccators 32474.00 1 1 Cristallizing dish, 320 ml 46243.00 1 1 PHYWE Systeme GmbH & Co. KG D- 37070 Göttingen Laboratory Experiments Chemistry 77
LEC Related concepts Kohlrausch s law, equivalent conductivity, temperature-dependence of conductivity, Ostwald s dilution law. Principle It is possible to differentiate between strong and weak electrolytes by measuring their electrical conductance. Strong electrolytes follow Kohlrausch s law, whereas weak electrolytes are described by Ostwald s dilution law. The examination of the concentration dependence of the conductivity allows the molar conductivities of infinitely diluted electrolytes to be determined, and facilitates the calculation of the degree of dissociation and the dissociation constants of weak electrolytes. Tasks 1. Determine the concentration dependence of the electrical conductivity of potassium chloride and acetic acid solutions. 2. Calculate the molar conductivity using data from the measurements taken and determine the molar conductivity at infinite dilution by extrapolation. 3. Determine the dissociation constant of acetic acid. Equipment Cobra3 Chem-Unit 12153.00* 1 Power supply 12 V/2 A 12151.99 1 Data cable, RS232 14602.00* 1 Software Cobra3 Chem-Unit 14520.61* 1 Conductivity / temperature electrode 13701.01* 1 Protective sleeve for electrodes 37651.15 1 Magnetic stirrer, mini 47334.93 1 Magnetic stirrer bar, l = 15 mm 46299.01 1 Retort stand, h = 750 mm 37694.00 1 Right angle clamp 37697.00 1 Spring balance holder 03065.20 1 Support rod with hole, l = 100 mm 02036.01 1 Glass beaker, 150 ml, tall 36003.00 2 Volumetric flask, 250 ml 36550.00 4 Volumetric flask, 500 ml 36551.00 4 Volumetric flask, 1000 ml 36552.00 6 Funnel, glass, d o = 80 mm 34459.00 1 Volumetric pipette, 1 ml 36575.00 2 Volumetric pipette, 5 ml 36577.00 4 Volumetric pipette, 25 ml 36580.00 4 Volumetric pipette, 100 ml 36582.00 1 Pipettor 36592.00 1 Pipette dish 36589.00 1 Pasteur pipettes 36590.00 1 Rubber bulbs 39275.03 1 Set of analytical balance Sartorius CPA 224S and measure software 49221.88 1 Weighing dishes, 80 x 50 x 14 mm 45019.25 1 Spoon 33398.00 1 Cristallizing dish, 320 ml 46243.00 1 Wash bottle, 500 ml 33931.00 1 Desiccator 34126.00 1 Porcelain plate for desiccators 32474.00 1 Silicone grease, 100 g 31863.10 1 Silica gel, orange, granulated, 500 g 30224.50 1 Acetic acid, 1 M, 1000 ml 48127.70 1 Potassium chloride, 250 g 30098.25 1 Water, distilled, 5 l 31246.81 1 PC, Windows 95 or higher Changes in the equipment required for use of the Basic-Unit: (instead of * above mentioned) Cobra3 Basic-Unit, USB 12150.50 1 Measuring module Conductivity 12108.00 1 Software Cobra3 Conductivity 14508.61 1 Conductivity probe 18151.02 1 Fig. 1. Experimental set-up. PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen P3060640 1
LEC Set-up and procedure Perform the experimental set-up according to Fig. 1. Prepare the solutions required for the experiment in the following manner: 0.1 molar KCl solution: Weigh 7.4551 g of dried potassium chloride into a 1000 ml volumetric flask, add some distilled water to dissolve it, and then make up to the calibration mark with distilled water. 0.05 molar KCl solution: Weigh 3.7275 g of dried potassium chloride into a 1000 ml volumetric flask, add some distilled water to dissolve it, and then make up to the calibration mark with distilled water. 0.01 molar KCl solution: Pipette 25 ml of the 0.1 molar KCl solution into a 250 ml volumetric flask and make up to the 0.005 molar KCl solution: Pipette 25 ml of the 0.05 molar KCl solution into a 250 ml volumetric flask and make up to the 0.001 molar KCl solution: Pipette 5 ml of the 0.1 molar KCl solution into a 500 ml volumetric flask and make up to the 0.0005 molar KCl solution: Pipette 5 ml of the 0.05 molar KCl solution into a 500 ml volumetric flask and make up to the 0.0001 molar KCl solution: Pipette 1 ml of the 0.1 molar KCl solution into a 1000 ml volumetric flask and make up to the 0.1 molar CH 3 COOH solution: Pipette 100 ml of the 1 molar acetic acid solution into a 1000 ml volumetric flask and make up to the 0.05 molar CH 3 COOH solution: Pipette 50 ml of the 1 molar acetic acid solution into a 1000 ml volumetric flask and make up to the 0.01 molar CH 3 COOH solution: