Composition And Structure Of The Atmosphere

Step 1: Understanding the question.
The question asks for the number of Mg cations in garnet of chemical composition P, based on the given diagram and garnet formula.
Step 2: Analyzing the solution.
The point P represents a specific composition in the garnet ternary diagram, which can be used to calculate the number of Mg cations. Using the given diagram and the molar proportions, we calculate the number of Mg cations as 0.50.
Step 3: Conclusion.
The correct answer is 0.50, representing the number of Mg cations in the garnet composition P.

Step 1: Understanding the question.
The question refers to a binary temperature-composition phase diagram and asks for the crystallization behavior of a starting melt with a composition of X₆₀Y₄₀. We are concerned with fractional crystallization and equilibrium crystallization.
Step 2: Analyzing the options.
(A) The first formed crystal has a composition of X₂₀Y₈₀: Correct — During fractional crystallization, the first crystal to form is typically richer in one component, in this case X₂₀Y₈₀.
(B) The final melt composition during equilibrium crystallization is X₆₀Y₁₀: Correct — In equilibrium crystallization, the final composition of the melt is typically enriched in the more refractory component, in this case Y.
(C) In case of fractional crystallization, the final melt is enriched in X than X₉₀Y₁₀: Correct — As the crystallization proceeds, the melt becomes progressively enriched in X, leading to a final melt composition like X₉₀Y₁₀.
(D) For fractional crystallization, the final crystal composition is X₆₀Y₄₀: Incorrect — The final crystal composition after fractional crystallization is typically not the same as the original composition, as the crystals become enriched in one component over time.
Step 3: Conclusion.
The correct answer is (A), (B), (C). These statements correctly describe the behavior of the system during crystallization.

Step 1: Understanding the question.
Forsterite is the magnesium end-member of the olivine solid solution. In olivine with chemical formula Mg₁₋ₓFeₓSiO₄, the mole fraction of forsterite is (1 - x), where x is the mole fraction of the Fe component.
Step 2: Analyzing the solution.
To calculate the mole percent of forsterite, we use the formula (1 - x) × 100. This gives the mole percentage of the forsterite component in the olivine crystal.
Step 3: Conclusion.
The correct answer is (1 - x) × 100, which gives the mole percent of forsterite in olivine.