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Freezing Point Depression 1 Freezing point depression is an example of a “colligative property”, along with vapor pressure lowering, boiling point elevation, and osmotic pressure. These are characteristics of solutions that depend only on the identity of the solvent and the concentration of the solute, but not on the solute’s identity. These properties depend on the entropy (lack of order) of the solutions involved. More solute increases entropy, i.e. it increases the disorder of the arrangement of solvent molecules, which 1) makes it more difficult to freeze; 2) gives it less driving force to vaporize, which in turn 3) makes it more difficult to boil; and 4) gives pure solvent a greater tendency to enter a solution to dilute it. [Look in Chapter 11 of the text for more thorough explanations.] The following equations describe the colligative properties of dilute solutions: ΔTf = kf m where ΔTf is the decrease in freezing point of a solution of molal concentration m relative to the pure solvent, and kf is the proportionality constant specific to a given solvent. ΔP = Po x2 where ΔP is the difference in vapor pressures between the pure solvent and a solution with a mole fraction of a nonvolatile solute x2, and Po is the vapor pressure of the pure solvent. ΔTb = kb m where ΔTb is the increase in boiling point from the pure solvent for a solution of molal concentration m, and kb is the proportionality constant specific to a given solvent. π = ΔM RT where π is the pressure needed to stop the flow of solvent from the less-concentrated to the more-concentrated sides of a semipermiable membrane. ΔM is the molar concentration difference. R is the gas constant, and T is the absolute temperature. Notice how none of the equations have any terms that depend on the identity of the solute. They have terms that depend on the concentration of the solute, but that is a reflection of the number of moles, not their chemical identity. Consequently, these properties are often used where a knowledge of a number of moles is useful; for instance, in determining a MW. A measured mass of an unknown can be dissolved in a particular solvent, and by looking at the freezing point depression or boiling point elevation or osmotic pressure, one can tell how many moles of solute there must have been, and consequently determine the molecular weight. If we are to believe the Freezing Point Depression equation ΔTf = kf m, it should be the case that when making solutions of two substances with different freezing points, we should not see the freezing point simply increase from that of the lower freezing substance to the higher freezing substance. Rather, the freezing points of solutions close in composition to either pure substance should be lower than the freezing points of the pure substances. This is what we are going to try to demonstrate today. We will make

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solutions of two fatty acids covering the complete range of possible compositions and measure their freezing points. A plot of Freezing Point vs mole fraction will demonstrate whether or not there is any merit to this Freezing Point Depression stuff or not. And we should also be able to use the equation ΔTf = kf m and a plot of ΔTf vs m to determine the freezing point depression constant, kf for both of the fatty acids. -------------------------------------------------------------------------------------------------------- Some Comments about the Concentrations used in this Experiment: The molality of a solution is defined as the number of moles of solute per kg of solvent. It commonly shows up in thermodynamic formulas since it is basically a ratio of quantities of two substances and doesn’t depend on more complicated properties such as volume which can change with temperature. The mole fraction is the ratio of the moles of one on the components in a solution to the total number of moles (solvent + solute). To do the necessary calculations in the lab today, you will need to know the molar masses of the fatty acids used: Stearic acid – C18H36O2 – 284.48 g/mole Lauric acid – C12H24O2 – 200.32 g/mole Calculate the mole fraction of stearic acid as follows:

g

AcidLauricmoleAcidLauricg

g

AcidStearicmoledStearicAcig

g

AcidStearicmoledStearicAcig

fractionmole

32.200

1

48.284

1

48.284

1

Furthermore, if one has a solution of 2 acids, the molality of the solute (the one in lesser amount) may be calculated as follows:

acidsolventkg

acidsolutemolesmolalitysolute

For example, if you used 4.000 g of Stearic acid and 0.1000 g of Lauric acid, perform the following calculation:

g

kgAcidStearicg

g

AcidLauricmoleAcidLauricg

molalityacidlauric

1000

1000.4

32.200

11000.0

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Recognize that to determine kf for Stearic Acid, one needs to plot ΔTf vs molality of Lauric acid in Stearic acid, and to determine kf for Lauric acid, one needs to plot ΔTf vs molality of Stearic acid in Lauric acid. --------------------------------------------------------------------------------------------------------- A Consideration Concerning the Plot of ΔT vs Concentration: One aspect of colligative properties we may see in today’s experiment is that the stated equations work best with very dilute solutions. Consequently in order to define the kf we to define the slop with the most dilute solutions – call it the “limiting slope”. When we determine kf by finding the slope of ΔTf vs concentration, we should only use the experimental points that define the limiting slope. In the case plotted below, for instance, the trendline is appropriate for determining kf. It was obtained by defining an additional series in the EXCEL plot which included only the first four points of the data series; and that series was used to define the trendline.

