The formulas to calculate the mole fraction of each phase are:
\[ Xₐ = \frac{B - T}{B - A} \]
\[ X_b = \frac{T - A}{B - A} \]
Where:
The Lever Rule is a tool used in thermodynamics to determine the mole fraction (or mass fraction) of each phase of a binary equilibrium phase diagram. It is based on the principle of conservation of mass and is called the “Lever Rule” because it can be visually represented as a lever on a fulcrum, where the lengths of the lever arms are inversely proportional to the amounts of the phases present.
Let's assume the following values:
Using the formulas to calculate the mole fractions:
\[ Xₐ = \frac{0.8 - 0.5}{0.8 - 0.2} = \frac{0.3}{0.6} = 0.5 \]
\[ X_b = \frac{0.5 - 0.2}{0.8 - 0.2} = \frac{0.3}{0.6} = 0.5 \]
The mole fractions of Phase A (Xₐ) and Phase B (X_b) are both 0.5.