In the Laboratory edited by
Computer Bulletin Board
Steven D. Gammon University of Idaho Moscow, ID 83844
Integrating Computers into the First-Year Chemistry Laboratory: Application of Raoult’s Law to a Two-Component System R. Viswanathan and G. Horowitz Department of Chemistry, Yeshiva College, 500 W. 185th Street, New York, NY 10033
Integration of computers into undergraduate chemistry education is becoming increasingly common owing to the availability of high-speed computers and user-friendly software. Spreadsheet calculations are used extensively in analytical and physical chemistry. We have introduced a laboratory experiment for the first-year chemistry course that uses spreadsheet calculations to prepare students for these latter courses. In a typical first-year chemistry course, students are introduced to the Clausius–Clapeyron equation and use it to predict the vapor pressure of pure liquids as a function of temperature. Later in the course, Raoult’s law is discussed and is used to determine vapor pressures of components in solution. Together these two concepts can be used to predict the boiling point of two-component mixtures containing a volatile solute. The use of a spreadsheet program greatly facilitates the calculations. Students calculate theoretical boiling points, which are then compared with experimental measurements. The two-component system used is a mixture of methanol and water. This experiment also serves as an introduction to the principles of fractional distillation, a technique commonly used in the organic chemistry laboratory for separation of mixtures. Background
p A = x A p A °; p B = x B p B °
(2)
Experiments have been conducted to verify Raoult’s law by measuring vapor pressure as a function of composition (2). However, in the present experiment, the Clausius– Clapeyron equation and Raoult’s law are combined to determine the boiling points of solutions as a function of composition. The total vapor pressure of the two-component solution is thus given by p tot = xA pA ° + xB pB° = x A pA° + (1 – x A )p B°
(3)
where pA ° and pB° are the equilibrium vapor pressures of the pure components at a given temperature, and xA and xB are the mole fractions of methanol and water respectively. Using eq 1, pA ° and pB° are calculated for temperatures ranging from the normal boiling point of pure methanol to that of pure water. By setting ptot equal to the atmospheric pressure in the laboratory, the composition of the two-component system that boils at a particular temperature can be calculated. The calculation is performed over the temperature range of interest and a plot of theoretical boiling point vs mole fraction is constructed. Experimental Procedure
The equilibrium vapor pressure for each component as a function of temperature is calculated using the Clausius– Clapeyron equation (1), assuming that the compounds behave ideally in the gas phase and that the enthalpies of vaporization are constant: pi° = p i*e ᎑χ
(1)
where χ = i = A or B; Ti* is the boiling point of component i at a pressure of pi*; ∆H vapi is the enthalpy of vaporization of component i at its boiling point; R is the gas constant in J/K mol; and pi° is the equilibrium vapor pressure at a temperature Ti. Students are provided with the enthalpies of vaporization of methanol (35.3 kJ/mol) and water (40.7 kJ/mol) at their normal boiling points. The spreadsheet program Excel is used to calculate the vapor pressure of the two components as a function of temperature (eq 1). By requiring students to perform these calculations during a recitation period, we make sure that ample help is available to them. The theoretical boiling point of the two-component system for various compositions is calculated as follows. According to Raoult’s law (1), the partial pressures of the (∆Hvapi/R)(1/Ti – 1/Ti*);
1124
components at a given temperature are
The boiling point of a given mixture is experimentally measured by placing 15 mL of solution in a 25-mL roundbottom flask equipped with a magnetic stir bar and reflux condenser. The flask is then heated in a sand bath and stirring is maintained. When the solution begins to boil vigorously, the temperature of the solution is measured using a thermocouple. The experiment has been repeated using a sump pump to circulate ice water through the reflux condenser to minimize the loss of methanol vapors. The boiling point measured using a cold-water-filled condenser agreed within ± 0.2 °C with that measured using an ice-water-filled condenser. Solutions of varying compositions (that span the entire range of mole fractions) are prepared prior to the beginning of the laboratory. Each student measures the boiling points of two of these solutions. Students pool their experimental boiling points for solutions of different mole fractions and plot this data against the theoretical results (Fig. 1). For all compositions, the experimental boiling points are observed to be lower than the theoretical boiling points. Students are asked to interpret their results in terms of differences in intermolecular forces.
Journal of Chemical Education • Vol. 75 No. 9 September 1998 • JChemEd.chem.wisc.edu
In the Laboratory
Discussion
370
Literature Cited 1. See for example: Atkins, P. Physical Chemistry, 5th ed.; Freeman: New York, 1996.
365 370
Boiling Point / K
This experiment enables comparison of experimental results to the results predicted by assuming ideal behavior in the vapor phase (Clausius–Clapeyron equation) and in the liquid phase (Raoult’s law). The theoretical calculations are made easy by the availability of spreadsheet programs like Excel. Assuming that the ideal gas assumption and the constancy of the enthalpy of vaporization are valid approximations, the deviation of experimental results from theoretical values can be attributed to differences in the strengths of intermolecular forces. For the entire composition range, the experimental boiling points are lower than those predicted. Within the accuracy of the present experimental measurements, this implies that the methanol–water system exhibits a positive deviation from Raoult’s law, and that the vapor pressure of the solution is greater than predicted. It is interesting to see that in this two-component solution, where one expects the nature of the intermolecular forces to be similar, significant deviation from ideal behavior is observed. It is also observed that a methanol-rich solution behaves more ideally than a methanol-poor solution.
360 355 350 345 340 335 0.0
0.2
0.4
0.6
0.8
1.0
Mole Fraction of Methanol Figure 1. Comparison of experimental boiling points ( 䉭) with those predicted theoretically ( 䊏 ), as a function of mole fraction of methanol in methanol–water mixtures. P ext = 753.1 mm Hg.
2. Koubek, E.; Elert, M. L. J. Chem. Educ. 1982, 59, 357. Koubek, E.; Paulson, D. R. J. Chem. Educ. 1983, 60, 1069. Burness, J. H. J. Chem. Educ. 1996, 73, 967.
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