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Today you will be making temperature measurements using one of the Pasport Chemistry Sensors. The device will be tied to your computer, and the computer will control it using the DataStudio software which should have been part of the standard load that came with your computer. _________________________________________________________________ Making measurements with Pasport Chemistry Sensors and DataStudio: The Pasport Chemistry sensors in conjunction with the Pasport interface and the DataStudio software allow you to measure, temperature, pressure, pH, or voltage as a function of time and store the measurements on your computer. Before starting the program, connect the probe to your computer through a USB port as shown in the figure in the Procedure section below. To start the program click on… Start–Programs-WFU Academic Tools–Scientific Tools–Data Studio 1.9.8r7. Then click on “Create an experiment”, and close the “Digits 1” window. Double click on any Display you want to see in the DISPLAYS window. You will probably want to see the measured value and a graph of the values, so you double click on “3.14Digits” and “Graph”. In each case select the Temperature Data Source. If you are running a Table, you will not want to be storing data very rapidly. Click on the “Setup” button and set the sampling rate suitably low (say 1 seconds). When you are ready to start measuring, click the “Start” button, and when you are ready to stop, click “Stop” To save the data for later work, click on File – Export Data, then give it a location to put a text file version of your data. You can control the number of decimal places in the exported values by double-clicking on the Run# in the Data window and selecting the Numeric tab. The exported text file can be opened in EXCEL, but you have to make EXCEL look for .txt files in the OPEN window. The files are TAB delimited, and only one run is kept in each file. When you save the EXCEL file, save it as a regular .xls or .xlsx file. _________________________________________________________________

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Procedure: You will be working in pairs today. Prepare a hot water bath by putting about 100mL of water in a 250mL beaker and bringing it to a boil on a hotplate. Prepare a holder in which to carry out the cooling curves. Clamp your largest test tube to a ring stand, and put a small wad of paper towel in the bottom. You will put a 20 x 150mm test tube containing the sample inside this clamped tube. The clamped tube will isolate the sample tube from the surroundings to minimize the occurrence of regions that will cool faster. Assemble the Pasport Chemistry Sensor with the temperature probe

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Determine freezing point of your pure solvent acid: - Transfer about 4 g (weigh accurately) of your solvent acid (Room 101 Stearic Acid, and Room 105 Lauric Acid) to a large test tube. The large test tube, 20x150, is the one that fits into the jumbo clamped test tube). - Heat in hot water above 85oC. All should be melted. - Remove from the hot water bath and quickly insert the temperature probe. Put the test tube in the clamped insulating tube. - Start the readings in Data Studio (take data at least as often as once every second). - Continue taking readings while stirring until formation of solid prevents stirring. - Repeat the melting and cooling process until you get two freezing points that agree within 0.25oC. Freezing point determination from cooling curve of pure acid.

Determine freezing points of an acid solution: In addition to the pure acid freezing point determined above, you will make a solution with your solute acid and determine the freezing point. Each group should prepare a slightly different mixture as follows. If you are in Room 101, accurately weigh the desired mass of lauric acid and add it to your stearic acid. The mass should be between 0.05 and 0.4 g, but different from the other groups in your room. In Room 105, do the same, but add 0.05-0.4 g of stearic acid to your lauric acid. (Be careful not to lose sample when taking the temperature probe out of the test tube.) - Repeat the melting and freezing steps as above, being certain to mix the solute well while collecting the cooling curve. - Repeat the melting and cooling process until you get two freezing points that agree within 0.25oC. If you expand the scale, you should be able to identify the freezing point by eye in Data Studio.

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Freezing point determination from cooling curve of solution

Data Analysis: Accurately determine the freezing point of each sample you worked with. This may be done in Excel by performing a linear fit on the two ends of the curve, and setting the resulting equations equal to one another. For easiest analysis, copy two selected portions of the data into new columns, and perform the linear fits separately. For each sample, calculate the mole fraction of stearic acid and the molality of your solute acid (see equations above). Submit your concentration and Tf results to the website. Collect the class’s results and plot Tf vs mole fraction. What does this plot say about the notion of Freezing Point Depression? Plot ΔTf (Tf for the pure acid – Tf for the solution; it should be a positive number) vs molality for your solvent acid, find the limiting slope, and determine kf for that acid. Be sure your lab report includes… …plots of temperature vs time for the pure fatty acid you used, and one of your solutions. Clearly identify the freezing points. … a plot of Tf vs mole fraction of the appropriate fatty acid (listen in pre-Lab or to your TA to figure this one out) using the complete set of the data from the class. … a plot of ΔTf vs molality for your solute/solvent combination. Include pertinent class data for this. Clearly identify the limiting slope. … a determination of kf for your fatty acid. …answers to the questions asked through the procedure. 1 See also, McCarthy and Gordon-Wylie, J.Chem.Ed, 82, 2005, p116-119.