Question

Considering garnet chemical formula in 12 oxygen basis, the number of Mg cations in a garnet of chemical composition P (as shown in the figure) is ........ (give answer in two decimal places).

Hint:

In ternary diagrams, the relative positions of points represent the composition of a mixture of three components. To calculate the proportion of a component, simply read the percentage from the diagram.

Answer 1

Correct Answer: 0.75

Step 1: Understanding the garnet composition.
In garnet chemistry, different compositions of garnet minerals are represented by three main components: Pyrope (Mg\(_3\)Al\(_2\)Si\(_3\)O\(_12\)), Almandine (Fe\(_3\)Al\(_2\)Si\(_3\)O\(_12\)), and Grossular (Ca\(_3\)Al\(_2\)Si\(_3\)O\(_12\)). The chemical composition of a garnet in the triangle is given in terms of the proportions of Pyrope, Almandine, and Grossular. The point P is located on this triangle, representing a specific composition.
Step 2: Using the ternary diagram.
From the ternary diagram of garnet compositions, the position of point P represents the relative proportions of Pyrope, Almandine, and Grossular. In this case, we are specifically interested in the amount of Mg cations. Mg is present in the Pyrope component, with the formula (Mg\(_3\)Al\(_2\)Si\(_3\)O\(_12\)).
Step 3: Interpreting the position of P.
From the diagram, it is clear that point P corresponds to a position between Pyrope and Almandine. The number of Mg cations is directly related to the proportion of Pyrope in the composition. As shown in the figure, the proportion of Pyrope is about 0.75, meaning that 75% of the garnet composition is Pyrope, and thus, 75% of the total number of cations will be Mg.
Step 4: Conclusion.
Therefore, the number of Mg cations in the garnet composition is 0.75.