Percentage, ppm, and ppb

One of the simplest quantitative expressions of concentration is the mass percentage of a component in a solution, given by 

Because percent means per hundred, a solution of hydrochloric acid that is 36% HCl by mass contains 36 g of HCl for each 100 g of solution. 

We often express the concentration of very dilute solutions in parts per million (ppm) or parts per billion (ppb). These quantities are similar to mass percentage but use 10 (a million) or 10 (a billion), respectively, in place of 100 as a multiplier for the ratio of the mass of solute to the mass of solution. Thus, parts per million is defined as 

A solution whose solute concentration is 1 ppm contains 1 g of solute for each million (10 ) grams of solution or, equivalently, 1 mg of solute per kilogram of solution. Because the density of water is 1 g/mL, 1 kg of a dilute aqueous solution has a volume very close to 1 L. Thus, 1 ppm also corresponds to 1 mg of solute per liter of aqueous solution. 

The acceptable maximum concentrations of toxic or carcinogenic substances in the environment are often expressed in ppm or ppb. For example, the maximum allowable concentration of arsenic in drinking water in the United States is 0.010 ppm that is, 0.010 mg of arsenic per liter of water. This concentration corresponds to 10 ppb. 

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The polymer solutions are stabilized with 500 ppm formaldehyde and kept practically oxygen free (<5 ppb O2). As the next figure shows (Fig. 8), clear viscosity differences arise even at a salinity of only 33 g/1 TDS (33,000 ppm) and reservoir temperatures of 195 °F (90 C). The viscosity values as measured at room temperature are expressed as a percentage of the original values before the temperature tests. 

These SI units are absolute measures of distance, mass, volume, and more. It is not always possible to measure absolute amounts in a meaningful way. In such cases, a relative measure of quantity is made reporting the abundance or concentration of an element, isotope, molecule, or compound. Concentrations are reported as a proportion of the total amount of material analyzed or as a ratio to another element, isotope, or molecule. Some of these measures include parts per hundred, or percentages (%), parts per thousand, aka parts per million (%o), parts per million (ppm), or parts per billion (ppb). 

Sometimes mass percent is symbolized as % (w/w), indicating that the percentage is a ratio of weights (more accurately, masses). You may have seen mass percent values on jars of solid chemicals to indicate the amounts of impurities present. Two very similar terms are parts per million (ppm) by mass and parts per billion (ppb) by mass grams of solute per million or per billion grams of solution. For these quantities, in Equation 13.6 you multiply by 10 or by 10, respectively, instead of by 100. 

SECTION 13w4 Concentrations of solutions can be expressed quantitatively by several different measures, including mass percentage [(mass solute/mass solution) X 10 ], parts per milion (ppm), parts per bilion (ppb), and mole fraction. Molarity, M, is defined as moles of solute per liter of solution molaity, m, is defined as moles of solute per kg of solvent Molarity can be converted to these other concentration units if the density of the solution is known. 

Two conversion factors can be written for a relationship stated within a problem, a percentage (%), parts per million (ppm) expressed as mg/kg, and parts per billion (ppb) expressed as /xg/kg. 

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