In the Laboratory
Exploring Fundamental Concepts in Aqueous Solution Conductivity: A General Chemistry Laboratory Exercise Frazier Nyasulu,* Kelly Stevanov, and Rebecca Barlag Department of Chemistry and Biochemistry, Ohio University, Athens, Ohio 45701 *
[email protected] Because of the high cost of instrumentation, quantitative measurements of conductivity are rarely performed in general chemistry laboratories. As a substitute, many instructors construct homemade devices that rely on a battery and LED for qualitative observations (1- 3). A homemade device that makes quantitative measurements of conductivity has been described (4). Today, conductivity sensors linked to a datalogger provide an affordable way to make quantitative measurements of conductivity (5- 7). In this introductory conductivity lab, fundamental factors that affect aqueous conductivity are explored. These factors are (i) concentration, (ii) temperature, (iii) ion charge, and (iv) size and mass of anion. By the time this lab is performed in the semester, students have learned in lecture that strong acids exhibit total ionization and weak acids exhibit low ionization. However, equilibrium constants have not yet been introduced. One parameter easily obtained from weak acid conductivity measurements is the fraction of ionization, R. If the conductivity of a solution of concentration c at 25 °C is Λ, the molar conductivity, ΛM, is ΛM ¼
Λ c
and the fraction of a weak acid ionized, R, is ΛM R ¼ Λo
ð1Þ
ð2Þ
Experimental Section Materials and Equipment Datalogger, conductivity sensor, temperature sensor, 1.00 mL autopipettor, 1.0 M HCl, 1.0 M HC2H3O2, 0.0010 M NaClO4, 0.0010 M MgSO4, 0.10 M NaCl, 0.10 M NaBr, 0.10 M NaI, 0.10 M NaClO4, 0.10 M NaOH, 0.10 M NH3, 0.10 M H3PO4, 0.10 M CaCl2, Mg(OH)2 (saturated solution), CO2(aq, from CO2(s)), 0.10 M sugar, Pepsi-Cola, orange juice, river water, and 2% milk. Effect of Concentration on Conductivity: HCl and HC2H3O2 Small volumes, 1.00 mL increments, of 1.00 M HCl or HC2H3O2 are added to 60.0 mL of water and conductivity is measured after each addition.
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Temperature and conductivity measurements are made every 30 s on a 0.10 M NaCl aqueous solution cooled by an ice bath. Effect of Charge Conductivity of 0.0010 M NaClO4 and 0.0010 M MgSO4 are measured. Effect of Anion Size and Mass Conductivity of 0.10 M NaCl, 0.10 M NaBr, 0.10 M NaI, and 0.10 M NaClO4 are measured. Measurement of the Conductivity of the Other Solutions The other solutions are tap water, 0.10 M NaCl, 0.10 M NaOH, 0.10 M NH3, 0.10 M H3PO4, CO2(aq), from CO2(s)), 0.10 M CaCl2, Mg(OH)2 (saturated solution), 0.10 M sugar, river water, orange juice, and Pepsi-Cola. Students are asked to answer questions based on the conductivities of these solutions (see the supporting information). Hazards
where Λo is the conductivity at infinite dilution. In addition to examining the factors that affect the conductivity of a solution, this lab has been written to provide students opportunities to construct knowledge. Six examples of constructed knowledge are included.
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Effect of Temperature on the Conductivity of a 0.10 M NaCl
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Sodium hydroxide is caustic and causes burns to any area of contact. Hydrochloric acid is corrosive and is hazardous in case of skin or eye contact. Results and Discussion Prelab Predictions Prior to coming to lab, students complete a four-question prelab exercise in which they are asked to predict the results or trends of the conductivity measurements under various conditions. At the beginning of the lab, students hand in the prelab exercise and then discuss their predictions with other students and, if necessary, alter their predictions on a separate prelab exercise sheet. The first question asked students to sketch a graph of conductivity versus concentration for an HCl solution. A majority of the students, 92%, predicted a straight line with a positive slope. When asked to make plots for HCl and HC2H3O2 on the same graph, 80% of the students predicted the slope for HC2H3O2 to be smaller than that for HCl; however, none of the students predicted that the HC2H3O2 plot would curve downward. The second question asked students to sketch a plot of conductivity versus temperature for NaCl(aq). A majority of the students, 88%, predicted that the conductivity
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In the Laboratory Table 1. Conductivity Data and Selected Calculated Values for an Acetic Acid Solution V(1.0 M HC2H3O2)/mL
a
[HC2H3O2]/ (mol/L)a
0
0
1
0.0161
2
Conductivity/ (μS/cm) 24
[H3Oþ] = [C2H3O2-]/ (mol/L)
Fraction ionized (R)
[HC2H3O2]/ (mol/L)
[H3Oþ][C2H3O2-]/ [HC2H3O2]
0
0
0
NA
251
0.0393
0.00063
0.0155
2.60 10-5
0.0318
357
0.0284
0.00090
0.0309
2.64 10-5
3
0.0469
433
0.0233
0.00109
0.0458
2.62 10-5
4
0.0616
497
0.0204
0.00126
0.0603
2.62 10-5
5
0.0758
553
0.0185
0.00140
0.0744
2.63 10-5
6
0.0895
598
0.0169
0.00151
0.0880
2.60 10-5
7
0.1029
640
0.0157
0.00162
0.1013
2.59 10-5
The volume of water added is 60.2 mL.
