When a small amount of nonvolatile solute is dissolved in a volatile solvent, the vapor pressure of the solvent over the solution will be less than the vapor pressure of the pure solvent at the same temperature. Therefore, the temperature at which the equilibrium vapor pressure reaches atmospheric pressure is higher for the solution than for the pure solvent. As a result the boiling point of the solution, \(T_{b}\), is higher than the boiling point of the pure solvent, \(T^{o}_{b}\). The amount by which the boiling point of the solution exceeds the boiling point of the pure liquid, \(\Delta T_{b} = T_{b} - T^{o}_{b}\), is called the boiling point elevation. Similarly, because of the reduction in vapor pressure over the solution the freezing point of the solution, \(T_{f}\), is lower than the freezing point of the pure solvent, \(T^{o}_{f}\). The amount by which the freezing point of the solution is decreased from that of the pure liquid, \(\Delta T_{f} = T^{o}_{f} - T_{f}\), is called the freezing point depression. Figure 1 below illustrates this behavior for water. Figure 1 The magnitude of the freezing depression produced by a solute is proportional to its colligative molality, \(m_{c}\): \[\Delta T_{f} =T^{o}_{f} - T_{f} =K_{f} \times m_{c} \label{1}\] \(K_{f}\) is known as the freezing point depression constant, and depends on the solvent used. In this experiment you will determine the molar mass of an unknown solid by dissolving a pre-weighed sample in a solvent, and measuring the resulting freezing point depression of the solvent. From the measured \(\Delta T_{f}\) and the known \(K_{f}\) value of the solvent, you can then determine the value of \(m_{c}\) using the above Equation \ref{1}. The colligative molality, \(m_{c}\), is related to the molality of the solution, \(m\), by the expression: \[m_{c} =i \times m \label{2}\] where \(i\) is the number of solute particles produced per formula unit of dissolved solute, and \(m\) is the number of moles of solute per kilogram of solvent. Since only non-dissociating solutes will be used in this experiment, the value of \(i\) for your unknown solute can be considered to be 1. Thus, you may assume that \(m_{c} = m\). From the experimentally determined value of \(m\) and the mass of solute added, you can determine the molar mass of the unknown solute. The solvent that will be used in this experiment is para-dichlorobenzene, shown in Figure 2 below. Para-dichlorobenzene has a \(K_{f}\) value of 7.10 °C·kg·mol-1. It also has a convenient freezing point that is just over 60 °C. Figure 2 In order to determine the freezing point of this pure solvent you must first heat it in a test tube to over 60 °C using a hot water bath, and then measure the temperature as a function of time as the liquid cools. At first the temperature will fall quite rapidly. When the freezing point is reached, solid will begin to form, and the temperature will tend to hold steady until the sample is all solid. This behavior is shown in Figure 3 below. The freezing point of the pure liquid is the constant temperature observed while the liquid is freezing to a solid. The cooling behavior of a solution is somewhat different from that of a pure liquid, also shown in Figure 3. As discussed earlier, the temperature at which a solution freezes is lower than that for the pure solvent. In addition, there is a slow gradual fall in temperature as freezing proceeds. The best value for the freezing point of the solution is obtained by drawing two straight lines connecting the points on the temperature-time graph. The first line connects points where the solution is all liquid. The second line connects points where solid and liquid coexist. The point where the two lines intersect is the freezing point of the solution. Note that when the solid first appears the temperature may fall below the freezing point, but then it comes back up as more of the solid forms. This effect is called supercooling, and is a phenomenon that may occur with both the pure liquid and the solution (see Figure 3). When drawing the straight line in the solid-liquid region of the graph, ignore points where supercooling is observed. To establish the proper straight line in the solid-liquid region it is necessary to record the temperature until the trend with time is smooth and clearly established. Figure 3
Chemicals: Para-dichlorobenzene (PDB), unknown sample, acetone Equipment: 600-mL beaker, large test tube, wire gauze, thermometer, two utility clamps, stand with ring clamp, Bunsen burner, split stopper, looped glass stirring rod, beaker tongs** **Be certain to use beaker tongs and not crucible tongs; beaker tongs have a rubber coating on the end where they grip the beaker; crucible tongs do not.
Waste Disposal All chemicals used must be disposed of in the proper waste container. The acetone and para-dichlorobenzene must not go down the sink!
Figure 4
Part 2: Determining the Freezing Point of PBD with about 2 g Unknown Solute
Clean Up
Experimental Data Unknown ID number: ____________________
Temperature Measurements: Record the temperature every 30 seconds as the pure solvent and two solutions are cooled. Note the temperature at which any solid first appears.
Graphical Analysis of Data Use Excel to create three separate graphs of “Temperature versus Time” for the pure solvent and the two solutions studied. Each graph should have an appropriate title and labeled axes with an appropriate scale. Add two trendlines to the data points of each graph. You can do this by hand with a ruler or by using Excel. The first line is applied to data points that correspond to the cooling of the liquid stat: these are the points on the steep part of the graph. The second line is applied to data points that correspond to the co-existence of both the solid and liquid (freezing): these are the points on the part of the graph where the temperature levels out. Extrapolate the two trendlines towards each other until they intersect. The temperature at the point of intersection is the solvent freezing point and should be clearly shown on each graph. Attach your three graphs to this report. Record the freezing point temperatures obtained from the graphs below:
Calculation of Molar Mass Complete the table below with the results of your calculations. Be sure to include all units. Note that \(K_{f}\) PDB = 7.10 °C·kg·mol-1.
Questions
Pre-Laboratory Assignment: Determination of Molar Mass by Freezing Point Depression
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