Two calculation approaches come to mind. One is to estimate the molar mass of a quantum dot without its ligands. The other is to estimate a number density of coverage of ligands and add it as a factor. Typical surface site number densities are estimated for example using the close packed plane. A -COOH group may need more than one site, so fewer ligands bind than determined by the area number density of surface sites.

Finally, some suppliers may have an estimate of the mass per quantum dot already. Contact Sigma-Aldrich and ask them.

Quantum dots are nanoparticles. Around them are located on the surface of the COOH group. You need to prepare a disperse system by calculating your solution for the amount of -COOH groups. You need to know the molar mass of -COOH. Take the precise, ever-functionalized quantum dots and determine the amount of -COOH groups by titrating with alkali as if you titrated any carboxylic acid. Determine the amount of carboxyl groups in grams, and then recalculate by 1 µM solution оf -COOH groups with quantum dots.

Interesting idea—do a simple acid/base titration. Can you provide any citations where this has been done on functionalized quantum dots?

I had also not considered the molarity based solely on functional groups. I see the utility for certain applications.

Young researchers use the word "solution" instead of the words "disperse system". It is not right. The word solution is used when ions, molecules are distributed in a solvent. Therefore, you can not speak "1 µM solution of CdTe quantum dots" . 1 µM disperse system - nonsense. You can not determine the exact diameter of a quantum dot. It is distributed in size. If you define it by the DLS method, it will be one. If determined by the SAXS method, it will be different. As a result of the size effect, the density of matter changes. Maybe the company makes quantum dots of the same size. Then, if we assume that the density does not change, we can determine the molar mass of quantum dots.