Two compounds (A and B) are partially miscible in the solid state, as shown in the phase diagram below. A mixture containing 30% of component A is prepared at 500°C and allowed to cool down. When it is cooled to 300°C, it separates into two phases: liquid phase and solid phase. Estimate from the graph the composition of the solid phase (in terms of mole fraction of A) (Accepted error ± 2%; You must enter a valid number, do not include a unit in your response.)

Question

BlackTom AI · Accepted Answer

The liquidus and solidus tie-line at 300°C gives the compositions of the coexisting liquid and solid phases. Read across the phase diagram at 300°C and use the intersection with the solidus curve to find the solid composition.

1) Relevant concepts
- Phase diagram boundaries: liquidus (above which only liquid exists) and solidus (below which only solid exists). Between them a two‑phase region (liquid + solid) occurs.
- At a fixed temperature in the two‑phase region, the horizontal tie‑line intersects the liquidus and solidus curves; those intersection points are the compositions of the liquid and solid phases, respectively.
- Mole fraction notation: percent converted to mole fraction (30% = 0.30).

2) Step‑by‑step reasoning
- Start composition: overall xA = 0.30 at 500°C (all liquid if above liquidus).
- Cool to 300°C: the system lies inside the two‑phase (liquid + solid) field, so it separates into a liquid phase with composition xL and a solid phase with composition xS.
- Draw (mentally) a horizontal line at T = 300°C. Locate where this line meets the solidus curve (left intersection) — that x coordinate is xS (mole fraction A in the solid).
- From the provided phase diagram, that left intersection reads approximately xS = 0.15 (mole fraction A).

3) Calculations / intermediate steps
- Convert initial composition: 30% A → xA = 0.30.
- Read solid composition directly from tie‑line: xS ≈ 0.15 (no algebra required because composition is read from the diagram).

4) Why this is correct
- The solid phase composition is defined by the solidus intersection at the given temperature. The diagram’s 300°C tie‑line clearly places the solid phase at about xA = 0.15. This is independent of the overall composition except that the overall composition must fall in the two‑phase region (which it does).

5) Why other answers would be incorrect
- Using x = 0.30 (the overall composition) is wrong because the overall composition is not the same as the composition of each phase in a two‑phase region.
- Picking the liquid‑phase intersection (the right tie‑line point) would give the liquid composition, not the solid composition.
- Any value far from 0.15 would contradict the tie‑line intersections shown on the phase diagram.

6) Conclusion
The solid phase composition (mole fraction of A) at 300°C is 0.15, which matches the provided answer.

类似问题

Match the following 1: Tie line is 2: Phase is 3: Critical point is 4: Azeotrope is 5: Phase diagram is 6: Eutectic is

If the plot is not displayed, please see Figure F13-4-2-b (the water phase diagram) in the eBook to answer this question. Above is the phase diagram of water. What is the name of the point at which the three lines intersect?

If the plot is not displayed, please see Figure F13-4-2-b (the water phase diagram) in the eBook to answer this question. Above is the phase diagram of water. Which point (pressure & temperature) corresponds to the triple point?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单