Empirical Formula of a Mineral

To determine the empirical formula of a mineral, we need to know the percentages of each element present in the compound. In this case, we have the following percentages:

- CaO = 48%
- P2O5 = 41.3%
- CaCl2 = 10.7%

Convert Percentages to Masses

To find the empirical formula, we need to convert the percentages to masses. We can assume a total mass of 100 g, which means we have the following masses:

- CaO = 48 g
- P2O5 = 41.3 g
- CaCl2 = 10.7 g

Convert Masses to Moles

Next, we need to convert the masses to moles by dividing by the molar mass of each compound. The molar masses are:

- CaO = 56.08 g/mol
- P2O5 = 141.94 g/mol
- CaCl2 = 110.98 g/mol

This gives us the following moles:

- CaO = 0.857 mol
- P2O5 = 0.291 mol
- CaCl2 = 0.0965 mol

Find the Smallest Whole Number Ratio

To find the empirical formula, we need to find the smallest whole number ratio of the moles. We can divide all the moles by the smallest number, which in this case is 0.0965. This gives us:

- CaO = 8.88
- P2O5 = 3.01
- CaCl2 = 1

We can then round these numbers to the nearest whole number to get the empirical formula:

- Ca8P3Cl2

Explanation

The empirical formula of the mineral is Ca8P3Cl2, which means that the compound contains 8 calcium atoms, 3 phosphorus atoms, and 2 chlorine atoms. This formula represents the smallest whole number ratio of the atoms in the compound. By knowing the percentages of each element present in the compound, we were able to convert those percentages to masses, then to moles, and finally find the smallest whole number ratio of the moles to determine the empirical formula.