# MOLECULAR WEIGHT BY BOILING POINT ELEVATION

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1 MOLECULAR WEIGHT BY BOILING POINT ELEVATION BACKGROUND This experiment demonstrates the use of colligative properties. The goal is to measure the molecular weight of a non-volatile solute by determining the concentration dependence of the boiling point elevation of a solution. The solvent used must be one of the compounds commonly referred to as volatile; that is, it must have an appreciable vapor pressure. One of the several useful aspects of colligative properties is the fact that the vapor pressure of volatile solvents is lowered when a non-volatile solute is used to make a solution. The result is that such a solution will necessarily have a higher boiling point than that of the pure solvent. The higher boiling point is due to the fact that a higher temperature is needed in the presence of the non-volatile solute, which is not making any contribution to the solution s vapor pressure, in order to cause the volatile component of the solution, the solvent, to exert one atmosphere of pressure. It must be remembered that the boiling point elevation being investigated in this experiment is a property of the solution as a whole and, for ideal dilute solutions, is directly proportional to the solute concentration as shown in Equation 1. T b = m K b 1 In Equation 1, m is the solution molality and K b is the boiling point elevation constant which is a function of the solvent not the solute. The value of T b is the boiling point of the solution minus that of the pure solvent, T b *. Based on the definition of molality it is possible to rearrange Equation 1 into Equation 2 in order to isolate the solute molecular weight, M. M = [g K b ] / [G T b ] 2 In Equation 2, T b is the boiling point elevation of a solution containing g grams of solute in G kilograms of solvent. It is interesting to note that K b for a solvent may be estimated by Equation 3. K b = [R T b *2 ] / [ H vap ] 3 The value of T b * in Equation 3 is, as mentioned, that of the boiling point of the pure solvent while H vap is the heat of vaporization of the pure solvent. Frequently, for dilute ideal solutions, the boiling points of the pure solvent and that of the solution may be used interchangeably. Equations 1, 2, and 3 assume non-volatile and non-electrolyte solutes in ideal dilute solutions. Since colligative properties are independent of the identity of the solute, depending only on total particle concentration, it is possible to obtain important information about electrolytes by measuring boiling point elevations. This is especially true in the case of weak electrolytes that are only partially dissociated in solution. To the extent that a solute dissociates in solution the net number of actual particles present will increase. A larger number of particles in solution will result in a larger measured boiling point elevation, T b, because the molality, m, in Equation 1

2 will be larger. In the case of a weak electrolyte it is more appropriate to re-write Equation 1 as shown in Equation 4. T b = K b m app = K b [g / (G M app )] 4 In equation 4, m app is the apparent total particle molality that results from the partial dissociation of the solute. M app is a weighted average molecular weight representative of the actual ions and molecules as they exist in solution. The value of m app may be evaluated in terms of the analytical molality, which is based on formula weight of solute, and the percent of the solute particles which undergo as shown in Equation 5. m app = m o + (1 m o 5 In equation 5, n represents the number of ions produced by the dissociation of one molecule of solute while m o represents the molality based on the formula weight of the solute ignoring any dissociation. Equation 5 can be rearranged into equation 6 where g and G have the same meaning they did in equation 2 while M o is the actual formula weight of the solute. m app = [{n - + 1] [g / (G M o )] 6 The value of m app may be evaluated as shown in Equation 7 with g, G, and M app as previously defined. m app = g / [G M app ] 7 Equations 6 and 7 may be combined to show = [M o - M app ] / [M app { n - 1}] 8 Since M app may be evaluated from the boiling point elevation as shown in Equation 4 it is easy to determine the degree of dissociation of a weak electrolyte using Equation 8. Inter-particle Forces In addition to the influence of electrolyte behavior the boiling point of solutions may be affected by the way in which solute particles interact with one another. Typically attractive forces exist between solute particles. These forces can have an influence on the value of the molecular weight as calculated using Equation 2. Equation 2 suggests a possible approach to attempt to correct for such inter-particle forces. A plot can be constructed of calculated molecular weight on the y-axis versus solution molality on the x-axis. Such a plot is extrapolated to zero molality, the y-intercept, to obtain what is referred to as the limiting molecular weight. This infinite dilution extrapolated molecular weight value may be thought of as the value of the molecular weight that would be obtained if only a single molecule were present in solution. Such a technique has the result of minimizing the influence of inter-particle forces. 2

3 Since Equation 2 requires values for the K b constants, the values for common solvents are shown in Table 1. Notice that since K b is sensitive to atmospheric pressure, the information is provided in Table 1 so that K b values may be corrected to the barometric pressure in the laboratory at the time the experiment is conducted. A final note of caution is appropriate. The heart of this experiment is the measurement of how the boiling point of a pure solvent changes as a solution is prepared. The only reliable manner to accomplish this measure of temperature change is to make an actual measurement of the boiling point of the pure solvent at the actual laboratory conditions rather than depending on literature values. Since boiling points show significant pressure variation the boiling point of the pure solvent may be significantly different from the literature value if the barometric pressure in the laboratory is significantly different from standard atmospheric conditions. Failure to actually measure the boiling point of the pure solvent under the conditions that the solution boiling points are measured can give rise to serious errors! Further, it is good to be mindful of the fact that when measuring the boiling point of a solution it is best to measure the actual boiling liquid itself rather than the vapor. When inserting thermometers into boiling liquid it is easy to experience difficulties associated with the superheating of the liquid. For this reason it is best to use an apparatus such as the Cottrell boiling point apparatus or similar equipment. It is also good to use one thermometer throughout in order to avoid any potential problems associated with faulty thermometer calibrations. Solvent TABLE 1: boiling point elevation constants Boiling Point, T b *. (deg C at 760 torr) K b (molal / 1 atm) K b / P (torr) (molal/deg/torr) Acetone Benzene Bromobenzene Chloroform Ethanol Ethyl ether Methanol Water PROCEDURE Apparatus and Materials Needed: 1 Cottrell boiling-point apparatus or equivalent (standard reflux/distillation set-up may be used if Cottrell apparatus not available; ask instructor for assistance). 3

5 Each solution s boiling point is measured and recorded. An aliquot of each solution is withdrawn and placed in a separate pre-weighed weighing bottle that is then cooled and set aside. Collect aliquots from four or five different solutions as directed by the instructor. Each of these aliquots are analyzed as described below. Once its contents have been cooled to room temperature each bottle and its contents are weighed on an analytical balance. These data permit the weight of solution to be determined. The top is now removed from the weighing bottle and the solvent is evaporated off. Typically a hot water bath may be used to accomplish the solvent evaporation. If directed by your instructor a drying oven may be used to remove the final residual of solvent to leave only solid solute in the weighing bottle. Cool the weighing bottle and the solid solute to room temperature and weigh it. Determine the weight of the solid solute (g in Equation 2). The weight of the solvent (G in Equation 2) may be determined by the difference. CALCULATIONS Equation 2 may be used to calculate the molecular weight of the solute for each of the different solution concentrations. Use g and G for each of the solutions to calculate the molality of the solution. Prepare a graph of molecular weight, M, on the y-axis versus the solution molality, m, on the x-axis. The resultant line may be extrapolated to zero molality to obtain what is referred to as the limiting molecular weight, M infinite. Calculate the degree of dissociation of the solute for each of the solutions whose boiling points have been measured. Prepare a plot of the degree of on the y-axis versus the molality, m o, on the x-axis and extrapolate to zero concentration to obtain a limit at infinite dilution of the degree of infinite. 5

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