Question

The following diagram shows phase relations in a system consisting of components A and B at 1 bar pressure. If the initial composition of liquid is R, during cooling and crystallization of magma, which of the following statement(s) is/are CORRECT?

• A. On complete crystallization of magma, the final composition (in wt.%) of rock consists of 25% of mineral A and 75% of mineral B.
• B. On cooling of magma, mineral A is the first mineral to crystallize.
• C. At point Q, the weight percentages of crystal and liquid are 37.5 and 62.5, respectively.
• D. The composition (in wt.%) of liquid at point E is 40% A and 60% B.

Hint:

In a binary phase diagram, the eutectic point represents the composition where two components crystallize simultaneously, and the proportions of the phases can be determined using the lever rule.

Answer 1

The Correct Option is A, C

The diagram provided shows the phase relations between components A and B at 1 bar pressure. Here’s an analysis of the statements:
- (A) On complete crystallization of magma, the final composition (in wt.%) of rock consists of 25% of mineral A and 75% of mineral B: At point E (the eutectic point), both minerals A and B crystallize together in a specific ratio. The composition of the final solid phase formed by the complete crystallization of the magma consists of 25% mineral A and 75% mineral B. This is the correct interpretation based on the phase diagram. Therefore, the correct answer is (A).
- (B) On cooling of magma, mineral A is the first mineral to crystallize: From the phase diagram, mineral A crystallizes only after the liquid composition reaches the eutectic point. Therefore, this statement is incorrect. The first mineral to crystallize would be the one corresponding to the higher proportion of the composition initially in the liquid phase, which is not necessarily mineral A. Hence, (B) is incorrect.
- (C) At point Q, the weight percentages of crystal and liquid are 37.5 and 62.5, respectively: At point Q, the diagram shows the proportions of crystal and liquid phases in the system. Using the lever rule, we can determine the crystal and liquid proportions. The values of 37.5% crystal and 62.5% liquid are consistent with the phase diagram at point Q. Therefore, (C) is correct.
- (D) The composition (in wt.%) of liquid at point E is 40% A and 60% B: Point E is the eutectic point, where both minerals A and B crystallize together. The composition of the liquid at this point should correspond to the eutectic composition, but the phase diagram indicates that the liquid composition at this point is 50% A and 50% B. Hence, (D) is incorrect.
Thus, the correct answers are (A) and (C).