There must be some misunderstanding. Molar concentration is used mostly for homogeneous solutions, and the number of mols is defined by the weight concentration and the molar weight (defined by the chemical formula):

n = m/M whe n is the number of mols, m is the mass, M is the molar mass. Molar concentration can be calculated from n and V, the solution volume. In principle you can use molar concentration for a very stable colloidal solution if the concentration is constant in the whole volume. If you have a slowly sedimenting suspension, you cannot use molar concentration, as it will depend on the height and on time.

There is an other case where the use of molar concentration is meaningful with respect to nanoparticles: if each particle is a single molecule (e.g. protein or DNA of a single type). If, however the particle is inorganic (e.g. silica) you cannot say that each particle is a molecule, or each "molecule" will have different molecular weight. In summary I believe that g/l concentration is meaningful for nanoparticle suspensions, while mol/l concentration should be used for homogeneous solutions. Another possibility is express the concentration as particles/volume which gives the same information as g/l concdentration and average particle size.

There must be some misunderstanding. Molar concentration is used mostly for homogeneous solutions, and the number of mols is defined by the weight concentration and the molar weight (defined by the chemical formula):

n = m/M whe n is the number of mols, m is the mass, M is the molar mass. Molar concentration can be calculated from n and V, the solution volume. In principle you can use molar concentration for a very stable colloidal solution if the concentration is constant in the whole volume. If you have a slowly sedimenting suspension, you cannot use molar concentration, as it will depend on the height and on time.

There is an other case where the use of molar concentration is meaningful with respect to nanoparticles: if each particle is a single molecule (e.g. protein or DNA of a single type). If, however the particle is inorganic (e.g. silica) you cannot say that each particle is a molecule, or each "molecule" will have different molecular weight. In summary I believe that g/l concentration is meaningful for nanoparticle suspensions, while mol/l concentration should be used for homogeneous solutions. Another possibility is express the concentration as particles/volume which gives the same information as g/l concdentration and average particle size.

I totally agree, you can not use, meaningful, molar concentrations for nanoparticles.

I don't think you can use the term Molar concentration for NPs. You may call it for %, that too may have some issues but molar concentration can't be used at all.

molar concentration means (number of particles)/(volume), if you want to use a similar number, you have to count your particle (for example using weigth and size distribution, or using direct measurement like nanopore) It is beneficial if use chemistry, like surface modification and you can not use the reactant with excess. but I would never say that (number of partilcles(/NA) are moles if I speak about nanoparticles or colloids. (NA is Avogadro number of course)

I agree with Banhegyi and Herranz. However, if you have metal nanoparticles like silver or gold or platinum, you can determine the metal concentration using ICPOES and convert the ppm to molarity therafter. What we have done before was to determine the concentrations of reductant and capping agents before and after synthesis. So if you start synthesis let say with 0.1M resvatrol and 50 mM AgNO3, you determine the concentration of resvatrol and silver metal in the final solution which have been purified to homogeneity. And if you use protein e.g. apoferitin, you also determine the concentration before and after synthesis. Usually we do this so that one could eliminate effect due to the reductant and capping agent. So in essence, I believe to some extent, you may be able to use molar concentration fr nanoparticles especially if you have established that the solution is not a sedimenting one.

This is a hard and nice question. Firstly you may consider that even when people use ''molar'' they probably consider that all metal (for instance) converted into nanoparticles, then one should check it, by another experiment, and check the weight of the converted - and as you wish, separate them by size and then consider the molarity. Hard work.

I am not totally sure but this is my opinion: As long as we know the concentrations and molecular weights of reactants we can theoretically estimate the molarity. For instance in preparing silver nanoparticles by silver nitrate and sodium borohydride, if we know silver nitrate molarity and molecular weight, then we will know how much amount of silver is present. Assuming all silver is converted to nanoparticles irrespective of size, we can determine molarity using classical equation (M1V1=M2V2; where and M1, V1 are molarity and volume of reactant i.e AgNO3 here and M2 V2 are that of products, i.e of silver nanoparticles.. where as M2 needs to be determined) . Hope this helps and i didn't confuse u more :)

There is ambiguity about this in the literature. First, if you want to use Molarity, you need to be able to express a nanoparticle in moles. To do this, you would need to know how many gold atoms are in a single nanoparticle in your solution. This can be predicted from the size of the particle given the density of gold (assuming its volume is known eg for a sphere this is well-defined).

This is not often done because most nanoparticle batches have particle size distributions. Therefore, people more commonly report the mean size and standard deviation of a sample, batches along with the number of particles per millileter. The size distribution and the number density as such are more informative about the real nature of the solution.

I think maybe you can calculate the distribution of particle or the amount or the persentage of metal nano using EDAX or AAS, If you using AAS you can get ppm of the metal.

I totally agree with Adam Hughes. while calculating molarity of nano particle solutions, you must consider the weight of one nano particle instead of molecular weight of the material by which the nano particle is made up of.

For calculating the molecular weight of nano particles, first you must know the particle size. Then find out the volume by assuming they are spherical. ( Check an HR TEM in case gold, sometimes it appears to be in different shapes, which may invite serious errors in calculation. In case the geometrical shape of particle is very different from spherical, calculate the volume by choosing a formula suitable for the shape of that nanoparticle). Multiplying the volume with density will give you the weight of a nanoparticle ( chance of a small error is there since there are defects in the crystallinity of nanoparticle, and this may cause slight variation in density) will give you the weight of nanoparticle.

Then find out the dry weight of nanopaticle solution which is free of any by products. Weight of particles per liter of solution / weight of one nanoparticle will give you the total number of nanoparticles per litre of soltion.

