Raoult vapor pressure depression

François-Marie Raoult investigated the depression of vapor pressure of a variety of solvents with many different non-volatile solutes dissolved in them. He discovered that the lowering of vapor pressure was a colligative property (to use a modern term): it was proportional to the concentration of dissolved solute but did not depend on the identity of that solute. He defined a quantity called the molecular reduction of the vapor pressure of a solution, that is to say, the relative reduction of pressure produced by 1 mole of a solute dissolved in 100 g of solvent. By relative reduction of pressure, he meant Δp/p; thus his molecular reduction of pressure (which he called K) is Δp/p for a 10-molal solution.

SolventMolecular weight of solvent M'Normal molecular reduction of pressure K
Water180.185
Phosphorus trichloride137.51.49
Carbon disulfide760.80
Carbon tetrachloride1541.62
Chloroform119.51.30
Pentene700.74
Benzene780.83
Methyl iodide1421.49
Ethyl bromide1091.18
Ether740.71
Acetone580.59
Methyl alcohol320.33
(To download these data in a spreadsheet file, click here.)
1) Is there a relationship between the "normal molecular reduction of pressure" of a solvent and the solvent's molecular weight? If so, what is it? Use a spreadsheet or plotting program to plot Δp/p vs. solvent molecular weight. If a relationship is apparent, but not a linear relationship, try plotting the natural logs of both columns. Use the program to determine the best-fit linear equation when you find a linear relationship.

2) Raoult's initial work established that vapor pressure reduction is proportional to the concentration of solute. His measure of vapor pressure reduction, K, is equal to Δp/p for a 10-molal solution. Set up a relationship like a typical colligative property relationship where the property (Δp) is proportional to the concentration (expressed in terms of molality, b). That is, derive a relationship of the form Δp = ___ x b . What is the proportionality constant (the blank in this equation)? [Note: I use the symbol b for molality because it will be convenient in solving the next problem to use m for mass rather than molality.]

3) The molality is one measure of the concentration of a solution. Mole fraction is another. The mole fraction of solute (xB) is defined as moles of solvent divided by total moles: xB = nB/(nA+nB) ≈ nB/nA , where n signifies the number of moles, A signifies solvent, and B signifies solute. The approximation in the last step is that the solution is relatively dilute, so the number of moles of solute is small compared to the number of moles of solvent. Express Δp in terms of xB. (Hint: Start by expressing b in terms of xB.) What is the proportionality constant? The result will be something close to the relationship commonly taught as Raoult's law.

Reference

François-Marie Raoult, "General Law of the Vapor Pressure of Solvents", Comptes Rendus, 104, 1430-3 (1887)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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