---
title: "The boiling-point composition phase diagram for a binary mixture of pentane (\\(\\text{C}_5\\text{H}_{12}\\)) and heptane (\\(\\text{C}_7\\text{H}_{16}\\)) at a constant pressure of \\(1.0\\text{ atm}\\) is shown above. In a fractional distillation experiment, a student heats a liquid sample with a pentane mole fraction of \\(\\chi_{\\text{pentane}} = 0.40\\) until it begins to boil at \\(62\\ ^\\circ\\text{C}\\). The equilibrium vapor generated at this initial boiling point is condensed and collected. Based on the diagram and principles of intermolecular forces, what is the mole fraction of pentane in the collected distillate, and why does this enrichment occur?"
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url: "https://nerd-notes.com/ubq/123700/"
date_modified: "2026-09-28T12:02:01+00:00"
---

# The boiling-point composition phase diagram for a binary mixture of pentane (\(\text{C}_5\text{H}_{12}\)) and heptane (\(\text{C}_7\text{H}_{16}\)) at a constant pressure of \(1.0\text{ atm}\) is shown above. In a fractional distillation experiment, a student heats a liquid sample with a pentane mole fraction of \(\chi_{\text{pentane}} = 0.40\) until it begins to boil at \(62\ ^\circ\text{C}\). The equilibrium vapor generated at this initial boiling point is condensed and collected. Based on the diagram and principles of intermolecular forces, what is the mole fraction of pentane in the collected distillate, and why does this enrichment occur?

The boiling-point composition phase diagram for a binary mixture of pentane (\(\text{C}_5\text{H}_{12}\)) and heptane (\(\text{C}_7\text{H}_{16}\)) at a constant pressure of \(1.0\text{ atm}\) is shown above. In a fractional distillation experiment, a student heats a liquid sample with a pentane mole fraction of \(\chi_{\text{pentane}} = 0.40\) until it begins to boil at \(62\ ^\circ\text{C}\). The equilibrium vapor generated at this initial boiling point is condensed and collected. Based on the diagram and principles of intermolecular forces, what is the mole fraction of pentane in the collected distillate, and why does this enrichment occur?

![A 2D Cartesian graph with axes labeled in grayscale. The horizontal axis is labeled Mole fraction of pentane (\(\chi_{\text{pentane}}\)) with linear tick marks at 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. The vertical axis is labeled Temperature (\(^\circ\text{C}\)) with linear tick marks at 30, 45, 60, 75, 90, and 105. Two distinct curves span from (0.0, 98) to (1.0, 36). The lower curve is a solid line labeled Liquid phase below it. The upper curve is a dashed line labeled Vapor phase above it. The region between the two curves is labeled Liquid + Vapor. A horizontal dotted tie-line at 62 degrees Celsius connects a marked point L on the solid curve at (0.40, 62) to a marked point V on the dashed curve at (0.70, 62). Vertical dotted drop-lines extend down from point L to 0.40 and from point V to 0.70 on the horizontal axis. No other particles, labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596921-o99S17.jpg)

- **A.** \(\chi_{\text{pentane}} \approx 0.70\), because pentane has a smaller, less polarizable electron cloud than heptane, resulting in weaker London dispersion forces and higher vapor pressure.
- **B.** \(\chi_{\text{pentane}} \approx 0.70\), because pentane forms stronger hydrogen bonds in the gas phase than heptane, allowing more pentane molecules to enter the vapor.
- **C.** \(\chi_{\text{pentane}} \approx 0.40\), because the mixture boils at a constant temperature of \(62\ ^\circ\text{C}\), causing the liquid and vapor phases to maintain identical compositions.
- **D.** \(\chi_{\text{pentane}} \approx 0.15\), because heptane has a larger surface area that allows it to absorb thermal energy more rapidly and vaporize preferentially.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123700/*