Then total number of nanoparticles per litre of soltion./ Avogadro number will give you the molarity of nanoparticles in solution . ( Considering nanoparticles as individual units instead of considering the material out of which it is made up of).

To my understanding of molarity, molarity is used for homogeneous solutions and it refers to number of moles of solute per volume of solvent and I thnk I will need a further explanation on how to find molarity of a solid or precipitate.

calculating the particle size distribution, weight of the particle may give the molar concentration of the NPs, but the value will have high error %. The size and weight of the particles can't be unique/uniform or homogeneous, which will vary particle to particle. Hence those methods will give you only approximate molar concentration values.

I wish to thank all for the opinion/knowledge they provided. Expressing solutes (not particulate) in molarity has been the standard way in science. I was puzzled when I came to molarity used for nano particles in peer reviewed publications. But when I attended a conference where I saw a scientist presenting her data in terms of molarity (1- and 5 mM) for the two sizes of gold nano particles- 14nm and 20nm, I could not stop myself to present this question on this site.

All of us are the opinion that molarity should be avoided as far as the insoluble (hence particulate) agents are concerned because assuming (all) nanoparticles, even of a single batch, to have an exact number of atoms is simply hypothetical. Most nanoparticles also have tendency of aggregation too! Therefore, I would like to advise to use concentrations of nanoparticles in straight w/V.

Actually none of the calculations won't give you the effect of nanoparticle, since the size and morphology of nanoparticle has a good influence in its various physical and chemical properties. Even though different sized nanoparticle are present in same w/v in suspensions, their properties will be different, since number of particles will be inversely proportional to size and directly proportional to surface area in this case. There for this kind of molarity calculations (based on number of particles) is necessary for conjugating nanoparticles with biomolecules, where they will give you an approximate idea of the concentration of biomolecules to be used for getting an optimum conjugtion. again these all depends whether the samples are mono disperse or not.

What an interesting debate, my opinion is that it is OK to use molarity of nanoparticles or number of nanoparticles per unit volume, as long as you can justify the reasons. It is understandable that number per volume and size distribution information may be more informative in many circumstances, but as also mentioned, if you are doing some comparative or quantitative analysis, then molarity is just fine for many ( biochemists or biologists for example). The calculation of molarity does indeed rely on many criteria that could introduce errors in calculation, but from my experience of using gold and silver nanoparticles, the errors are not as much as what you may think. One key point not mentioned is that while the use of the Beer-Lambert law is OK for gold nanoparticle molar concentration calculations, it is not for other nanoparticles due to an inability or difficulty to obtain extinction coefficients. Anyone interested to be able to approximate fairly well silver nanoparticle sphere extinction coefficients or potentially any other absorbing / scattering nanoparticles, watch this space...

Very easy calculation

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Moles/Molarity is related with number of molecules (can be extended to atoms) in a solution. It is best described for the homogenious solutions. In most of the cases Nano Particles do not makes solutions (rather suspended). But ofcourse one can do excercise to calculate number of atomes per unit volume of of the liquid in which particles are suspended as discussed in many of the answers above. However, in my view it is worthless excercise.

I agree that one should avoid using molarity for nanoparticles / colloidal dispersions. I give you an example:

I am working with Polyaniline, which is an organic nanometal (conductive polymer). Many scientists (including the Nobel prize winners Heeger, MacDiarmid and Shirakawa) believed that certain polyaniline (or other ICP) / solvent systems are true solutions, they ignored the results of lots of experiments which showed that these transparent and colourful liquids in fact are dispersions, containing polyaniline (or other ICPs) in form of nanoparticles having a size of between 10 - 30 nm (or even up to 100 nm, depending on dispersion capability).

Nevertheless, the scientific community still until today uses GPC to determine "molecular weight" of polyaniline, i.e. believing that these "solutions" can be compared with standard PS solutions, they ome to the conclusions polyaniline having a Mw of (let's say:) 40,000 (or 1,000,000)

However, as they had used dispersions, GPC can only tell how these nanoparticles behave in the column, but can not tell the Mw.

Therefore, any molarity information is totally misleading because in this case the Mw is even not known, but worse: has been measured using in inappropriate method.

When using MALDI-TOFF, we found much lower Mw values, i.e. Polyaniline only being an oligomer built from around 10 monomer units.

Molarity = [mass (g) of np *1 mol/ molar mass of substance (g)]/Volume of solution nanoparticles are dispersed in (L)

so if you have solutions in g/L then you would divide your solutions by the molar mass of your nanoparticle

@Mohd Javed Akhtar

If you are still interested in the correct answer, let me know.

Colleagues tried very hard to help you, but the diligence cannot replace qualification .

Always try to use the standard unit that used by others. Although your particle is having very small sizes, just convert it to the standard size by multiply or divide by the required value.

David Sir, kindly send full PDF of your mentioned article. 

I have one doubt, dose the ICPOES value meant to say the concentration of nanoparticles or the ions. If it mean ion concentration, then how can assume for nanoparticles concentration.

Thank you so much Sir. surely it will help full me to understand the concept.

 Thank you very much sir Dr. David J. Lewis for sharing this. It is very useful to me also .

Dear Mohd Javed Akhtar

I low know topic and attach picture of topic molar extinction coefficient

You can get the molarity of nanoparticle from UV-vis absorption peak if you know their molar extiction coefficient. However, for the nanoparticles whose molar extiction coefficient is unknown, its a bit difficult, there you will really need molecular mass of the nanoparticle. 

Dear Ammu, thanks for the reply. can u explain in the detail. 

 Using beer Lambert law you can find the concentration of nano particle, provided you know the molar extinction coefficient. Otherwise it has to be found out using techniques such as AAS,TEM etc.