The Lever Rule is a simple graphical relationship between the proportions of phases in a mixture. If you have a good understanding of the Lever Rule, you will have a powerful tool at your disposal for the study of igneous and metamorphic rocks. Because the weight percent proportions must add up to 100,

**when there are only two phases**(such as brine and halite) there is only one variable. If the weight percent of one phase is known to be X, the weight percent of the other phase must be (100-X). If the bulk composition of the mixture is known, the weight percent of each phase can be calculated. The Lever Rule works like a composition axis from 0% to 100% that is stretched from the composition of one phase to the composition of another phase in a two-phase mixture. In the case of a brine-halite mixture, the "lever" or "tie line" extends from the brine composition to the halite composition. These relationships are shown in Figure 3.05. Click on Figure 3.05 to expand the figure, then click on the Lever Rule button.

As you saw in the enlarged version of Figure 3.05, the bulk composition of a mixture of two phases divides the line between them (a tie line) into two parts whose relative lengths give the relative masses of the two phases. This relationship is called the Lever Rule because the mass of one phase would balance the mass of the other phase if the tie line were a lever and a fulcrum was placed at the position of the bulk composition. Figure 3.06 shows a lever and weights (circles whose area are proportional to the masses) for the brine-halite equilibrium shown in the previous figures. Click on Figure 3.06. Drag the fulcrum to change the masses and see how the Lever Rule works.

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- The brine has all the water (50g of H2O).
- The brine is saturated with halite and must, therefore, be 25 weight percent NaCl and 75 weight percent H2O.
- 75 weight percent of the brine is all the H2O (50g).
- The 25 weight percent of the brine that is NaCl must be 50g*(25/75) = 16.67g.
- The mass of the brine is 50g (H2O) + 16.67g (NaCl) = 66.67g
- The remaining NaCl (50g - 16.67g = 33.33g) must be in halite.
- The weight percent of brine in the mixture is 100*[66.67g/(66.67g + 33.33g)] = 66.67%.

You can check this result using the enlarged version of Figure 3.05. Click on the Coordinates button to locate the bulk composition (50 weight percent H2O and 50 weight percent NaCl. Click on the Lever Rule button. Drag the Lever Rule handle to match that bulk composition and you will be able to read the weight percent brine in the mixture.