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Application to Mineral Extraction from ``country rock''

The CRC Handbook of Chemistry and Physics gives the concentrations in milligrams per kilogram of elements in Earth's crust. We chose iron and the five metals of the 1980-1990 Ehrlich-Simon bet. gif

To apply formula (4) we need to use the concentrations by weight given in the Handbook to compute the mole fractions of the ores of the elements in the table in earth's crust. However, we don't know the average molecular weight of the earth's crust. The earth's crust is 57 percent SiO tex2html_wrap_inline152 , which has molecular weight 60, so let's take that as the average, although maybe it should be larger. We also don't know what molecules the elements of interest are found in, but the only thing that matters for the purpose of computing their mole fractions is how many atoms of the particular element are in a molecule. We make the more conservative assumption is that there is one atom per molecule, e.g. we are assuming FeO rather than Fe tex2html_wrap_inline152 O tex2html_wrap_inline156 . The mole fraction of the ore of an element can then be obtained by multiplying its mass fraction by


We also must decide on a temperature at which we imagine the extractions to take place. We have chosen 1000 degrees Kelvin as the temperature--for lack of anything better and for the benefit of the arithmetic. Then (4) gives the energy required to extract one mole of the mineral containing the element. We assume that the energy costs $.05 per kilowatt hour, and this enables us to compare the second law part of the cost of extracting the mineral from random rock with the 1990 price of the element.

These calculations are summarized in the table:



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next up previous
Next: About this document Up: The Second Law of Previous: Theory

John McCarthy
Thu Aug 21 09:12:21 PDT 1997