Pipette 25 ml of the 0.1 molar acetic acid solution into a 250 ml volumetric flask 0.005 molar CH 3 COOH solution: Pipette 25 ml of the 0.05 molar acetic acid solution into a 250 ml volumetric flask 0.001 molar CH 3 COOH solution: Pipette 5 ml of the 0.1 molar acetic acid solution into a 500 ml volumetric flask Fig. 2: Measurement parameters 0.0005 molar CH 3 COOH solution: Pipette 5 ml of the 0.05 molar acetic acid solution into a 500 ml volumetric flask 0.0001 molar CH 3 COOH solution: Pipette 1 ml of the 0.1 molar acetic acid solution into a 1000 ml volumetric flask Connect the conductivity / temperature probe to the appropriate input of the Cobra3 Chem-Unit. Call up the Measure programme in Windows and enter <Chem- Unit> as measuring instrument. Set the measurement parameters as shown in Fig. 2. In <Preferences>, under <Conductivity>, select <Conductivity> as mode, <auto> as range, <µs> as unit, and in Temperature compensation select < with Pt 1000> and <linear>. Under <Temperature> select < C> as unit and <Average over 1 value>. Under the menu point <Displays>, set the <Range> for Conductivity to 0 12000 µs. Set digital display 1 to <Conductivity>. Under Diagrams select <Line diagram> for Diagram1, <Conductivity> for Diagram 1a, and <from 0 to 10> and <no auto range> for the display range. Confirm your entries with <OK>. Now calibrate your sensor under the menu point <Calibrate> at <Conductivity>, either by entering the value of the calibration solution and, after immersion of the sensor, pressing <Calibrate>, or by entering the value of the cell constant of your sensor. For <Temperature> you can either enter a temperature value measured with a thermometer, or calibrate against the level of a temperature probe connected to T1, T2 or T3. After having made these settings, press <Continue> to reach the field for the recording of measured values. Arrange the displays as you want them. When measuring the conductivity, always begin with the solution having the lowest concentration in each series of measurements. Before each new measurement, thoroughly rinse the probe, the glass beaker and the magnetic stirrer bar, first with distilled water and then with the solution to be subsequently measured. Determine the conductivity of the distilled water that is used for the dilution of the solutions and note the result. This is to enable the conductivity of the water used to be taken into consideration in the evaluation. Place a glass beaker containing a magnetic stirrer bar on the magnetic stirrer. Pour the first potassium chloride solution to be measured into the glass beaker, and immerse the previously well-rinsed conductivity cell to a depth of approximately 5 cm in the solution. Adjust the magnetic stirrer to a medium stirring speed. Record the first value by pressing <Save value>. Fig. 3: Conductivity of potassium chloride solutions as a function of the concentration 2 P3060640 PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen
LEC Subsequently determine the respective conductivities of the other solutions in the same manner, whereby in each case the solution with the next higher concentration is measured. While recording the measuring series, pay strict attention to cleanliness as even the slightest trace of contaminants (e.g. by carrying over some of one solution into another) would result in the registration of erroneous data. Stop the measurement by pressing <Close> and save the data with <File> <Save the measurement as...>. To have the plot of conductivity versus concentration carried out, make the following alterations. Under the menu point <Information> <x-data> enter <Concentration> as Title, <c> as Symbol, <mol/l> as Unit and <4> for Digits beyond point. Under <Data table> change the numbers 1 7 into the corresponding concentrations 0.0001 0.1 M in the right order. Fig. 3 shows the graph as it is now presented by the programme. Before measuring the conductivities of the acetic acid solutions, change the <Range> for Conductivity under the menu point <Displays> to 0 600 µs. Carry out the measurements and the alterations under <Information> and <Data table> using the same procedure as above. In addition, under <Display options> <left y-axis>, you can select the second button for the