of NaCl increased linearly with temperature. The third question asked the students which solution was more conductive, NaClO4(aq) or MgSO4(aq). A majority of the students, 76%, predicted that MgSO4 would have a higher conductivity than NaClO4. Finally, the students were asked to rank NaCl(aq), NaBr(aq), NaI(aq), and NaClO4(aq) solutions in order of increasing conductivity. The students, 80%, predicted the conductivity trend to be NaCl > NaBr > NaI > NaClO4. Effect of Concentration To save time, 1.0 M HCl and the 1.0 M HC2H3O2 solutions were used without standardization, and the conductivity sensor was not temperature calibrated. A plot of conductivity, Λ, versus HCl concentration, c, was linear with the equation Λ ¼ ð3:71 105 Þc þ 3:4 102
R2 ¼ 0:9996 ð3Þ
A plot of molar conductivity, ΛM, versus HCl concentration, c, can be described by ΛM ¼ - ð4:4 10 Þc þ 4:1 10 5
5
Figure 1. The effect of HC2H3O2 concentration on conductivity.
conductivity versus
R ¼ 0:9825 ð4Þ
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c is
√ ΛM ¼ - ½1:81ð ( 0:05Þ 105 c þ 4:23ð ( 0:01Þ 105
2
As concentration increases, ion pairing to form the neutral and nonconductive HCl molecule increases. When a plot of molar conductivity versus concentration is implemented, the plot deliberately includes the c = 0 to illustrate conductivity at infinite dilution, Λo. Since plots of molar conductivity versus concentration for various substances are expected to have different lines and different curvature, these can cross. When a crossover occurs, substance A can have a higher conductivity than substance B at some concentration and a lower conductivity at another concentration. Therefore, the most meaningful way to compare conductivities is to compare Λo values, as Λo values have no ionpairing effects. Constructed Knowledge 1: To accurately compare conductivities, compare molar conductivity at infinite dilution ( Λo). Working with an Excel spreadsheet, students explore various relationships between molar conductivity and HCl concentration. The goal is to find the most linear relationship between molar conductivity and some function of concentration, which can then be extrapolated to determine Λo. Some of the are suggested by the instructor (ΛM vs c, ΛM vs √ relationships c, ΛM vs c2, ...) and some are student conceived. √ About 80% of the students find the molar conductivity versus c to be the most linear and the remainder find conductivity versus c to be most linear. An example of the equation of the line for the molar
√
R2 ¼ 0:9974
ð5Þ
Therefore, Λo for HCl at ∼20 °C is 4.23((0.01) 105 μS/ (cm mol L-1). The literature value is 4.25 105 μS/(cm mol L-1) (8). The results of the effect of HC2H3O2 concentration on conductivity are shown in Table 1 and a plot of conductivity versus HC2H3O2 concentration is shown in Figure 1. In comparing HCl and HC2H3O2, the following observations are made: (i) The conductivities of HC2H3O2 solutions are significantly lower than those for HCl. (ii) The HCl plot of conductivity versus concentration is linear whereas the corresponding HC2H3O2 plot√is significantly curved. (iii) Unlike the HCl plot of ΛM versus c or the ΛM versus c, which are linear, the HC2H3O2 plots curve significantly. Because no simple relationship between concentration and conductivity yields a sufficiently linear line, a literature value of Λo is provided. The conductivity at infinite dilution HC2H3O2 is determined from a combination of Λo values for NaC2H3O2, HCl, and NaCl (9); this is beyond the scope of the general chemistry laboratory. The fraction ionized (R) decreases considerably with increasing concentration (Table 1). Because the literature Λo value, 3.955 105 μS/(cm mol L-1), was determined at 25.0 °C, and the measurements were performed at ∼20 °C, there is a systematic error in the values of R.
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In the Laboratory
Constructed Knowledge 2: The fraction acetic acid ionized ( R) decreases with increasing concentration. With R calculated, the concentrations of H3Oþ, C2H3O2-, and HC2H3O2 are calculated. By consideration of various arithmetic operations involving [H3Oþ], [C2H3O2-], and [HC2H3O2], students discover that two operations provide a numerical result that remains constant irrespective of the nominal acetic acid concentration. These are [H3Oþ][C2H3O2-]/[HC2H3Ο2] and [HC2H3Ο2]/[H3Oþ][C2H3O2-]. The value for [H3Oþ][C2H3O2-]/[HC2H3Ο2] is 2.61((0.02) 10-5. The difference between the reported value and the literature value (1.75 10-5) is mainly caused by the differences in temperature; 25 °C versus ∼20 °C. It can be mentioned that these ratios are the forward and reverse equilibrium constants and will be discussed later in the lecture. Constructed Knowledge 3: The product [H3Oþ][C2H3O2-]/ [HC2H3Ο2] is a constant.
