Raoult freezing point depression

François-Marie Raoult investigated the depression of the freezing point of a variety of solvents with many different solutes dissolved in them. The table below reports the depression of the freezing point of benzene when various substances were dissolved in it. The reported depressions are for solutions of one gram solute dissolved in 100. g benzene.
Substancemolecular weightdepression of freezing point, °C
methyl iodide1420.335
chloroform119.50.428
carbon tetrachloride1540.333
carbon disulfide760.654
ethyl iodide1560.331
ethyl bromide1090.461
hexane860.597
ethylene chloride990.491
turpentine (α-pinene)1360.366
nibrobenzene1230.390
naphthalene1280.391
anthracene1780.287
methyl nitrate770.640
dimethyl oxalate1180.417
methyl salicylate1520.339
diethyl ether740.671
diethyl sulfide900.576
ethyl nitrile550.938
ethyl formate740.666
ethyl valerate1300.384
allyl thiocyanate990.519
nitroglycerine2270.220
trigylceride of butyric acid3020.161
trigylceride of oleic acid8840.056
acetaldehyde441.107
chloral147.50.342
benzaldehyde1060.473
camphor1520.338
acetone580.850
dibutyl ketone1420.359
(To download these data in a spreadsheet file, click here.)
1) The freezing point of a solution is depressed compared to that of a pure solvent. The difference in freezing point depends on the identity of the solvent and on the quantity (but not the identity) of dissolved solute. The quantitative relationship is:
ΔT = Kfm ,
where ΔT is the freezing point of the pure solvent minus that of the solution, m is the molality of the solution (moles of solute per kg of solvent), and Kf the freezing-point depression constant or cryoscopic constant. For any three solutes from the table above, compute the molality of the solution (1.00 g solute in 100. g solvent) and determine Kf.

2) Data such as those in the table above established the law of freezing point depression. As Raoult wrote in paper in which he presented these data,

"One can say, so far, that in a multitude of cases, the depression of the freezing point of a solvent depends only on the ratio of the numbers of molecules of the dissolved substance and of solvent; it is independent of the nature, the number, the arrangement of the atoms which compose the dissolved molecules."
Use a spreadsheet to compute the freezing point depression constant from the data for all of the solutes. How constant is the freezing-point depression constant? Compute the mean and standard deviation of the constant according to these data. Are there any data points more than two standard deviations from the mean? Would it be justified to discard such points?

Reference

François-Marie Raoult, "Law of freezing of neutral substances dissolved in benzene", Comptes Rendus 95, 187-9 (1882) [pdf page images available from the National Library of France (en Français,)]
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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