7. Antimony and lead form a simple eutectic phase diagram like those discussed in class. Antimony melts at 640.5°C and 1 bar, lead melts at 327.4°C and 1 bar. A eutectic point is observed at 80.5 mol% lead. a. What is the general definition for eutectic point? b. Roughly sketch the phase diagram at 1 bar, labeling the points described above for reference. Label each phase region and the eutectic point with the # of degrees of freedom (f). Show calculations explicitly using the phase rule. c. Sketch a cooling curve for a 10 mol% mixture of lead.

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**Problem 7: Antimony and Lead Eutectic Phase Diagram**

Antimony and lead form a simple eutectic phase diagram similar to those discussed in class. Antimony melts at 640.5°C and 1 bar, and lead melts at 327.4°C and 1 bar. A eutectic point is observed at 80.5 mol% lead.

**Tasks:**
 
a. **What is the general definition for a eutectic point?**

b. **Roughly sketch the phase diagram at 1 bar, labeling the points described above for reference.** Label each phase region and the eutectic point with the number of degrees of freedom (f). Show calculations explicitly using the phase rule.

c. **Sketch a cooling curve for a 10 mol% mixture of lead.**

---

**Instructions for solving:**

- **Eutectic Point Definition:** Understand the concept of a eutectic point, where the lowest melting point of a mixture occurs, forming a single liquid phase upon heating.

- **Phase Diagram Sketch:** Create a simple representation of the phase diagram at 1 bar. Indicate the melting points of pure antimony and lead, the eutectic composition, and the respective phases.

- **Degrees of Freedom (f):** Utilize the Gibbs Phase Rule (f = C - P + 2, where C is the number of components and P the number of phases) to determine the degrees of freedom at various points in the diagram.

- **Cooling Curve:** Illustrate the cooling behavior of a 10 mol% lead mixture, highlighting the phase transitions as the temperature decreases.
Transcribed Image Text:**Problem 7: Antimony and Lead Eutectic Phase Diagram** Antimony and lead form a simple eutectic phase diagram similar to those discussed in class. Antimony melts at 640.5°C and 1 bar, and lead melts at 327.4°C and 1 bar. A eutectic point is observed at 80.5 mol% lead. **Tasks:** a. **What is the general definition for a eutectic point?** b. **Roughly sketch the phase diagram at 1 bar, labeling the points described above for reference.** Label each phase region and the eutectic point with the number of degrees of freedom (f). Show calculations explicitly using the phase rule. c. **Sketch a cooling curve for a 10 mol% mixture of lead.** --- **Instructions for solving:** - **Eutectic Point Definition:** Understand the concept of a eutectic point, where the lowest melting point of a mixture occurs, forming a single liquid phase upon heating. - **Phase Diagram Sketch:** Create a simple representation of the phase diagram at 1 bar. Indicate the melting points of pure antimony and lead, the eutectic composition, and the respective phases. - **Degrees of Freedom (f):** Utilize the Gibbs Phase Rule (f = C - P + 2, where C is the number of components and P the number of phases) to determine the degrees of freedom at various points in the diagram. - **Cooling Curve:** Illustrate the cooling behavior of a 10 mol% lead mixture, highlighting the phase transitions as the temperature decreases.
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