Formulas for Solid Solutions

As our next example, we consider a sample of oUvine that has the analysis MgO, 26.2%, FeO, 37.1%, and Si02, 35.0%. Olivine contains the nesosilicate ion SiO. Determine the empirical formula of this sample. 

Assuming a 100 g sample, we convert percentages to mass, and then convert the masses to moles by dividing by the molar mass. 

All of the silicon must be present in the Si04 ion, so we can use it as our standard that is, because we know that the sample contains the SiO/ ion we can say that 0.582mol represents the silicate ion. The mole amounts of magnesium and iron must be calculated relative to the anion. Thus, we divide the other mole amounts (notice that MgO and FeO have one mole of cation per mole) by 0.582  

It is tempting to think that all of these numbers are really 1.00 that, in other words, there is considerable experimental error in the measurements. However, if the error were that large, the numbers should not be reported to three significant figures. Thus, it is unlikely that we can assign both Mg and Fe the value of 1.00. 

Because solid solutions exist for many minerals, let us briefly digress and consider a very small sample of olivine that contains 100 silicate ions, 118 magnesium cations, and 82 iron cations. (Notice that the number of 2+ cations must be twice the number of 4-anions, in order to achieve electrical neutrality.) The empirical formula of this sample is 

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Only those substances whose compositions were known at least qualitatively have been included. For the notation of the formulae see section 1.2. In the formulae for solid solutions, paraitheses have been used with the host atom or host compound listed first and separated by a comma firom the additive, e.g. (Te, Se)Sn. Phases which cannot be assigned to a specific stoichiometry, for whatever reason, and which cannot be explained as a solid solution, are identified by the symbols of their atoms, separated by a comma, and not enclosed in parentheses, e.g. Sb,Te. 

Only those compoimds whose compositions were known at least qualitatively have been included. In the formulae for solid solutions parentheses have been used for elements substituting each other the elements enclosed in parentheses are also arranged alphabetically and separated by a comma. For reasons of clearness and depending on the problem, a series of solid solution may be presented in two different ways (e.g. DyTe-ErTe = DyxEri jTe). If the separation of a substance formula is necessary, a multiplication sign is used and the second line is indented. 

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