Question

In graphical solution of a binary flash distillation using an XY equilibrium diagram, prove that the mass balance operating line intersects the y=x line at the feed composition, y=x=z. What determines the slope of the operating line?

Answer 1

Let f be the fraction vaporized per mole of feed.

Feed = 1 mol

Top product = f mol

Bottom product = (1-f) mol

let y be the mole fraction of the more volatile component in the top product.

Let x be the mole fraction of the more volatile component in the bottom product.

z is the mole fraction of the more volatile component in the feed.

By component balance of the more volatile component,

z*1 = yf + x(1-f)

This equation is of the straight line equation form, i.e y = mx + c , where m is the slope

Put y = x in the mass balance equation

On solving, we get

.: x = z

.: x = y = z

This implies that the mass balance operating line intersects the y=x line at the feed composition.

Slope of the line m = -(1-f)/f

The fraction of feed to be vaporized (f) determines the slope of the operating line.