The difference between ppm and µg/mL is often confused. A common mistake is to refer to the concentration units in ppm as a shortcut (parts per million) when we really mean µg/mL. One ppm is in reality equal to 1 µg/g. In similar fashion, ppb (parts per billion) is often equated with ng/mL. One ppb is in reality equal to 1 ng/g. To convert between ppm or ppb to µg/mL or ng/mL, the density of the solution must be known. The equation for conversion between wt./wt. and wt./vol. units is:
(µg/g) × (density in g/mL) = µg/mL
and/or
(ng/g) × (density in g/mL) = ng/mL
Therefore, if we have a solution that is 1000 µg/mL Ca2+ and know or measure the density to be 1.033 g/mL, then the ppm Ca2+ = (1000 µg/mL) / (1.033 g/mL) = 968 µg/g = 968 ppm.
When making dilutions, the following equation is useful:
(mLA)(CA) = (mLB)(CB)
For example, to determine how much of a 1000 µg/mL solution of Ca2+ is required to prepare 250 mL of a 0.3 µg/mL solution of Ca2+, we would use the above equation as follows:
(mLA)(1000 µg/mL) = (250 mL)(0.3 µg/mL)
(mLA) = [(250 mL)(0.3 µg/mL)] / (1000 µg/mL)
(mLA) = 0.075 mL = 75 µL
Preparation
Weight ≠ Volume
Standard chemical solutions can be prepared to weight or volume. The elimination of glass volumetric flasks may be necessary to eliminate certain contamination issues with the use of borosilicate glass, or to avoid chemical attack of the glass. It is often assumed that 100 grams of an aqueous solution is close enough to 100 mL to not make a significant difference, since the density of water at room temperature is very close to 1.00 (0.998203 at 20.0 °C). Diluting/preparing standard solutions by weight is much easier. Still, the above assumption should not be made. The problem is that trace metals standards are most commonly prepared in water + acid mixtures, where the density of the common mineral acids is significantly greater than 1.00. For example, a 5% v/v aqueous solution of nitric acid will have a density of ~1.017 g/mL, which translates into a fixed error of ~1.7%. Higher nitric acid levels will result in larger fixed errors. This same type of problem is true for solutions of other acids, to a degree that is a function of the density and concentration of the acid in the standard solution, as described by the following equation (to be used for estimation only):
dS = [(100 − %) + (dA)(%)] / 100
Where:
- dS = density of final solution
- % = the v/v % of a given aqueous acid solution
- dA = density of the concentrated acid used
For example, let's estimate the density of a 10% v/v aqueous solution of nitric acid made using 70% concentrated nitric acid with a density of 1.42 g/mL.
dS = [(100 − %) + (dA)(%)] / 100 = [(100 − 10) + (1.42)(10)] / 100 = (90 + 14.2) / 100 = 1.042 g/mL
Acid Content
Another area of confusion is the expression of the acid content of the solution. We all agree that it is important to matrix match the standard and sample solutions, to avoid a fixed error in the solution uptake rate and/or nebulization efficiency, sometimes referred to as a matrix interference. If a solution is labeled as 5% HNO3, what does this mean? If we take 5 mL of 70% concentrated nitric acid and dilute to a volume of 100 mL, then this is 5% HNO3 (v/v), where the use of 70% concentrated acid is assumed. However, nitric acid can be purchased as 40%, 65%, 70%, and >90%. Therefore, note the concentration of the concentrated acid used if different from the "norm," as well as the method of preparation, i.e., v/v, wt/wt, wt/v, or v/wt. The wt. % concentrations of the common mineral acids, densities, and other information are shown in the following table: