Lecture_5b

However eq 533 can indeed be justified on physical

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Unformatted text preview: d be dV = V 1 dn 1 + V 2 dn 2 ,which is simply another application of the chain rule in partial differentiation. However, Eq. (5.33) can indeed be justified on physical grounds as follows. Consider a large volume of solution containing ethanol (E) and water (W). We now add a small amount of water, say, ∆nW moles of water, to this solution. We would want to express the new volume of the solution as V new = V old + Dn W V  ,m , W where V  ,m is the molar volume of pure water. However, this will give us the final W volume only in the case of an ideal solution. In the ethanol-water solution, the effective molar volumes of both substances are different from their molar volumes in the absence of the other substance. Designating the actual molar volume of water in the presence of ethanol as VW,m, the change of volume of the solution is DV = Dn W V W,m Therefore, we get V W,m = DV . Dn W The partial molar volume of water, VW, is defined as the value of the fraction on the right hand side i...
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