Phase Equilibria and The Phase Rule

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What is the temperature at which a minute amount of solid thymol separates out to form a two-phase solid-liquid system in system X?

29°C

What is the composition of the mixture at the eutectic point in the salol-thymol system?

34% thymol in salol

What is the consequence of forming eutectic mixtures in pharmaceuticals?

They may liquefy at ambient temperature

What is the eutectic temperature of the 1:1 mixture of lidocaine and prilocaine?

18°C

What happens as system X is progressively cooled?

More and more of the thymol separates as solid

What is the lowest temperature at which a liquid phase can exist in the salol-thymol system?

13°C

What is the primary purpose of the phase rule in thermodynamics?

To calculate the number of variables that can be changed independently without affecting the system's equilibrium

What does the number of degrees of freedom represent in the context of phase equilibria?

The number of intensive variables that must be fixed to describe the system completely

What is the primary characteristic of a one-component system in terms of phase equilibria?

It can exist in multiple phases at a single temperature and pressure

What is the purpose of a phase diagram, such as the one shown in Figure 2?

To illustrate the relationship between temperature, pressure, and phase equilibria

What is the significance of the phase rule in understanding the behavior of a system at equilibrium?

It allows for the prediction of the system's phase behavior at a given temperature and pressure

What is the primary purpose of a tie line in a two-component system?

To calculate the composition of each phase.

What is the relationship between the number of degrees of freedom and the number of intensive variables in a system?

The number of degrees of freedom is the least number of intensive variables that must be fixed to describe the system completely

What is the minimum number of phases present in a two-component system at equilibrium?

2

What happens to the composition of the phases when the temperature of a two-component system is increased?

The composition of the phases changes.

What is the purpose of the phase rule in a two-component system?

To determine the number of variables that can be changed independently.

Suppose we prepare a system containing 60% by weight of thymol in salol and raise the temperature of the mixture to 50°C. What can be said about the system at this point?

The system is at equilibrium.

What is the importance of knowing the composition of each phase in a two-component system?

It is used to determine the weight of each phase.

What is the role of the tie line in determining the weight of each phase?

It is used to determine the weight of each phase directly.

What happens to the weight of each phase when the temperature of a two-component system is increased?

The weight of each phase changes.

Study Notes

Phase Equilibria and The Phase Rule

  • The phase rule is a relationship that determines the least number of independent variables (e.g., temperature, pressure, density, and concentration) that can be changed without changing the equilibrium state of the system.
  • The number of variables that may be changed independently without causing the appearance of a new phase or disappearance of an existing phase is referred to as the number of degrees of freedom.
  • The number of degrees of freedom is the least number of intensive variables that must be fixed/known to describe the system completely.

One Component Systems

  • A phase diagram for water at moderate pressures is shown in Figure 2.

Two Component Systems

  • Importance of Tie line:
    • Calculation of the composition of each phase.
    • Determination of the weight of each phase.

Phase Diagrams and Eutectic Points

  • A system containing 60% by weight of thymol in salol:
    • Remains a single liquid until the temperature falls to 29°C, at which point a minute amount of solid thymol separates out to form a two-phase solid–liquid system.
    • As the system is progressively cooled, more and more of the thymol separates as solid.
  • A system containing salol and thymol:
    • The solid phase that separates at 22°C is pure salol.
    • The lowest temperature at which a liquid phase can exist in the salol–thymol system is 13°C, and this occurs in a mixture containing 34% thymol in salol.
    • This point on the phase diagram is known as the eutectic point, where three phases (liquid, solid salol, and solid thymol) coexist.

Pharmaceutical Importance

  • Numerous drugs form eutectic mixtures (solid dispersion), with the consequence that they may liquefy at ambient temperature owing to the melting point decrease characteristic at the eutectic point.
  • Example: Lidocaine and prilocaine, two local anesthetic agents, form a 1:1 mixture having a eutectic temperature of 18°C.

Understand the phase rule, which determines the minimum independent variables required to maintain equilibrium in a system, and how it relates to degrees of freedom.

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