# Equilibrium and the Separation Process

The consideration of a single equilibrium stage is the first step in the analysis of multistage operations Also, the knowledge about phase equilibria, which is what entry number two is all about, is a prerequisite in analyzing equilibrium stage calculations. .
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V₁, Y₁ V₂, Y₂.
L₀, X₀ L₁, X₁.
Figure 1. A diagram for a single equilibrium stage.
As can be seen in the diagram, two streams (L₀ and V₂) enter in a single equilibrium stage and two streams (L₁ and V₁) also leave the stage. The composition of the entering liquid stream, L₀, can be represented as X₀ while the composition of the leaving liquid stream, L₁, can be represented as X₁. Conversely, the composition of the entering vapor stream, V₂, may be written as Y₂ while the composition of the leaving vapor stream ,V₁, may be written as Y₁. Σ is designated to be the sum of the entering streams that are thoroughly mixed together. Similarly, the overall composition of the mixture may be denoted as Z. Mass balances for a ternary system consisting of a, b and c in an equilibrium stage can be written as follows:.
Total mass balance: L₀ + V₂ = Σ (Equation 1).
Component a balance: L₀Xa₀ + V₂Ya₂ = ΣZa (Equation 2).
Component c balance: L₀Xc₀ + V₂Yc₂ = ΣZc (Equation 3).
For the leaving stream, mass balances can also be formed: .
Total mass balance: L₁ + V₁ = Σ (Equation 4).
Component a balance: L₁Xa₁ + V₁Ya₁ = ΣZa (Equation 5).
Component c balance: L₁Xc₁ + V₁Yc₁ = ΣZc (Equation 6).
A component mass balance for b can also be written, but it would be dependent since it can just be obtained from the equation Xb = 1 – Xa –Xc. Mass is transferred between the phases in the mixture Σ until equilibrium is established. .
According to McCabe, et al. (1993), for mass transfer to take place, the streams entering the stage must not be in equilibrium with each other, for it is the departure from equilibrium conditions that provides the driving force for transfer.

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