Chemists use a variety of units to express the concentrations of solutions. Solutions have two components: the solute, which represents the compound present in the smaller amount, and the solvent; the solute and solvent together represent the solution. Mass percent — sometimes called weight percent — given by (mass of solute) / (mass of solution) x 100, represents one of the more common concentration units. In extremely dilute solutions, however, concentrations expressed as mass percents become very small numbers. For convenience, chemists may opt to multiply the solute/solvent mass ratio by 1 billion, or 10^9, instead of 100. The concentration units then represent parts per billion, or ppb.
Determine the mass of solute and mass of solution. This requires knowledge of the solution’s preparation. If you are dealing with a water-based solution, then 1 milliliter of solution represents 1 gram of solution. For example, a solution prepared by dissolving 0.005 grams of sodium chloride, or NaCl, in water and then diluting it to a total volume of 1.0 liter, contains 0.005 grams of solute and 1,000 grams of solution because 1 liter is equal to 1,000 milliliters and 1,000 milliliters is equal to 1,000 grams.
Divide the mass of the solute by the mass of the solution using a calculator. For dilute solutions, this will result in a small number. Continuing the previous example, 0.005 / 1000 = 0.000005.
Calculate the concentration in ppb by multiplying the ratio of the mass of solute to mass of solution by 1 billion, or 1,000,000,000. In the case of a mass ratio of 0.000005, this would give 5,000 ppb.
TL;DR (Too Long; Didn't Read)
When you are dealing with aqueous solutions, the calculation of ppb can be simplified to micrograms of solute per liter of solution). You can convert grams to micrograms by dividing the mass in grams by 1 million, or 1,000,000.