ICP-OES technique can be used.

just refer page no. 41 of following thesis

http://ira.lib.polyu.edu.hk/bitstream/10397/3948/2/b22328865_ir.pdf

Moles is an amount not a concentration. What concentration do you really want?

How did you prepare the solution? You should be able to calculate the concentration of particles based on your preparation methods and results you have for particle sizes.

As said Dr Weimer: what did you mean by "concentration in Moles"?

If your know the conventional concentration of particles as "particles per liter", you can just divide it to 6,022·1023 - it will be the concentration in "moles per liter". The mole is just the number of particles.

If your question is about the relation between the concentration of particles and the amount of metal in your suspension, it is not self-evidently. Except the nanoparticles, in solution there are some nucleuses (very small particles about 1 nm - the initial stage for particles) and the free metal ions. The quantitative properties depend on the synthesis method and conditions.

Good luck!

There are two possible answers:

1) No, since nanoparticles are not clusters and you cannot deal with them as you would do with ions/molecules

2) Yes, if you neglect the considerations given above. In this case, if you can convert the average particle size into their nuclearity (number of atoms/structural units), you can also calculate the molarity of suspension.

Which data is reliable to take as average size of nanoparticle? DLS/SEM/TEM which one?

Dr. Weimer, thats my mistake. I wanted the molar mass (g/mol) of the metal nanoparticle provided the atomic weight of the parent metal atom and average diameter of the particle are known. Currently I am using  Mass/Vol concentrations.

> Which data is reliable ... DLS/SEM/TEM ...?

Your question does not have a simple answer.

When done properly, the three averages should all agree within their standard uncertainties of the distributions. Certainly, you will need far more TEM images to get comparable confidence in the sample statistics to what you can get from SEM images. This is because the TEM images likely sample a smaller number of particles than the SEM images. The DLS potentially samples the largest number of particles and does so in solution. The others require that you precipitate your particles. This could cause some agglomeration. Therefore, DLS should have the best confidence on the mean (smallest value of SM). However, DLS requires some intrinsic assumptions in how it calculates particle size, whereas imaging methods "see" the particles directly.

When you want to use just one value from any of these three instruments, you have an average that is probably uncertain by at least ± 20% relative or more. I would call measurements of just one image or sample an "engineering first guess". So, by example, when you report an average particle size of 50 nm from just one measurement, you should understand this to be 50 ± 10 nm at best (and probably worse).

In summary ... You would do well to measure averages and standard uncertainties using distribution counts from a 3 or more DLS samples (perhaps at different particle concentrations in solution), many more SEM images, and lots and lots of TEM images to get a good representation of the true statistics of the particle sizes.

Every method has own advantages and disadvantages. Microscopy (TEM, SEM, AFM, etc.) provides the size for few particles (10, 50, 100 from the billions (!)) and it is possible to have the artifacts with sample preparation: e.g. - the selective sorption on the substrate (mica, carbon film, etc).

The optical methods (DLS and others) provide the average particle size for the big ensemble, but they can have a systematic error and shift. It is not like TEM, where we can see the physical image of the particles, it is just a fitting for mathematical models.

It is impossible to say "this method is the best!", it is necessary to use few methods, compare and discuss the results.

Good luck! 

I would suggest a simple answer to your original question. Calculate the concentration in number of particles per volume. This is called the number density. Suppose you know the mass m of metal that you added in the reaction solution volume V, the bulk density d of the metal, and the (average) particle size r (radius) that forms. For a perfectly homogeneous particle distribution, the number of particles per volume is ...

     (m / d) / (V (4 Pi r3/3))

Large values of number densities are easier to grasp than small values of molar concentrations. I see you are in a bio-thrust. Perhaps you are using the nanoparticles further with cell systems for examples. In this case, convert your cell concentration also to number of cells per unit volume. Then, you might begin to appreciate what it means to have a solution that has 10 nano-particles per cell versus one that has 0.01 nano-particle per cell.

Most important is to know the diameter of nanoparticles, since we loss significante of reactant during washing steps and iterations. 

> I wanted the molar mass (g/mol) of the metal nanoparticle provided the atomic weight of the parent metal atom and average diameter of the particle are known.

Assume the particle has the same density d as its bulk metal. When you have the particle radius r, the "molar mass" of the particle M is 

      M = No (4 Pi r3/3) d

where No is Avogadro's number.

I would still recommend number density concentrations over molar concentrations.

Thanks Dr. Weimer

Dear Arun as Dr Weimer has mentioned that you can know the concentration of your metal nanoparticle in the solution by your preparation method. As it seems from your question you probably synthesized it in water medium and you might have taken some precursor of the metal such as metal salt  and then reduced it by suitable reducing agent. then by calculating the initial concentration of the metal present in your solution and then calculating the subsequent volume change during the synthetic process, one can determine the final concentration of the metal nanoparticles.

As Dr David has mentioned ICP-AES can be used to determine the metal concentration, similarly if the sample is UV-Vis active, one can also do colorimetric determination of the concentration of the unknown  suspension.

Meanwhile the determination of mean diameter with DLS method may not be as accurate because dynamic light scattering (DLS) method is always going to give you the hydrodynamic diameter of the nanoparticles, which is most often higher than the actual particle size. As in this process the particles of bigger in size are going to scatter the light more hence one may get a high intense peak for a small number of the bigger size particles.

TEM or HRTEM are better instrument for the analysis of particle size

@ Bikash Sharma  Electron microscopy (and SAXS, for example) probes the electron-dense region of a particle and cannot ‘see’ the stabilizing surfactant or polymeric coatings which stabilize the particle and thus affects its bulk transport properties such as diffusion which DLS will see.  The stabilizing coating is just as much a part of the particle as its core, so it’s disingenuous to say that a hydrodynamic diameter is somehow incorrect or ‘wrong’. More information is provided if both techniques are used.  Electron microscopy (essential) and DLS are required in nanoparticle research as well as many other techniques.  A good illustration of the wide range of useful techniques and the understanding they bring is hinted at in the NIST certificate and report of investigation for RM8011, a nominally 10 nm citrate-capped god colloid.  See: https://nemo.nist.gov/srmors/certificates/8011.pdf

Thanks Dr Alan for your useful answer and a good reference article to compare the particle size with different analytical technique.