Model Answer
0 min readIntroduction
The Gibbs Phase Rule is a fundamental principle in physical chemistry and petrology, providing a relationship between the number of degrees of freedom (variance), the number of components, and the number of phases in a system at equilibrium. It is mathematically expressed as F = C – P + 2, where F is the degrees of freedom, C is the number of independent components, and P is the number of phases. Understanding this rule is critical for interpreting mineral assemblages and predicting the stability of rocks under varying conditions of temperature and pressure. This answer will define the Gibbs Phase Rule and then apply it to calculate the variance of the given mineral assemblage.
Gibbs Phase Rule: Definition and Explanation
The Gibbs Phase Rule, formulated by Josiah Willard Gibbs, describes the number of independently variable intensive properties (temperature, pressure, composition) that can be changed without altering the number of phases in a system at equilibrium. It’s based on the principle that at equilibrium, the chemical potential of each component must be equal in all phases.
Identifying Components, Phases, and the Chemical System
For the given assemblage – enstatite + forsterite + Mg-spinel + Mg-cordierite + corundum – we need to determine the number of components and phases.
- Phases (P): The number of physically distinct and homogeneous portions of the system is 5 (enstatite, forsterite, Mg-spinel, Mg-cordierite, corundum).
- Components (C): Determining the components requires defining the chemical system. All minerals are based on the elements Mg, Si, O, and Al. However, corundum (Al2O3) is a pure endmember and can be considered as a fixed component. Therefore, the independent components are MgO, SiO2, and Al2O3. Thus, C = 3.
Calculating the Variance (F)
Applying the Gibbs Phase Rule: F = C – P + 2
Substituting the values: F = 3 – 5 + 2 = 0
Therefore, the variance of the assemblage is 0.
Interpretation of the Result
A variance of 0 indicates that the system is invariant. This means that the temperature and pressure are fixed for this specific mineral assemblage. Any change in temperature or pressure will cause the assemblage to become unstable and new phases will form or existing phases will disappear. This assemblage represents a specific point in a phase diagram.
Considerations and Assumptions
- We have assumed that the system is closed, meaning no mass is added or removed.
- We have assumed that the system is at equilibrium.
- The chemical composition of each phase is known and fixed.
Detailed Breakdown of Component Determination
The determination of components is crucial. If we incorrectly identified the components, the variance calculation would be wrong. Let's consider the chemical formulas of the minerals:
- Enstatite: MgSiO3
- Forsterite: Mg2SiO4
- Mg-Spinel: MgAl2O4
- Mg-Cordierite: Mg2Al4Si5O18
- Corundum: Al2O3
From these formulas, we can see that the system is composed of MgO, SiO2, and Al2O3. Corundum provides a fixed Al2O3 component, reducing the degrees of freedom but not changing the number of independent components.
Conclusion
In conclusion, the Gibbs Phase Rule provides a powerful tool for understanding the relationships between phases, components, and degrees of freedom in geological systems. For the given assemblage of enstatite + forsterite + Mg-spinel + Mg-cordierite + corundum, the calculated variance of 0 indicates an invariant system, meaning the temperature and pressure are fixed for this specific mineral assemblage. This highlights the importance of understanding phase equilibria in interpreting the formation conditions of rocks and minerals.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.