Talk:Molar refractivity

It is definitely not a measure of the volume of a substance, but somehow related to its polarizability at optical ("very high") frequencies. In crude models, the polarizability of an atom is proportional to its volume. But this is a very simplified view and only holds for simple systems such as single atoms or mono-atomic ions.

The statement: "Therefore, the molar refractivity is the volume of the substance (in cubic meters) taken up by each mole of that substance." is absolutely wrong.

Note that polarizabilities alpha are very often referred to by alpha/(4 Pi epsilon), where epsilon is the vacuum permittivity. alpha/(4 Pi epsilon) has also units of volume (m^3).

Dependence on T, P, n

Hi,

I saw that following the previous comment on this talk page, the first half of the first sentence of this article has been revised.

I would like to ask about the second half of the same sentence (also appearing in this article since the first version):

"Molar refractivity [...] is dependent on the temperature, the index of refraction, and the pressure".

This sentence refers to the third expression for A in the article, using an approximation of the Lorentz-Lorenz relation (take a look at the first version of this article, where this was the only expression for A).

My question is: does this expression really imply the stated dependence? Are the three quantities T, P, n independent, such that changing them affects A according to this formula?

Hypothetically, an alternative scenario is that the molar refractivity is actually a property of the material, independent of the physical conditions, and then this formula actually relates e.g. the index of refraction to the temperature and pressure, and A is just a parameter.

If this is true, then saying that A depends on the other three quantities is like saying that the speed of light depends on the frequency and the wavelength of light, because $c=\lambda f$, which is absurd.

I'm not an expert, and I don't know if my concern is justified; I'm just asking. Any insightful comments or references which would answer either way would be very welcome.

Thanks! E L Yekutiel (talk) 14:17, 9 October 2024 (UTC)

Hi,

I think that I was right...

If you have access to academic papers, take a look at the paper by A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, Dispersion measurement of inert gases and gas mixtures at 800 nm (which is one of the references used by https://refractiveindex.info).

In that paper, equation (8) is an expression for the refractive index:

$n(\omega ,p)-1={\frac {3p}{2RT}}\sum _{m}x_{m}A_{m}(\omega )$

where $x_{m}$ are the fractions of the materials in the mixture, and $A_{m}$ are their molar refractivities.

Note the $p$-dependence explicitly written in the left hand side, whereas in the right hand side $p$ only appears before the sum, and the molar refractivities depend only on the wavelength $\omega$.

A small additional note:

For a pure material (only one ingredient), this expression can be rewritten as:

$n(\omega ,p)-1={\frac {3p}{2RT}}A(\omega )$

This is exactly the third equation in the Wikipedia article, with the additional approximation $n+1\approx 2$ (see equation (6) in that paper and the explanations between these two equations, and specifically the sentence immediately preceding equation (8)).

If there is no objection, I will rephrase the textual explanation (and maybe the formulas) to something more neutral, which doesn't imply the dependence in the way described in my previous message.

Thanks again! E L Yekutiel (talk) 10:42, 10 October 2024 (UTC)