The x-y diagram depicts vapor-liquid equilibrium data, where any point on the curve shows the variations of the amount of liquid that is in equilibrium with vapor at different temperatures. In a binary system containing substances A and B, a point on the equilibrium curve can be separated into the mole percentage of the vapor that is substance A on the y axis and the mole percentage of the liquid that is substance A on the x axis. Of, course, the remaining mole percent in both cases is substance B. Since the best way to understand this concept is visually, look at the following curves. Each depicts a binary system at 1.013 bar. Most of the examples chosen show a typical simple system. However, the ethanol-water example shows a more interesting system. The use of the x-y diagram simplifies distillation calculations because bubble point or dew point calculations are no longer needed on a tray-by-tray basis. If either the vapor or liquid fraction of substance A leaving a tray is known, they other can be immediately read from the graph.
The above diagrams were created from known experimental data; a more encompassing way to create the x-y diagram is through the use of constant relative volatility. Relative volatility compares the volatility of one component to the other, and typically varies based on composition. However, when the range of values is small, the relative volatility can be considered constant and the following equation can be used.
Knowing the relative volatility for a system is also useful in determining the amount of separation possible. A relative volatility of 1 indicates that both components are equally volatile and no separation takes place, and when the relative volatility is low, ( a < 1.05), separation becomes difficult and expansive because a large number of trays are required The higher the relative volatility, or the lower the pressure, the more separable are the two components; this connotes fewer stages in a distillation column in order to effect the same separation between the overhead and bottoms products.
Typical experimental values for any binary system can be found in
Vapor-Liquid Equilibrium Data Collection
Dechema Chemistry Data Series, Frankfurt am Main, Germany, 1997