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.(To download these data in a spreadsheet file, click here.)
Solvent Molecular weight of solvent M' Normal molecular reduction of pressure K Water 18 0.185 Phosphorus trichloride 137.5 1.49 Carbon disulfide 76 0.80 Carbon tetrachloride 154 1.62 Chloroform 119.5 1.30 Pentene 70 0.74 Benzene 78 0.83 Methyl iodide 142 1.49 Ethyl bromide 109 1.18 Ether 74 0.71 Acetone 58 0.59 Methyl alcohol 32 0.33
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.
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