How to Calculate Concentration in PPM

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Chemists have various methods for defining the concentrations of mixtures and solutions. Solutions consist of two components: the solute, which by definition is the component present in a lesser amount; and the solvent, which is the component present in a greater amount.

Solutions may comprise two liquids: a solid dissolved in a liquid; two gases; a gas dissolved in a liquid; or (less commonly) two solids. Weight percent, which is usually abbreviated w/w, is one of the more common concentration units; it represents the mass of the solute divided by the mass of the solution – which includes the masses of both the solute and solvent – multiplied by 100.

Concentration in parts per million, or ppm, closely resembles weight percent, except you multiply the mass ratio by 1,000,000 instead of 100. That is,

ppm = (mass of solute ÷ mass of solution) x 1,000,000.

Scientists generally use ppm to express concentration when weight percent would result in an inconveniently small number. For example, it's easier to describe an aqueous solution containing 0.0012 percent sodium chloride as containing 12 ppm of sodium chloride.

  1. Determine Mass of Solute

  2. Determine the mass of the solute in grams. Problems from textbooks typically state this information explicitly (e.g.,“100 grams of sodium chloride dissolved in water”). Otherwise, this normally represents the amount of the solute you weighed out on a balance before adding it to the solvent.

  3. Determine Mass of Total Solution

  4. Determine the mass, in grams, of the total solution. The solution, by definition, includes both the solute and the solvent. If you know the individual masses of the solute and solution, you can add these values to get the mass of the solution.

  5. Use Equation

  6. Enter the mass of the solute and the mass of the solution into the following equation:

    ppm = (mass of solute ÷ mass of solution x 1,000,000.

    For example, the ppm of sodium chloride in a solution containing 1.5 grams of sodium chloride dissolved in 1000.0 grams of water would be

    (1.5 g ÷ (1000.0 + 1.5 g)) x 1,000,000 = 1,500 ppm.

    Tips

    • Very dilute aqueous solutions exhibit a density close to 1.00 grams per milliliter. The volume of the solution in milliliters is equal to the mass of the solution in grams. Thus, the units of grams and milliliters of such solutions become interchangeable. The equation for determining ppm then simplifies to:

      ppm = milligrams of solute ÷ liters of solution.

References

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