Bismuth and cadmium form a simple eutectic mixture like those discussed in class. Bismuth melts at 271°C and 1 bar, whereas cadmium melts at 321°C and 1 bar. The enthalpy of fusion of bismuth is 11.30 kJ/mol, and that of cadmium is 6.19 kJ/mol. A eutectic point is observed at 55.5 mol% cadmium. Calculate the melting temperature of the eutectic mixture. Assume ideal behavior. b. Roughly sketch the phase diagram at 1 bar, labeling the points described above for reference. Sketch a cooling curve that passes through the eutectic point. а. C.

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**Question 8: Eutectic Mixture of Bismuth and Cadmium**

Bismuth and cadmium form a simple eutectic mixture like those discussed in class. Bismuth melts at 271°C and 1 bar, whereas cadmium melts at 321°C and 1 bar. The enthalpy of fusion of bismuth is 11.30 kJ/mol, and that of cadmium is 6.19 kJ/mol. A eutectic point is observed at 55.5 mol% cadmium.

a. **Calculate the melting temperature of the eutectic mixture.** Assume ideal behavior.

b. **Roughly sketch the phase diagram at 1 bar,** labeling the points described above for reference.

c. **Sketch a cooling curve that passes through the eutectic point.**

**Explanation of Graphs and Diagrams:**

For the phase diagram (part b), plot the temperature on the y-axis versus composition on the x-axis (in mol% of cadmium). Label the melting points of pure bismuth (271°C) and cadmium (321°C). The eutectic point should be marked at 55.5 mol% cadmium, with the corresponding eutectic temperature indicated.

For the cooling curve (part c), illustrate temperature decreasing over time. The curve should show a characteristic horizontal segment at the eutectic temperature, where the mixture transitions from liquid to solid.
Transcribed Image Text:**Question 8: Eutectic Mixture of Bismuth and Cadmium** Bismuth and cadmium form a simple eutectic mixture like those discussed in class. Bismuth melts at 271°C and 1 bar, whereas cadmium melts at 321°C and 1 bar. The enthalpy of fusion of bismuth is 11.30 kJ/mol, and that of cadmium is 6.19 kJ/mol. A eutectic point is observed at 55.5 mol% cadmium. a. **Calculate the melting temperature of the eutectic mixture.** Assume ideal behavior. b. **Roughly sketch the phase diagram at 1 bar,** labeling the points described above for reference. c. **Sketch a cooling curve that passes through the eutectic point.** **Explanation of Graphs and Diagrams:** For the phase diagram (part b), plot the temperature on the y-axis versus composition on the x-axis (in mol% of cadmium). Label the melting points of pure bismuth (271°C) and cadmium (321°C). The eutectic point should be marked at 55.5 mol% cadmium, with the corresponding eutectic temperature indicated. For the cooling curve (part c), illustrate temperature decreasing over time. The curve should show a characteristic horizontal segment at the eutectic temperature, where the mixture transitions from liquid to solid.
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