7.3 Calculating other concentrations

To calculate concentration, you need to know the amount of a substance and the volume it is dissolved in.

Example 1: Mass per volume concentration

12 µg of protein is dissolved in 200 µl of water. What is the final concentration in mg ml–1?

Remember: \text{concentration} = \frac {\text{mass}}{\text{volume}}

First convert the mass to mg and the volume to ml to get the answer in the correct form.

12 µg = 0.012 mg

200 µl = 0.2 ml

\text{Concentration (mg ml^{-1})} = \frac { \text{mass}}{ \text{volume}} = \frac { \text{0.012 mg}}{ \text{0.2 ml}} = \text{0.06 mg ml^{-1}}

Example 2: Weight to volume percentage

What is the weight/volume percentage (w/v (%)) concentration of 250 ml of aqueous sodium chloride solution containing 25 g of NaCl?

In this case we assume that 1 ml is equivalent to 1 g.

w/v (%) = (mass solute ÷ volume of solution) × 100

Mass of solute (NaCl) = 25 g

Solution volume = 250 ml

w/v (%) = (25 ÷ 250) × 100 = 10%

Example 3: Volume to volume percentage

What is the percent by volume (v/v (%)) of a solution formed by mixing 15 ml of isopropanol with 60 ml of water?

v/v (%) = (volume of solute ÷ total volume of solution) × 100

Mass of solute (isopropanol) = 15 ml

Total volume of solution = 60 ml + 15 ml = 75 ml

v/v (%) = (15 ÷ 75) × 100 = 20%

Example 4: Calculating ppm and ppb

Parts per million (ppm) and parts per billion (ppb) are examples of expressing concentrations by mass. Volume/volume (v/v) and weight/volume (w/v) concentrations are sometimes expressed in ppm, especially if very dilute.

1 ppm is 1 part by weight, or volume, of solute in 1 million parts by weight, or volume, of solution.

\text{ppm} = \frac {\text{mass solute}}{\text{mass of solution}} \times 10^{6}

\text{ppb} = \frac {\text{mass solute}}{\text{mass of solution}} \times 10^{9}

What is the concentration of a solution, in parts per million, if 0.03 g of NaCl is dissolved in 1 l of water?

First convert the volume of solution to a mass:

1 l = 1 kg = 1,000 g

\text{ppm} = \frac {0.03}{1,000} \times 10^{6} = 30 \text{ppm}

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