VAPOR PRESSURE-VAPOR COMPOSITION CURVES OF IDEAL SOLUTIONS OF TWO VOLATILE, CONSOLUTE LIQUIDS H. S. VAN KLOOSTER, RENSSELAER POLYTECANIC INSTITUTE, TROY, NEWYom
Introduction
It is an established fact that a binary system of two consolute, volatile liquids gives sometimes a straight-line relationship between the vapor pressure (at constant temperature) and the composition of the solution when the latter is expressed in mol fractions of the two components. This case is comparatively rare and applies only to liquid pairs in which there is practically no volume change, nor any heat effect, on mixing, as, for instance, in dissolving - benzene in its nearest homolog, toluene. This is the example most frequently quoted in textbooks. Such a pair of liquids might be called an "ideal" liquid solution. Now the straight line connecting the points PIand Pz,representing the vapor pressures of the consolute ideal liquids A and B (see Figure I), shows a t once the relation between the vapor pressure of a given solution and the composition (in mol fractions) of the liquid phase with which the vapor is in equilibrium. In none of the texts consulted by the writer is there any reference to the fact that the points indicating the composition of the vapor in mol fractions lie on an equilateral hyperbola through the points PIand P2. This is rather surprising when one considers that for non-ideal liquids two curves are always drawn, viz., one for the composition of the liquid and one for the composition of the vapor. These curves are either without a maximum or a minimum (convex for the liquid and concave for the vapor) or else they exhibit a maximum with a common horizontal tangent or a minimum with a common horizontal tangent as the case may be. Discussion Since the hyperbolic vapor pressurevapor composition curve can be readily constructed and its equation established the following brief discussion may be of interest. 1455'
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JOURNAL OF CHEMICAL EDUCATION
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AUGUST, 1932
For the composition N (Figure 1) the total vapor pressure is represented by NL (= BL'), the partial pressure of B by N M (= BM') and that of A by ML (= K N = MIL'). The mol fraction of B in the vapor is M'B/LfB and that of A is L'M1/ L'B. Draw the line V'LL' parallel to AB. Connect B with V' and draw M' V parallel to B V'. V then represents the point which indicates the composition of the vapor V in equilibrium with the liquid L. For any other solution the composition of the vapor can be similarly found when that of the coexisting liquid phase is given. Mathematical Development If the (total) vapor pressure is p and the mol fraction of B in the vapor is x, while the corresponding mol fraction of B in the liquid is x ' , the following
relations hold: MN = x% = xp (1 - x')P1 = ( I - x)p
LM ( = K N )= Adding (I) and (11) we get: xrpZ
+ ( 1 - x')P, = p or:
Substituting this value in (I) : P, - p xp = P,
- Pn
P2
=
Moving the p-axis to the left over a distance of Pz/(PI- PE), the equation takes the form: xp
=
PIP* ---P, - Pz
which is the expression for an equilateral hyperbola through PI and Pz. In the particular figure presented in the text PI is taken as 3P2 and the distance AB (= 1) equal to PI-PZ in which case the vertical asymptote lies to the left of A a t a distance of ' / d B .
