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How to calculate solid concentration

Updated February 21, 2017

Whether a mixture contains two mixed solids, two mixed liquids, or a solid dissolved in a liquid, the compound present in the greater amount is called the "solvent" and the compound present in the smaller amount is called the "solute." In a solid/solid mixture, the concentration of solute is most easily expressed as mass per cent. If the solute is extremely dilute (i.e., substantially less than 1 per cent by mass), then concentration is usually expressed as parts per million (ppm). Some calculations involving concentration require the solute to expressed as a mole fraction.

Calculate concentration in mass per cent by dividing the mass of the solute by the total mass of the sample and multiplying by 100. For example, if a sample of metal alloy contains 26g of nickel (Ni) and the total mass of the sample is 39g, then

(26g Ni) / (39g) x 100 = 67% Ni

Express concentration of dilute solutes in ppm by dividing the mass of the solute by the total mass of the sample and multiplying by 1,000,000. Thus, if a sample of metal alloy contains only 0.06g of Ni and the total mass of the sample is 105g, then

(0.06g Ni) / (105g) x 1,000,000 = 571 ppm

Calculate mole fraction by dividing moles of solute by the total moles of solute and solvent. This first involves converting the masses of the solute and solvent to moles, which requires knowledge of the amounts of both solute and solvent. The conversion to moles further requires the formula weights of the solute and solvent. For example, consider a nickel/iron (Ni/Fe) alloy that contains 25g of Ni and 36g of Fe. The formula weight of the Ni (determined from the periodic table) is 58.69 grams per mole (g/mol) and the formula weight of Fe is 55.85g/mol. Therefore,

Moles of Ni = (25g) / (58.69g/mol) = 0.43 mol

Moles of Fe = (36g) / (55.85) = 0.64 mol

The mole fraction of Ni is then given by (0.43) / (0.43 + 0.64) = 0.40.

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