McCabe Thiele Diagram Labeled – Lines, Curve and Stages

All 12 parts on the diagram

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The frame 4

Equilibrium curve The vapor composition in balance with each liquid composition. It bows above the diagonal from corner to corner.
Diagonal line (x = y) The line where vapor and liquid have the same composition.
Liquid composition (x) The horizontal axis: the lower-boiling liquid as a share of the liquid.
Vapor composition (y) The vertical axis: the lower-boiling liquid as a share of the vapor.

The operating lines 4

Rectifying operating line The operating line for the column above the feed. It starts where the distillate composition meets the diagonal.
Stripping operating line The operating line for the column below the feed. It starts where the bottoms composition meets the diagonal.
Feed line (q-line) It starts where the feed composition meets the diagonal. Its slope shows the condition of the feed.
Intersection of the operating lines Here the feed line meets the two operating lines.

Read off the chart 4

Theoretical stage One step between an operating line and the curve. Counting the steps gives the number of theoretical stages.
Distillate composition The composition of the top product, the distillate.
Feed composition The composition of the mixture fed to the column.
Bottoms composition The composition of the bottom product, the bottoms.

How this list was compiled: Every name checked on 2026-10-03 in two texts. (1) Wikipedia, text only, McCabe-Thiele method: both axes give the mole fraction of the lighter component, the horizontal axis in the liquid and the vertical in the vapor; the x = y line; the vapor-liquid equilibrium line from (0,0) to (1,1); vertical lines for the feed, the distillate (top product) and the bottoms compositions drawn up to the x = y line; the rectifying section operating line; the stripping section operating line; the q-line of slope q/(q-1), vertical for a saturated liquid and level for a saturated vapor; the steps from operating lines to equilibrium line as theoretical plates. (2) Newcastle University, M. T. Tham, Introduction to Distillation: Distillation Column Design (archived course page): the equilibrium curve; the diagonal line; operating lines as the mass balance between liquid and vapor; the operating line for the rectification section from the top product composition on the diagonal, with slope R/(R+1); the operating line for the stripping section from the bottom product composition; each corner of the construction as a stage; the feed line or q-line through the intersection of the operating lines and the feed composition on the diagonal. Licence: own work

The drawing: Drawn for this site on 2026-10-03 by script from six numbers of a made-up mixture. Own work, nothing traced. Licence: own work

How it works

This McCabe-Thiele diagram is labeled part by part: the equilibrium curve, the diagonal, the two operating lines, the feed line and the steps between them. Study the names, then quiz yourself. The mixture is made up; no numbers are asked.

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How the chart is built

Both axes give the share of the lower-boiling liquid: in the liquid along the bottom, in the vapor up the side. The equilibrium curve bows above the diagonal. The rectifying line runs down from the distillate point on the diagonal, the stripping line up from the bottoms point, and the feed line passes through the point where they meet.

Counting stages

Steps are drawn between the operating lines and the curve, from the distillate down to the bottoms. Each step is one theoretical stage.

The feed line stands upright when the feed is a saturated liquid and lies level when it is a saturated vapor.

Questions and answers

What is a McCabe-Thiele diagram used for?

It models the separation of two liquids in a distillation column. The steps drawn between the operating lines and the equilibrium curve give the number of theoretical stages the separation needs.

What is the q-line on a McCabe-Thiele diagram?

The feed line. It starts where the feed composition meets the diagonal, and its slope, q divided by q minus 1, shows the condition of the feed. Here q is the liquid fraction of the feed.

What do the operating lines show?

The balance between the liquid and the vapor that pass each other in the column: the rectifying line for the section above the feed, the stripping line for the section below it.

What does the 45-degree line mean?

On the diagonal the vapor and the liquid have the same composition. The three upright composition lines are carried up to it, and the operating lines start from those points.