Table 2. Conductivities of Other Measured Solutions Substance
Conductivity/(μS/cm)
0.10 M NaCl
9665
0.10 M NaOH (aq)
17760
0.10 M HCl (aq)
31582
0.10 M NH3 (aq)
1289
0.10 M H3PO4 (aq)
3005
CO2(aq, saturated, T is ,20 °C)
247
0.10 M Sugar (aq)
28
0.10 M CaCl2(aq)
15555
Pepsi-Cola
903
Tap water
666
Hocking river water
258
Orange Juice
4216
Effect of Temperature
Milk
4931
The effect of temperature on the conductivity of a 0.10 M NaCl(aq) is described by the equation ð6Þ Λ ¼ 217:6T þ 5004 R2 ¼ 0:9997
Mg(OH)2, saturated
195
where T is the temperature in °C. As the temperature increases, the conductivity increases even though the concentration remains constant. The kinetic molecular theory is used to explain the increased mobility of the ions resulting in the increased conductivity.
Students also are asked to comment on the presence of H3Oþ and OH-. They note that whenever stoichiometric H3Oþ or OH- are generated (as from strong acids and strong bases), solutions have unusually high conductivities. In addition to movement of the entire ion, Hþ “hopping” between H3Oþ and adjacent H2O or between H2O and OH- adds to the conductivity (9). Constructed Knowledge 6: H3Oþ and OH- solutions have unusually high conductivities.
Effect of Anion Mass and Size
Conclusion
The conductivities of 0.10 M NaCl, 0.10 M NaBr, 0.10 M NaI, and 0.10 M NaClO4 are 9.67 103, 1.05 104, 1.03 104, and 1.07 104 μS/cm, respectively. In the interest of time, single conductivity measurements in 0.10 M solutions are performed in place of the procedure to determine Λo. Ion size or mass has little effect because of hydration. Hydration of each of the ions masks the expected differences in conductivity that would otherwise be expected based on size or mass. Constructed Knowledge 4: The ion size or mass has little effect on conductivity. Effect of Charge The conductivities of 0.0010 M concentrations of NaClO4 and MgSO4 are 143 and 169 μS/cm, respectively. In the interest of time, single conductivity measurements in 0.10 M solutions are performed in place of the procedure to determine Λo. The results indicate that higher charges generate greater conductivity. The movement of higher charged ions carries greater current and generates greater conductivity. Other Solutions The conductivities of the other solutions are shown in Table 2. The student learnings are summarized in the supporting information. From the data students are asked to assess the relative acid strengths of HC2H3O2, H3PO4, and HCl. Having concluded the anion mass or size exhibits limited effect on conductivity, the order in increasing acid strength is HC2H3O2 < H3PO4 < HCl. Constructed Knowledge 5: Order in acid strength is HC2H3O2 < H3PO4 < HCl 1366
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The fundamental factors that affect conductivity in aqueous solution are explored. Significant data manipulations and graphing are performed in the Excel spreadsheet. In addition to reinforcing the conductivity concepts learned in lecture, this lab exercise adds to it, and on a number of occasions students are able to construct knowledge. Students tend to learn, enjoy, and retain the material better when they construct or discover knowledge. Having made predictions and discussed the predictions with labmates, students show much greater interest in the results than they do for other laboratories in which predictions are not made. Literature Cited 1. Katz, D. A.; Willis, C. J. Chem. Educ. 1994, 71, 330–332. 2. Murov, S. L. Experiments in General Chemistry, 1st ed.; West Publishing: pp 75-82. 3. Ganong, B. R. J. Chem. Educ. 2000, 77, 1606–1608. 4. Burns, D.; Lewis, D. J. Chem. Educ. 1997, 74, 570–571. 5. Coe, A.; Jasien, P. G. Chem. Educator 1999, 4, 171–172. 6. Lunsford, S. K.; Speelman, N.; Yeary, A.; Slattery, W. J. Chem. Educ. 2007, 84, 1027–1030. 7. Adami, G. J. Chem. Educ. 2006, 83, 253–256. 8. CRC Handbook of Chemistry and Physics, 73rd ed.; Lide, D. R., Ed.; CRC Press Inc: Boca Raton, FL, 1993; pp 5-110. 9. Atkins, P. Physical Chemistry, 6th ed.; W. H. Freeman: New York, 1998, p 741.
Supporting Information Available Instructor notes; student handout; Excel workup. This material is available via the Internet at http://pubs.acs.org.
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