You can easily calculate the amount of Gold in your colloidal solution of Gold nanoparticles by "Inductive Coupled Argon Plasma (ICAP) Atomic Emission
Spectroscopy". I did this spectroscopy to determine the concentration (ppm) of Copper nanoparticles in water & oil both. It is very good and accurate technique. The only condition with mine instrument was that, the liquid phase should have the boiling point above 80 degree celsius.
If you need any further information then please let me know.
If you have no possibility to measure ICP methods and you know the average size (perhapy from TEM or DLS) and form you can easily estimate the concentration. Have you prepared the particles by yourself? Then you know how much salt (HAuCl4?) you used. 1. Calculate the mass of Au inside the salt. 2. Calculate the mass of 1 gold nanoparticle (using the volume and density of gold). 3. Devide 1./2. and than you have the number of nanoparticles in your solution.
via UV vis spectroscopy. digest the gold sample in HCl/HNO3 then use Rhodanine in Pyridine to complex gold ions.
Elsourdy, H., Harris, R., Press, A., Rao, G., Kaneda, Y., Eldawy, A., … Robertson, A. (1975). Improved Rhodanine Method for the Spectrophotometric Determination of Gold, 47(3), 465–468.
I use it and is quite reliable but of course can't compete with ICP/MS.