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**Unformatted text preview: **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 in the limit of an infinitesimal change in the number of moles
of water. Mathematically, we write
V W =,Lim0 DV = dV .
n W @ Dn W
dn W
Once we impose the conditions that temperature, pressure and the number of
moles of ethanol, nE, are to be held constant, the derivative on the right hand side
becomes identical to the definition of the partial molar volumes used above and in
Eq. (5.33):
V W = æ ¹V ö
ç ¹n ÷
è W ø T , P, n E
8 An example of the applications of Eq. (5.33):
Consider a 40% by mass ethanol solution of ethanol in water at 25°C. From the
figure of partial molar volumes of ethanol and water in the presence of each other,
estimate the volume of 1000 g of the solution. Compare this to the volume that
would have resulted if the solution was ideal. D...

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