Le Moyne College



Raoult vapor pressure depression Solution

1) Plotting the normal reduction of pressure vs. the molar mass of the solvent yields quite a straight line, suggesting direct proportionality. (That is, the y-intercept is small as well.) So ∆p/p is directly proportional to M’.

[pic]

2) Φιρστ, νοτε τηατ:

Δp/p = K when b =10 .

That is what it means to define K as the relative reduction of pressure for a 10-molal solution. Rearrange this result to solve for Δp of a 10-molal solution:

Δp = Kp when b = 10 .

Finally, we know that Δp is proportional to b. So there must be a factor of b on the right hand side of this equation, but there must also be a factor which makes the right hand side Kp when b = 10:

Δp = Kp · (b/10) or Δp = (Kp/10) · b .

This is the desired relationship: vapor pressure reduction is proportional to molality, all right, and it is also proportional to the vapor pressure itself (more precisely, to the vapor pressure of the pure solvent).

3) Molality is moles of solute per kg of solvent:

b = nB/mA ,

where mA is the mass of solvent (in kg). We can express this mass in terms of moles and molar mass:

[pic] .

(The last conversion factor emphasizes that we want the solvent mass in kg, but molar masses are customarily given in g/mol.) Putting this result back into the molality definition, we have

[pic] ,

where we have recognized the ratio of solute to solvent moles as being approximately equal to the mole fraction of solute. The expression for vapor pressure lowering becomes

[pic] .

This last result states that the reduction in vapor pressure is proportional to the vapor pressure of the pure solvent and the concentration of solute (expressed here as mole fraction). The proportionality constant is 100/MA times Raoult’s “normal molecular reduction of pressure.” But Raoult’s data show that K/MA ≈ 0.010, so 100K/MA ≈ 1, and the expression for vapor pressure lowering finally becomes:

Δp = xBp .

Note: The relationship called Raoult’s law is usually expressed as

psolution = xApsolvent .

That is, it is usually written for the vapor pressure of the solution, rather than the reduction of the vapor pressure compared to the pure solvent. Subtracting from the vapor pressure of the solvent the expression we derived yields Raoult’s law:

psolvent – ∆p = psolvent – xBpsolvent ,

psolvent – (psolvent – psolution) = (1–xB)psolvent ,

psolution = xApsolvent √

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