Thermodynamics Binary Phase Diagram Problem

In summary, when a mixture of 70 weight percent B and 30 weight percent A is held at 950 °C for a long time, the resulting equilibrium state has 77.67 percent of the mixture in the solid phase and 22.33 percent in the liquid phase. The percentages of A and B in the solid and liquid phases can be found at the ends of the tie line. These results are consistent with the given overall composition.
  • #1
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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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  • #2
The percentages of A and B in the solid and in the liquid phases are at the two ends of your tie line.
 

1. What is a binary phase diagram?

A binary phase diagram is a graphical representation of the relationship between temperature, pressure, and the composition of a binary mixture. It shows the phases that are present at different combinations of temperature and pressure, and how these phases change as the composition of the mixture is altered.

2. How do you interpret a binary phase diagram?

To interpret a binary phase diagram, you first need to identify the composition of the mixture you are studying. Then, find the point on the diagram that corresponds to the temperature and pressure conditions of your system. The phases present at that point will be indicated by different regions on the diagram. The boundaries between these regions represent phase transitions.

3. What is the difference between a liquidus and a solidus line?

The liquidus line on a binary phase diagram represents the temperature at which a mixture will start to melt and become a liquid. The solidus line, on the other hand, represents the temperature at which a mixture will start to solidify and become a solid. The area between these two lines is known as the "two-phase region" and represents the coexistence of liquid and solid phases.

4. How do you use a binary phase diagram to predict the behavior of a mixture?

A binary phase diagram can be used to predict the behavior of a mixture by identifying the composition of the mixture, finding the corresponding point on the diagram, and then following the phase boundaries to determine the phases that will be present at different temperatures and pressures. This information can be used to understand how the mixture will behave under different conditions and to design processes for separating the components of the mixture.

5. Why is the knowledge of binary phase diagrams important in thermodynamics?

Binary phase diagrams are important in thermodynamics because they provide valuable information about the thermodynamic properties of mixtures. They can help us understand how mixtures behave under different conditions, and they are essential in the design and optimization of processes involving mixtures, such as distillation, crystallization, and extraction. Additionally, binary phase diagrams can also provide insights into the chemical and physical properties of individual components within a mixture.

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