Thermodynamics Binary Phase Diagram Problem

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SUMMARY

The discussion focuses on solving a binary phase diagram problem involving substances A and B, with melting points of 600 °C and 1200 °C, respectively. At 950 °C, a mixture of 70 weight percent B and 30 weight percent A reaches equilibrium, resulting in 77.67 percent solid and 22.33 percent liquid. The percentages of A and B in both solid and liquid phases can be determined using the tie line method on the phase diagram. The calculations confirm consistency with the overall composition of the mixture.

PREREQUISITES
  • Understanding of binary phase diagrams
  • Knowledge of phase equilibrium concepts
  • Familiarity with weight percent calculations
  • Ability to interpret thermodynamic data
NEXT STEPS
  • Study the construction and interpretation of binary phase diagrams
  • Learn about tie lines and their significance in phase equilibrium
  • Explore the calculation of phase compositions using lever rule
  • Investigate the effects of temperature on phase transitions in materials
USEFUL FOR

Chemical engineers, materials scientists, and students studying thermodynamics or phase equilibria will benefit from this discussion.

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Homework Statement


Refer to the attached binary phase diagram. Substance A has a melting point of 600 °C and B has a melting point of 1200 °C. A mixture of 70 weight percent B and 30 weight percent A is held at 950 °C for a long time - long enough to reach equilibrium.
a) Determine the weight percent that is solid and the weight percent that is liquid.
b) Determine the percentages by weight of A and B in the solid and likewise in the liquid.
c) Check that your answers to a) and b) when taken together are consistent with the given overall composition.


Homework Equations



See attached pictures, (easier to visualize subscripts)


The Attempt at a Solution



Drawing a horizontal line at 950°C, I was able to find W(l) and W(s). I also found W(o) by putting a vertical line at the 70 percent mark on the horizontal axis. From this I was able to find the weight percent, however I'm not sure if it is the weight percent solid or liquid. That is pretty much where I am stuck.
Correction:
I figured out that it is 77.67 percent solid, 22.33 percent liquid.
Now I'm just having trouble on parts b and c.
 

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Last edited:
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The percentages of A and B in the solid and in the liquid phases are at the two ends of your tie line.
 

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