Question

Consider four minerals P, Q, R, and S in a three-component chemical system (A-B-C) as shown in the figure. For a crossing tie-line relationship, the variance (degrees of freedom) of the equilibrium mineral assemblage at X is
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Hint:

The variance in a system can be calculated using the Gibbs phase rule, taking into account the number of components and phases.

Answer 1

Step 1: Understanding the question.
The question involves the use of the Gibbs phase rule to calculate the variance (degrees of freedom) for the mineral assemblage at point X in a three-component system.
Step 2: Analyzing the solution.
The Gibbs phase rule for a system with \(C\) components and \(F\) phases is given by: \[ F = C - P + 2 \] Where \(F\) is the variance, \(C\) is the number of components, and \(P\) is the number of phases. In this case, for a three-component system with a crossing tie-line, there are 3 components and 2 phases at point X, so the variance is: \[ F = 3 - 2 + 2 = 2 \] Step 3: Conclusion.
The correct answer is 2, the variance at point X.