The Lever Rule

At temperature-composition points within a single-phase region, the abscissa of the phase diagram is the actual composition. In two-phase regions, on the other hand, the abscissa gives the overall composition of the two co-existing phases. Figure 8.16 shows a two-phase region (shaded area) bounded on the left by phase I and on the right by phase II. This diagram represents any of the two-phase regions with single-phase neighbors in the phase diagrams depicted in this chapter. At point P in the two-phase region of Fig. 8.16, the overall composition is xB. The compositions of the two phases present are located at the intersections of the horizontal line through P with the upper and lower

Fig. 8.16 Illustration of the lever rule

phase boundaries of the adjacent single phases - that is, at points a and b. The lengths of the line segments a-P and P-b give the relative quantities (in moles) of phases I and II in the mixture. This can be shown by material balances. If the mixture contains nI moles of phase I of composition xBI and nII moles of phase II of composition xBII, the total number of moles is N = nI + nII and the total moles of component B in the mixture is:

xbN = xBInI + xBIInn

These two equations are solved for the fraction of phase I in the mixture:

fraction phase I = ^ = —^ = ^ N x„„ - x„ ab

This formula is known as the lever rule. It applies to any two-phase region in a phase diagram but has no meaning if applied to a single-phase zone.


1. D. R. Gaskell, Introduction to Metallurgical Thermodynamics, 2nd Ed., McGraw-Hill (1981)

2. K. Valsaraj, Elements of Environmental Engineering, 2nd Ed. Lewis (2000) p. 648

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Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

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