Derivation of a Chemical Formula from the Analysis of a Mineral

The chemical formulas which are assigned to minerals have in every case been calculated from chemical analysis. An analysis gives the percentage composition of a mineral or, in other words, the parts by weight in one hundred of the different elements or radicals present. Considerer the following analysis of chalcopyrite:

Percentages   Atomic weights     Ratio S  = 34.82  ÷  32.06 = 1.086 = 2.00 Cu = 34.30  ÷ 63.6 = 0.539 = 0.99 or 1.00 Fe = 30.59  ÷ 55.9  = 0.547 = 1.00 99.71

The percentage numbers given indicate the proportions by weight of the different elements in the mineral. But as these elements have different atomic weights, the numbers do not represent the ratio of the different atoms to each other in the chemical molecule. In order to derive the relative proportions of the atoms of the different elements to each other, the percentages as given are divided in each case by the atomic weight of the element. This gives a series of numbers which does represent the ratio of the atoms to each other in the molecule. In the analysis of chalcopyrite this ratio becomes S : Cu : Fe = 2 : 1 : 1. Consequently CuFeS2 will constitute the chemical formula for the mineral.

If the mineral is an oxygen compound the results of the analysis are given as percentages of the oxides present and by a calculation similar to that outlined above the ratio of these oxide radicals to each other in the molecule is determined; the only difference in the process being that in this case the percentage numbers are divided by the sum of the atomic weights of the elements present in the different radicals. As an example consider the following analysis of gypsum: 

Percentages   Molecular weights     Ratio SO3  = 46.61  ÷  83.06 = 0.583 = 1.00 CaO = 32.44  ÷ 56.1 = 0.578 = 0.99 or 1.00 H2O = 20.74  ÷  18.0  = 1.152 = 1.98 or 2.00    99.79

From this it is seen that the ratio of the radicals to each other in the molecule is SO3 : CaO : H2O = 1: 1 :2, and consequently the composition of gypsum can be represented by the formula CaO.SO3. 2H2O or Ca SO4. 2H2O.

Calculation of the Percentage Composition of a Mineral from Its Chemical Formula
If frequently happens that it is desirable to determine what the theoretical composition of a mineral ism having given its formula. The process of calculation is the reverse of that described in the preceding division. Take, for example , the mineral chalcopyrite, CuFeS2; what are the proportions by weight of the different elements in one hundred parts of the mineral? The process consists in first adding up the atomic weights of the different elements present and so obtaining the molecular of the compound, as follows:

Atomic weights Cu   = 63.6 Fe   = 55.9 S = 32.06 x 2 = 64.62 Molecular weight Cu Fe S2 = 183.62

It is obvious from the above that in 183.62 parts by weight of chalcopyrite there are 63.6 parts of copper, etc. In order to find the parts of copper in 100 parts of the mineral, or I other words, its percentage, the following proportion is made:

: 63.6 = 100 : x.

When this equation is solved, x becomes 34.64, or the percentage of copper in chalcopyrite. The percentages of the iron and sulfur are to be obtained in a similar manner.