Method of intercepts

With a condensed monolayer, such as cholesterol, it may safely be assumed that each molecule occupies essentially the same area in both pure and mixed films (4). This value is approximately 38 sq. A. per cholesterol molecule. By making this assumption it is possible to obtain, by the method of intercepts (16), the partial molecular areas, (dA/dn)rr,T, at constant r and temperature, of the expanded component in a cholesterol-mixed film. An extrapolation (10) through MN (Type I, Figure 12), or MO if linear (Type II, Figure 12) to the Ai ordinate, yields the area per molecule of the expanded component in the mixed films, where the cholesterol content is either equal to or in excess of the compositions denoted by point N (Type I) or point O (Type II). Such... 

This method is known as the method of intercepts and is of proven value in determining partial molar quantities. 

The partial molar volumes Fj = (dVldn ) listed in Table 13 have been calculated using the method of intercepts. Partial molar volumes of Si02 in the melt differ only... 

Method of Intercepts.— The method of intercepts is useful in many instances, especially as it gives simultaneously the partial molar properties of both constituents of a binary mixture of any composition. Let a represent the mean value of a particular extensive property per mole of mixture, so that the observed value of the property O for the system is given by... 

The evaluation of partial molar volumes from the experimentally determined dependency of the molar volume on composition in binary systems is made generally using the method of intercepts. Let us consider a binary melt at constant temperature and pressure in which just one mole of the mixture is present. Then it holds... 

The partial molar volumes Va and Fb in a binary mixture can be evaluated by the method of intercepts. To use this method, we plot experimental values of the quantity V/n (where is A + b) versus the mole fraction xb. V/n is called the mean molar volume. 

A variant of the method of intercepts is to plot the molar integral volume of mixing given hy... 

A general method to evaluate the partial molar quantities Xa and Xb in a binary mixtore is based on the variant of the method of intercepts described in Sec. 9.2.3. The molar mixing quantity AX(mix)/n is plotted versus xb, where AX(mix) is (X—nAX —n X ). On this plot, the tangent to the curve at the composition of interest has intercepts equal to Xa—X ... 

A binary liquid mixture in a system maintained at constant T and p can spontaneously separate into two liquid layers if any part of the curve of a plot of AGm(niix) versus xa is concave downward. To understand this phenomenon, consider Fig. 11.4. This figure is a plot of AGm(mix) versus xa- It has the form needed to evaluate the quantities (/ta - A a) and (/tb - / b) the variant of the method of intercepts described on page 233. On this... 

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