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Archaeological Chemistry - Corrected Elemental Concentration

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Answer the following questions, showing calculations and equations where appropriate:
1. Steponaitis, Blackman, and Neff (American Antiquity 61:555-572, 1996) use the following correction for bulk elemental concentrations measured in shell- tempered pottery: e' = (1000000*e)/(1000000-2.5Ca), where e' = corrected elemental concentration, e = originally measured elemental concentration, Ca = concentration of calcium, and all measurements are in parts per million (ppm). Explain how this correction works. Hint: Assume that the shell temper is pure calcium carbonate, CaCO3.

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e' = 1000000*e/(1000000 - 2.5Ca)
divide by 10^6 (=1000000) in numerator and denominator, we get,
=> e' = e/[1 - {2.5*Ca*10^(-6)}]
=> e' = e/[1 - {(100/40)*Ca*10^(-6)}]
Now look at this expression: (100/40)*Ca*10^(-6)
because,
Ca = concentration in ppm
therefore,
Ca*10^(-6) = parts of calcium per unit of the material, i.e., ...

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