Up to which dilution can one assume that 1 mg/l = 1 ppm?

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?

• One can always calculate the correct concentration and see. It much depend on the application. Worse case is the often "wrong" use of % in which one does not even know what denominator has been used. – Alchimista Jan 2 at 9:03

"Parts per …" are dimensionless entities: to derive $$\pu{ppm}$$ from mass concentration $$γ$$ (e.g. $$\pu{1 mg L-1})$$ one uses density of water $$\rho(\ce{H2O}) = \pu{1E6 mg L-1}$$ for normalization:
$$\frac{γ}{ρ(\ce{H2O})} = \frac{\pu{1 mg L-1}}{\pu{1E6 mg L-1}} = \pu{1E-6} = \pu{1 ppm}$$
Once the solution is too concentrated, you obviously are not allowed to use $$ρ(\ce{H2O})$$ and have to use the real concentration of the solution. However, this occurs at the concentration levels way higher than those to be expressed with $$\pu{ppm}$$ anyway: that's why "parts per …" are so ubiquitously used in biochemistry. Higher molar masses, lower molar concentrations, primarily aqueous media: no need to account for the error stemming from the difference in the densities of pure water and the solution.