Interpolation (spline interpolation), so that the programme constructs a curve. If the conductivity of a solution is to be measured, then the measurements of the cell (length and area) must be known. Therefore, the cell is usually calibrated with a solution with a known conductivity. The ratio of the measured to the tabulated conductivity of a calibration solution directly provides the ratio of the length to the cross section. This ratio is also known as the cell constant. Usually it can be found in the accompanying test certificate. As a result of the strong concentration dependency, the conductivity is not appropriate for comparing electrolytes. For these purposes it is better to determine the molar conductivity. This is calculated from the specific conductivity k and the concentration c (in mol l -1 ) of the substance in the electrolyte solution: Fig. 5: m k c Parameters of channel modification (3) Theory and evaluation The resistance of a conductor having a uniform cross section is proportional to the length l and inversively proportional to the cross sectional area A of the conductor. R r l A l k A l L (1) The substance constant r is known as the specific resistance; its reciprocal k as the specific conductivity, and the reciprocal of the resistance as the conductance L. It is usual to use r for metallic conductors and k for electrolytes. The conductivity for an electrolytic solution results in the following: k l R l A l A L (2) having the dimension Ω -1 cm -1. Fig. 4: Conductivity of acetic acid solutions as a function of the concentration Fig. 6: Concentration dependence of the molar conductivity for potassium chloride and acetic acid solutions m S cm 2 >mol c mol>l PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen P3060640 3
LEC When the concentration dependence of the conductivity in electrolytes is examined, one finds that the conductivity basically increases with the concentration because the number of the charge carriers (ions) increases. The plot of molar conductivity versus concentration can be calculated with <Channel modification> under menu prompt <Analysis> by setting the parameters as given in Fig. 5. In this operation you can also substract the conductivity of the distilled water. With <Assume channel> under <Measurement> the two diagrams for potassium chloride and acetic acid can be shown in one (Fig. 6). The molar conductivity approaches a limit with increasing dilution. This is the conductivity infinite dilution. Kohlrausch found the following conformity to natural law for the concentration dependency of the molar conductivity for strong electrolytes: m q k 2c (4) According to Kohlrausch s law, plotting the molar conductivity of KCl against the square root of the concentration should result in a straight line. This line s intersection with the ordinate is the molar conductivity at infinite dilution. Weak electrolytes do not dissociate completely and have a lower conductivity than strong electrolytes. As the concentration increases, the dissociation equilibrium shifts in the direction of non-dissociated molecules. The degree of dissociation a of weak electrolytes is the quotient of the molar conductivity divided by the molar conductivity at infinite dilution. Ostwald s dilution law is valid for weak electrolytes. It enables dissociation constants to be calculated: K a2 c 1 a 2 m c 1 q m 2 q The limiting value of the molar conductivity of weak electrolytes at infinite dilution is first reached at extremely low concentrations; therefore, exact measurements in this are no longer possible. Consequently cannot be obtained by extrapolating m > 2c -curves for weak electrolytes. Equation (7) is derived by transforming Ostwald s law of dilution: 1 1 m c 2 m q k q From equation (7) it can be seen that a linear relationship exists between the reciprocal of the conductivity and the product of the molar conductivity and the concentration of weak electrolytes. Furthermore, Ostwald s law of dilution shows that the molar conductivity at infinite dilution can be obtained from the line s point of intersection of the line with the ordinate 1/ m over c m. (6) (7) a m (5) 4 P3060640 PHYWE series of publications Laboratory Experiments Chemistry PHYWE SYSTEME GMBH & Co. KG D-37070 Göttingen