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A mouthwash states it has among other ingredients, menthol 0.042% w/v. What is the correct interpretation?

This chemistry.stackexchange.com answer says it's weight per volume with unspecified units, so it is ambiguous. Kilograms per litre or grams per cubic light-year or whatever.

Alternatively, could it mean that 0.042% w/v is the concentration by weight and by volume, presumably because they are interchangeable?

The only reason to think they are interchangeable is that the density of menthol is 0.890 g·cm−3 which is close to water's density so perhaps it is also close to the density of this solution before the addition of menthol.

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  • $\begingroup$ In chemistry we usually use grams for mass and for volume we use litres or millilitres. I don't think that they would put 0.042 gram menthol in 100 litres of water. So in your scenario w/v means $g/mL$ or $kg/L$ This is the what w/v mostly means. Always use comparable units. You cannot compare grams with cubic lightyear. Kg and L ; g and mL are comparable units. $\endgroup$
    – Harjot Dhillon
    Commented Nov 6, 2023 at 13:21

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Percentage (one of hundred), ppm (one of million), ppb (one of billion) and similar units are relative quantities, relating two values of the quantity of the same kind. Like two masses/weights, two volumes, two molar amounts.

As this is source of possible misinterpretation, it is often marked explicitly like w/w, v/v, n/n. For these reasons, it is generally recommended to avoid these relative units, especially without explicit meaning, using explicit absolute quantities like e.g. $\pu{mg/L}$, $\pu{g/kg}$, $\pu{\mu mol/mol}$ etc.

The mixed percentage (w/v) is a trick, assuming $\pu{1 mL}$ of solution has mass $\approx \pu{1 g}$ and therefore 1 % w/v as $\pu{1 g}$ in $\pu{100 g}$ means also $\pu{1 g}$ in $\pu{100 mL}$.

Particularly, $\pu{0.042 \% \text{w/v}}$ means $\pu{420 mg}$ of the substance in $\pu{1 L}$ of the product, as it is considered as $\pu{0.042 g}$ in $\ce{100 g}$(=$\pu{100 mL}$).

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  • $\begingroup$ But it doesn't say w/V. It says w/v. Both lowercase. $\endgroup$
    – H2ONaCl
    Commented Nov 6, 2023 at 14:13
  • $\begingroup$ It is the same, is was just capitalization glitch. :-) As volume has as the symbol the capital V, but in this percentage context is used small v. $\endgroup$
    – Poutnik
    Commented Nov 6, 2023 at 15:42
  • $\begingroup$ Please show your rationale for equating 0.042 % w / v with 420 mg / L . I can start by equating the original to 0.00042 w / v by reversing the implication of the percent sign. Please show the next step that you employed to equate it to 420 mg / L. $\endgroup$
    – H2ONaCl
    Commented Feb 1 at 4:27
  • $\begingroup$ As previously noted, 1% w/v means 1 g/100 mL or 10 g/L, 0.042% w/v means 10 . 0.042 g/L = 0.42 g/L = 420 mg/L $\endgroup$
    – Poutnik
    Commented Feb 1 at 7:10

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