On a McCabe–Thiele diagram, what is the slope of the feed (q-line) when the feed entering the distillation column is a saturated liquid (q = 1)?

Introduction / Context:
The McCabe–Thiele method graphically determines the number of ideal stages for binary distillation. The feed condition is represented by a feed line (q-line) whose slope depends on feed thermal state. Correctly identifying q-line slope is essential for accurate construction of operating lines and stage counts.

Given Data / Assumptions:

• Binary distillation under constant molar overflow assumptions.
• Feed is a saturated liquid: q = 1.
• Standard McCabe–Thiele coordinates: y (vapor composition) on the vertical axis and x (liquid composition) on the horizontal axis.

Concept / Approach:
The feed line slope is given by slope = q / (q − 1). For a saturated liquid, q = 1. Substituting gives slope = 1 / (1 − 1) which is undefined (division by zero) and, in the geometric construction, corresponds to a vertical line—i.e., infinite slope.

Step-by-Step Solution:
Start from slope formula: slope = q / (q − 1).Insert q = 1 (saturated liquid).Compute: slope = 1 / 0 → vertical line → infinite slope.Therefore the q-line is vertical through the feed composition point.

Verification / Alternative check:
For a saturated vapor (q = 0), slope = 0 (horizontal). For subcooled liquid (q > 1), slope is positive > ∞ trend; for partially vaporized feeds (0 < q < 1), slope is negative. These limiting cases confirm the saturated liquid case is vertical.

Why Other Options Are Wrong:
0 or exactly 1: correspond to saturated vapor or special cases, not saturated liquid.> 1 or < 1: finite slopes that contradict the vertical-line requirement.

Common Pitfalls:
Forgetting the formula and misplacing the q-line, which distorts operating lines and stage count.Confusing vertical with horizontal at q = 0.

Final Answer:
∞