The olivine series of minerals consists of crystals in which Fe and Mg ions may substitute for each — Solid State Chemistry Question
Question
The olivine series of minerals consists of crystals in which Fe and Mg ions may substitute for each other. The density of forsterite ($\text{Mg}_2\text{SiO}_4$) is $3.3 \text{ g/ml}$ and that of fayalite ($\text{Fe}_2\text{SiO}_4$) is $4.2 \text{ g/ml}$. What is the percentage of fayalite in an olivine with a density of $3.9 \text{ g/ml}$?
💡 Solution & Explanation
Molar mass of forsterite ($M_{Mg}$) is 140; fayalite ($M_{Fe}$) is 204. Molar volumes are $V_{Mg} = 140/3.3 = 42.42$ and $V_{Fe} = 204/4.2 = 48.57$. Let $x$ be the mole fraction of fayalite. Density $d = \frac{204x + 140(1-x)}{48.57x + 42.42(1-x)} = 3.9$. Solving gives $x \approx 0.635$. The mass percentage of fayalite is $\frac{0.635 \times 204}{0.635 \times 204 + 0.365 \times 140} \times 100 \approx 72\%$. Therefore, correct answer is 0072.