Question

Based on 8 oxygen atoms, the number of silicon atoms in a plagioclase of composition \( \text{Ab}_{20}\text{An}_{80} \) is .......... (answer in one decimal place). 
 

Hint:

In mineral formulas, use stoichiometry to determine the number of atoms of a particular element based on the formula's composition and oxygen content.

Answer 1

Correct Answer: 2.2

To determine the number of silicon atoms in a plagioclase of composition \( \text{Ab}_{20}\text{An}_{80} \) based on 8 oxygen atoms, we must first understand the composition structure of the minerals involved in plagioclase:

• Albite (\( \text{NaAlSi}_3\text{O}_8 \)): Composed of 1 Na, 1 Al, 3 Si, and 8 O.
• Anorthite (\( \text{CaAl}_2\text{Si}_2\text{O}_8 \)): Composed of 1 Ca, 2 Al, 2 Si, and 8 O.

The composition \( \text{Ab}_{20}\text{An}_{80} \) indicates that the mineral is made up of 20% albite and 80% anorthite. We now calculate the total number of silicon atoms:

• In 1 mole of Albite, there are 3 silicon atoms. Therefore, in 20% Albite: \( 0.2 \times 3 = 0.6 \) silicon atoms per 8 oxygen atoms.
• In 1 mole of Anorthite, there are 2 silicon atoms. Therefore, in 80% Anorthite: \( 0.8 \times 2 = 1.6 \) silicon atoms per 8 oxygen atoms.

Summing these, we have the total number of silicon atoms in the plagioclase mineral composition:

\( 0.6 + 1.6 = 2.2 \) silicon atoms.