In the context of extremely dilute solutions, concentrations are often expressed in parts per million (PPM) or 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 1,000,000 parts of the solution, which can be mathematically represented as \(10^6\).
For aqueous solutions, a useful equivalence to remember is that 1 PPM is equivalent to 1 milligram of solute per 1 liter of solution. When calculating PPM in terms of mass, the formula is:
\[ \text{PPM} = \frac{\text{grams of solute}}{\text{grams of solution}} \times 10^6 \]
Conversely, when considering volume, the formula adjusts to:
\[ \text{PPM} = \frac{\text{milliliters of solute}}{\text{milliliters of solution}} \times 10^6 \]
This approach is similar to calculating mass percent, where the formula involves grams over grams multiplied by 100%. However, in the case of PPM, the multiplication factor is \(10^6\) to account for the 1,000,000 parts in the solution. Understanding these concepts is crucial when discussing very dilute concentrations in various scientific contexts.