Parts per Million (ppm): Videos & Practice Problems

In the context of extremely dilute solutions, concentrations are often expressed in parts per million (PPM) and parts per billion (PPB). These units can represent either mass or volume. Specifically, parts per million indicates the number of parts of a substance in relation to one million parts of the total solution. This can be mathematically represented as:

For mass:
\[\text{PPM} = \frac{\text{grams of solute}}{\text{grams of solution}} \times 10^6\]

For volume:
\[\text{PPM} = \frac{\text{milliliters of solute}}{\text{milliliters of solution}} \times 10^6\]

In aqueous solutions, a useful equivalence is that 1 PPM is equivalent to 1 milligram of solute per 1 liter of solution. This relationship simplifies the understanding of PPM, especially in practical applications. The concept of PPM is similar to mass percent, where the formula involves a ratio of the solute to the solution, but instead of multiplying by 100% for a percentage, we multiply by 1,000,000 to reflect the parts per million scale.

Understanding PPM and PPB is crucial when discussing very dilute concentrations, as these measurements provide a clear way to quantify the presence of substances in solutions.

Parts per billion (PPB) is a unit of measurement that indicates the concentration of a substance in a solution, representing the number of parts per billion parts, which can be expressed in grams or milliliters. Specifically, 1 PPB is equivalent to 1 microgram of solute per liter of solution, establishing a direct relationship in aqueous solutions.

When calculating PPB in terms of mass, the formula is:

PPB = \(\frac{\text{grams of solute}}{\text{grams of solution}} \times 10^9\)

In contrast, when considering volume, the formula adjusts to:

PPB = \(\frac{\text{milliliters of solute}}{\text{milliliters of solution}} \times 10^9\)

This distinction is crucial as it highlights the differences in measurement approaches depending on whether mass or volume is being analyzed. Understanding these relationships is essential for accurately interpreting concentrations in various scientific contexts.

To determine the concentration of ammonia in an aqueous solution expressed as parts per billion (ppb), we start with the formula for calculating ppb in terms of volume:

ppb = (Volume of solute in mL / Volume of solution in mL) × 10⁹

In this case, we have a 2.4 liter sample of solution containing 0.012 milliliters of ammonia. First, we need to convert the volume of the solution from liters to milliliters:

2.4 liters = 2.4 × 1000 mL = 2400 mL

Now, we can substitute the values into the ppb formula:

ppb = (0.012 mL / 2400 mL) × 10⁹

Calculating this gives:

ppb = (0.012 / 2400) × 10⁹ = 5,000 ppb

Thus, the concentration of ammonia (NH₃) in the solution is 5,000 parts per billion. This indicates a very low concentration of ammonia in the aqueous solution, which is important for understanding its potential effects and applications in various contexts.