Rayleigh equation

Rayleigh equation:
For batch distillation process where a fixed quantity of feed is charged to the distillation column and separation of volatile products is done by supplying heat through the still or reboiler. As the boiling point of liquid is reached a portion of liquid starts to vaporize to the top of the column and directed to the condenser, the vapor leaving the column is always at equilibrium with the liquid in the bottom of the column, thus a material balance equation is produced by Rayleigh called Rayleigh Equation which provides standard equilibrium data. For research and calculation of process condition this data is used to generate design equations. To determine the composition change with time Rayleigh equation is used and can be derived as:
Consider a liquid mixture of ‘Ao’ moles is fed to the batch column. Let ‘A’ moles of liquid remained in the bottom of the column. At give instant of time let y and x be composition of vapor and liquid.
Material Balance:

Total moles of component B left in the vessel: xA
Let dA be amount of liquid is vaporized than the mole of component B varies is: ydA or dAB
: dAB = Adx+xdA

Liquid and vapor composition balance equation

By integration to the limits of initial and final concentrations we produce a Rayleigh Equations:
Rayleigh Equations to calculate equilibrium between vapor and liquid
simple distillation experiment is used to calculate the vapor liquid equilibrium data of various liquid mixtures by applying the above Rayleigh Equation