## Other Units for Solution Concentrations

By the end of this lesson and the next few, you should be able to:

- Define the concentration units of mass percentage, volume percentage, mass-volume percentage, parts-per-million (ppm), and parts-per-billion (ppb)
- Perform computations relating a solution’s concentration and its components’ volumes and/or masses using these units

In previous lessons, we introduced molarity, a very useful measurement unit for evaluating the concentration of solutions. However, molarity is only one measure of concentration. In this lesson and the next set of lessons, we will introduce some other units of concentration that are commonly used in various applications, either for convenience or by convention.

## Mass Percentage

In a previous lesson, we introduced percent composition as a measure of the relative amount of a given element in a compound. Percentages are also commonly used to express the composition of mixtures, including solutions. The **mass percentage** of a solution component is defined as the ratio of the component’s mass to the solution’s mass, expressed as a percentage:

\(\text{mass percentage} \)\(= \cfrac{\text{mass of component}}{\text{mass of solution}} × 100\%\)

We are generally most interested in the mass percentages of solutes, but it is also possible to compute the mass percentage of solvent.

Mass percentage is also referred to by similar names such as *percent mass, percent weight, weight/weight percent*, and other variations on this theme. The most common symbol for mass percentage is simply the percent sign, %, although more detailed symbols are often used including %mass, %weight, and (w/w)%. Use of these more detailed symbols can prevent confusion of mass percentages with other types of percentages, such as volume percentages (to be discussed in the next lesson).

Mass percentages are popular concentration units for consumer products. The label of a typical liquid bleach bottle (see image below) cites the concentration of its active ingredient, sodium hypochlorite (NaOCl), as being 7.4%. A 100.0-g sample of bleach would therefore contain 7.4 g of NaOCl.

## Calculation of Percent by Mass

A 5.0-g sample of spinal fluid contains 3.75 mg (0.00375 g) of glucose. What is the percent by mass of glucose in spinal fluid?

### Solution

**Note: **Cerebrospinal fluid (CSF) is a clear, colorless body fluid found in the brain and spinal cord. It is produced in the choroid plexuses of the ventricles of the brain. It acts as a cushion or buffer for the brain, providing basic mechanical and immunological protection to the brain inside the skull.

The spinal fluid sample contains roughly 4 mg of glucose in 5000 mg of fluid, so the mass fraction of glucose should be a bit less than one part in 1000, or about 0.1%. Substituting the given masses into the equation defining mass percentage yields:

\(\%\text{glucose} \)\(= \cfrac{3.75\text{ mg glucose} × \frac{1\text{ g}}{1000\text{ mg}}}{5.0\text{ g spinal fluid}} \)\(= 0.075\%\)

The computed mass percentage agrees with our rough estimate (it’s a bit less than 0.1%).

Note that while any mass unit may be used to compute a mass percentage (mg, g, kg, oz, and so on), the same unit must be used for both the solute and the solution so that the mass units cancel, yielding a dimensionless ratio. In this case, we converted the units of solute in the numerator from mg to g to match the units in the denominator. We could just as easily have converted the denominator from g to mg instead. As long as identical mass units are used for both solute and solution, the computed mass percentage will be correct.

## Calculations Using Mass Percentage

“Concentrated” hydrochloric acid is an aqueous solution of 37.2% HCl that is commonly used as a laboratory reagent. The density of this solution is 1.19 g/mL. What mass of HCl is contained in 0.500 L of this solution?

### Solution

The HCl concentration is near 40%, so a 100-g portion of this solution would contain about 40 g of HCl. Since the solution density isn’t greatly different from that of water (1 g/mL), a reasonable estimate of the HCl mass in 500 g (0.5 L) of the solution is about five times greater than that in a 100 g portion, or 5 × 40 = 200 g.

In order to derive the mass of solute in a solution from its mass percentage, we need to know the corresponding mass of the solution. Using the solution density given, we can convert the solution’s volume to mass, and then use the given mass percentage to calculate the solute mass. This mathematical approach is outlined in this flowchart:

For proper unit cancellation, the 0.500-L volume is converted into 500 mL, and the mass percentage is expressed as a ratio, 37.2 g HCl/g solution:

\(500\text{ mL solution} \left ( \cfrac{1.19\text{ g solution}}{\text{mL solution}} \right ) \left ( \cfrac{37.2\text{ g HCl}}{100\text{ g solution}} \right ) \)\(= 221\text{ g HCl}\)

This mass of HCl is consistent with our rough estimate of approximately 200 g.