Question

For aqueous solutions it is often assumed that 1 milligram per liter equals 1 ppm. Are there any guidelines up to which concentration this shortcut is admissible? Are there any formulas which calculate the error when using this shortcut?

Answer 1

The 1 mg/L to 1 ppm approximation is acceptable for dilute aqueous solutions similar in density to water. At higher concentrations or different densities, the error can be significant. To calculate the error, use the formula that compares 'actual ppm' to 'approximated ppm'.

Step-by-step explanation:

For aqueous solutions, the equivalence of 1 milligram per liter (mg/L) to 1 part per million (ppm) is a useful approximation, considering that the density of water is approximately 1 g/mL. This approximation holds true for dilute solutions, where the mass of the solute is negligible compared to the mass of the solvent. The shortcut is generally acceptable when the solution's density is close to that of water and when working with low concentrations.

However, for solutions with densities significantly different from water or at higher concentrations, the error in this approximation increases. The assumption that 1 mg/L is equivalent to 1 ppm is based on the premise that 1 L of water weighs 1,000,000 mg, which is not accurate for all solutions or at all temperatures. To calculate the error for a specific concentration and density, you would use the formula:

Actual ppm = (measured mass of solute in mg) / (volume of solution in L × density of solution in g/mL) × 106

The error can then be determined by comparing the 'actual ppm' with the 'approximated ppm' assumed from the 1 mg/L = 1 ppm shortcut.