Finding Concentration Using Index of Refraction

[Sayuri09]

1. The problem statement, all variables and given/known data
Is there any way to calculate a solution's concentration (mass percentage - that is, the percentage of the solute mass to the solution mass) just by knowing its index of refraction?

If it helps, the solute is NaCl, so I know the molar mass of the solute. I also have the solution's mass, the solution's volume, and, by calculation, the solution's density.


2. Relevant equations
None that I know of...


3. The attempt at a solution
In the beginning, I tried to establish a relationship between a solution's index of refraction and its density experimentally (i.e. making a table of solutions with different densities and their corresponding indexes of refraction to extrapolate some kind of equation to relate them) and then find a relationship between its density and its concentration, but this method has the potential to be extremely inaccurate and may not even work at all (if the index of refraction - density table cannot determine a relationship between index of refraction and density).

I'm hoping there is some kind of equation or experimental method more practical/accurate than the one I came up with to figure this out.

Thanks in advance!!!

[symbolipoint]

Yes there is, and it is very common. When done right, it is called Brix, or Degrees Brix, and it is usually for estimating or measuring sugar concentration. Other solutions are also measured this way, whether application in this manner valid or not. Not all dissolved materials will give the same scale values as sugars. The reading scale may not always be graded in Refractive Index, but may instead show a scale of range from 0 to 100, or some range within that.

[mgb_phys]

Yes it's a standard way of measuring concentration of sugar/salt in water, especially in beer and wine making.
I think you normally work against calibration curves of given concentrations, it's probably possible in theory to calculate what the refractive index is for a given concentration from first principles but I don't know of an eqution

[Sayuri09]

Thanks for the quick replies, everyone!

What I actually meant by this problem was that the concentration of the solution has to be found, in some way, using its index of refraction. It's probably easier to do it in a different way, but in this case, the index of refraction must be used.

Any help is much appreciated!

[mgb_phys]

You can buy very accurate refractometers designed just for this, either simple hand held ones or complex digital versions. They are called Abbe refractometers
You can probably get them for salt/sugar that are calibrated directly in concentration, otherwise they will read refractive index and you can look it up in a table.