Two liquids (A and B) are partially miscible, as shown in the phase diagram below. A mixture containing 40% of component A is prepared at room temperature. This mixture separates into two phases. When it is heated, the two phases convert into one phase. At what temperature does this occur? (Accepted error ± 2 degrees; You must enter a valid number, do not include a unit in your response.)

Question

BlackTom AI · Accepted Answer

At a fixed overall composition of 40% A (xA = 0.40), draw a vertical line on the phase diagram. The temperature where that vertical line first exits the two‑phase region and enters the single‑phase region is the temperature at which the separated phases convert into one homogeneous phase — this is the binodal (miscibility) boundary or the upper critical solution temperature (UCST) at that composition.

1) Relevant knowledge points and concepts
- Partially miscible liquids show a two‑phase region bounded by a binodal (miscibility) curve on a temperature vs composition diagram.
- For a given overall composition, the system is two‑phase while the composition–temperature point lies inside the miscibility gap; heating moves vertically upward until the binodal is crossed and a single phase forms.
- The temperature at the binodal intersection for that composition is the temperature of mixing (or of phase disappearance).

2) Step‑by‑step reasoning
- Start with overall composition xA = 0.40 at room temperature: the point lies inside the two‑phase region, so the mixture separates.
- Heat the sample: temperature increases while overall composition remains 40% A (vertical line).
- Locate where the vertical line at 40% meets the binodal curve. That intersection is the temperature where the two phases become one.

3) Intermediate steps / “calculation”
- Represent composition as xA = 0.40.
- Move along T from room temperature upward along xA = 0.40.
- Intersection with binodal occurs at T = 60 (read directly from the diagram at that composition).

4) Why the correct answer is correct
- At 60° the vertical composition line exits the two‑phase region; above 60° the mixture is fully miscible (single phase). Thus 60 is the transition temperature.

5) Why other temperatures would be incorrect
- Any lower temperature (e.g., 40°) would still lie inside the two‑phase region so separation persists. Any higher temperature (e.g., 80°) is already single‑phase, but the conversion happens at the binodal intersection (60°), not at a higher temperature.

6) Conclusion
- The two phases convert into one phase at 60 (°C). This matches the provided answer: 60.

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