if we are taking 2 materials of different concentrations (one is the precursor and the other one is the stabilizing agent) for synthesizing nanoparticles as a catalyst, how can I calculate the concentration of the resulting material?
Do you mean the Number Concentration (that is the number of nanparticles per cubic centimeter of dispersion) or the Mass Concentration (that is the mass of the product material forming the nanoparticles, per cubic centimeter of the dispersion) ?
Considering that at the end of the process all the main material has been transformed in nanoparticles (no residues, no precipitates), the answer would generally be:
1. in the former case, you need to have a clear estimate or measurement of the resulting shape and size of the nanoparicles, hoping they constitute a monodispersion. Then, you need also a mass density of the material in the nanoparticle state, which can be different from that of the bulk material for very small nanoparticles. Having such information, the number concentration could be easily calculated as mass concentration of the original main component (if it is a compound or molecule you must consider only the mass fraction provided by the nanoparticle material at the end of the process, e.g. silver in AgNO3 when forming Ag NPs) divided by the mass of each nanoparticle (that you have calculated by using the above said density in nano state times volume of each NP).
2. in the latter case, the answer would be the same concentration as the original main component, because the whole mass has just changed from precursor to nanomaterial states. Note that this is a good approximation inasmuch the nanoparticles are not chemically capped with layers from the second stabilizing component. This is the case of Ag nanoparticles stabilized by citrate in water, for example. However, if the stabilizer builds a chemically stable shell onto the nanoparticle core, as is the case of PVP capped Ag nanoparticles for example, the mass concentration could be slightly but significantly larger than that of pure uncapped nanoparticles.
Beer-Lambert law is very useful for calculating the concentrations based on UV-vis absorption measurements:
A = εlc where A is absorbance, ε is the molar extinction coefficient (which depends on the nature of the chemical and the wavelength of the light used), l is the length of the path light must travel in the solution in centimetres, and c is the concentration of a given solution.
Oya Tagit I think this may be easy to find the concentration. but how to find the molar extinction coefficient? (where A and l are known)
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