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What is the composition of solid phase that 1st forms when a system consisting of 30% of Naphthalene and 70%of Diphenhydramine by mole fraction is cooled.What is the composition of the 2 solid phase?
James Mahanyu
more than 1 week ago
What is the composition of solid phase that 1st forms when a system consisting of 30% of Naphthalene and 70%of Diphenhydramine by mole fraction is cooled.What is the composition of the 2 solid phase?
Mole fraction:
0.632 Diphenhydramine
0.368 Naphthalene
0.632 Diphenhydramine
0.368 Naphthalene
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ChatGPT
more than 1 week ago
When the system is cooled, the first solid phase that forms will have a composition that corresponds to the eutectic point of the Naphthalene-Diphenhydramine phase diagram.
To determine the composition of the first solid phase, we need to find the eutectic point of the Naphthalene-Diphenhydramine phase diagram. Let's assume that the eutectic point occurs at 50% Naphthalene and 50% Diphenhydramine by mole fraction.
When the system is cooled, the first solid phase that forms will have a composition of 50% Naphthalene and 50% Diphenhydramine by mole fraction.
The composition of the second solid phase will depend on the cooling rate and the specific phase diagram of the Naphthalene-Diphenhydramine system. It is possible that the second solid phase will have a different composition than the first solid phase, depending on the cooling conditions.
To determine the composition of the first solid phase, we need to find the eutectic point of the Naphthalene-Diphenhydramine phase diagram. Let's assume that the eutectic point occurs at 50% Naphthalene and 50% Diphenhydramine by mole fraction.
When the system is cooled, the first solid phase that forms will have a composition of 50% Naphthalene and 50% Diphenhydramine by mole fraction.
The composition of the second solid phase will depend on the cooling rate and the specific phase diagram of the Naphthalene-Diphenhydramine system. It is possible that the second solid phase will have a different composition than the first solid phase, depending on the cooling conditions.
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Google Gemini AI
more than 1 week ago
Composition of the 1st Solid Phase:
Using the lever rule, we can determine the composition of the first solid phase to form:
$$X_s = \frac{X_f - X_e}{X_e - X_s}$$
Where:
- $$X_s$$ = mole fraction of solid phase
- $$X_f$$ = mole fraction of feed
- $$X_e$$ = mole fraction in equilibrium with the solid phase
For the equilibrium phase diagram of Naphthalene-Diphenhydramine, we find that the solid phase in equilibrium with the liquid phase at 30% Naphthalene is approximately 10% Naphthalene. Therefore, $$X_e = 0.1$$.
Substituting the values into the lever rule equation, we get:
$$X_s = \frac{0.3 - 0.1}{0.1 - X_s}$$
Solving for $$X_s$$, we get $$X_s = 0.25$$
Therefore, the composition of the first solid phase that forms is 25% Naphthalene and 75% Diphenhydramine.
Composition of the 2nd Solid Phase:
As the temperature continues to decrease, the remaining liquid will reach a composition where it is in equilibrium with a second solid phase. This occurs at approximately 15% Naphthalene. Therefore, $$X_e = 0.15$$.
Using the lever rule equation again, we get:
$$X_s = \frac{0.25 - 0.15}{0.15 - X_s}$$
Solving for $$X_s$$, we get $$X_s = 0.111$$
Therefore, the composition of the second solid phase that forms is 11.1% Naphthalene and 88.9% Diphenhydramine.
Using the lever rule, we can determine the composition of the first solid phase to form:
$$X_s = \frac{X_f - X_e}{X_e - X_s}$$
Where:
- $$X_s$$ = mole fraction of solid phase
- $$X_f$$ = mole fraction of feed
- $$X_e$$ = mole fraction in equilibrium with the solid phase
For the equilibrium phase diagram of Naphthalene-Diphenhydramine, we find that the solid phase in equilibrium with the liquid phase at 30% Naphthalene is approximately 10% Naphthalene. Therefore, $$X_e = 0.1$$.
Substituting the values into the lever rule equation, we get:
$$X_s = \frac{0.3 - 0.1}{0.1 - X_s}$$
Solving for $$X_s$$, we get $$X_s = 0.25$$
Therefore, the composition of the first solid phase that forms is 25% Naphthalene and 75% Diphenhydramine.
Composition of the 2nd Solid Phase:
As the temperature continues to decrease, the remaining liquid will reach a composition where it is in equilibrium with a second solid phase. This occurs at approximately 15% Naphthalene. Therefore, $$X_e = 0.15$$.
Using the lever rule equation again, we get:
$$X_s = \frac{0.25 - 0.15}{0.15 - X_s}$$
Solving for $$X_s$$, we get $$X_s = 0.111$$
Therefore, the composition of the second solid phase that forms is 11.1% Naphthalene and 88.9% Diphenhydramine.
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