Question

A harzburgite contains pure forsterite and pure enstatite in a molecular ratio of 60:40. The mole % of MgO in the rock is ........

Hint:

To calculate mole % of a component in a mixture, use mole ratios, chemical formulas, and molar masses to determine the total mole of each element in the sample.

Answer 1

Correct Answer: 60

Mineral formulas:

• Forsterite: Mg₂SiO₄
• Enstatite: MgSiO₃

Given:

• Fo(Mg₂SiO₄) = 0.6
• En(Mg₂Si₂O₆) = 0.4

Analysis:

$$\text{Mg}_2\text{SiO}_4 = 2\text{MgO} + \text{SiO}_2 \rightarrow \text{mole \% of MgO in Fo} = \frac{2}{3} \times 100$$

$$\text{Mg}_2\text{Si}_2\text{O}_6 = 2\text{MgO} + 2\text{SiO}_2 \rightarrow \text{mole \% of MgO in En} = \frac{2}{4} \times 100$$

Total (aggregate) mole % of MgO:

$$= \frac{2}{3} \times 0.6 \times 100 + \frac{2}{4} \times 100 \times 0.4$$

$$= \frac{2}{3} \times 0.6 \times 100 + \frac{2}{4} \times 100 \times 0.4$$

$$= 40 + 20$$

$$= 60%$$