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Given the adjacent analysis of a plagioclase crystal, what are the activities of albite and anorthite in the solution?

Plagioclase Analysis

Oxide	Wt. percent
SiO2	44.35
Al2O3	34.85
CaO	18.63
Na2O	0.79
K2O	0.05

Answer: According to the local charge balance model, the activity of albite will be equal to the mole fraction of Na in the octahedral site. To calculate this, we first must convert the weight percent oxides to formula units of cation. The first step is to calculate the moles of cation from the oxide weight percentages. First, we can convert weight percent oxide to weight percent cation using the formula:

Next, we calculate the moles of cation:

Combining these two equations, the atomic wt. cation terms cancel and we have:

Next, we want to calculate the number of moles of each cation per formula unit. A general formula for feldspar is: XY₄O₈, where X is Na, K, or Ca in the A site and Y is Al or Si in the tetrahedral site. So to calculate formula units in the A site, we divide the number of moles of Na, K, and Ca by the sum of moles of Na, K, and Ca. To calculate formula units in the tetrahedral site, we divide the number of moles of Al and Si by the sum of moles of Al and Si and multiply by 4, since there are four ions in this site. Since the number of oxygens is constant, we can refer to these quantities as the moles per eight oxygens. The following table shows the results of these calculations.

Cation formula units

	Mol. wt. oxide	Moles cation	Moles per 8 oxygens
Si	60.06	0.7385	2.077
Al	101.96	0.6836	1.923
Ca	56.08	0.3322	0.926
Na	61.98	0.0255	0.071
K	94.2	0.0011	0.003

The activity of albite is equal to the mole fraction of Na, 0.07; the activity of anorthite is 0.93.