# Solubility of Silver Nanoparticles [closed]

(i) What happens when you put $\ce{Ag_{10}}$ and $\ce{Ag_5}$ clusters into an aqueous solution of pH = $13$

(ii) What happens when you put $\ce{Ag_{10}}$ and $\ce{Ag_5}$ clusters into an aqueous solution of pH = $5$

In the previous questions they have asked to calculate the solubility product of $\ce{AgCl}$ and the standard potentials of $\ce{Ag_5}$ and $\ce{Ag_{10}}$ which I calculated them to be $1.4 \times 10^{-10}$,$\ -0.5184\ \mathrm{V}$,$0.0816\ \mathrm{V}$ respectively. The question has given no other data.

I have no idea how these 3 values that I have calculate has anything to do with the solubility of $\ce{Ag_5}$ and $\ce{Ag_{10}}$ let alone how I am suppose to relate it to pH.

Could anyone point me into the right direction. Any help is much appreciated.

Thanks.

## closed as off-topic by A.K., Mithoron, Todd Minehardt, Karsten Theis, Mathew MahindaratneMar 30 at 1:39

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• I don't think the $K_{sp}$ of AgCl has anything to do with it, but if you gave me this question without further info, my first thought would be "surely one species must be favored over the other under different conditions." If you assume there's excess silver ions in the solution, could you maybe use the Nernst Equation to figure out where the equilibrium lies? – chipbuster Jan 3 '16 at 9:49
• @chipbuster how could I figure out where the equilibrium lies from the nernst equation? Also, how can I relate this to pH? – Nanoputian Jan 3 '16 at 9:53
• Let's say you have hydrogen ions in solution, along with some silver ions. There will be some half reactions that turn silver clusters into silver ions, and vice versa. The Nernst Equation will tell you what the potentials are away from equilibrium (e.g. if you add acid, you move the equilibrium--the Nernst eqn tell you how much). You can use the pH to find the concentration of H+ ions that you're actually dealing with. Note that this is just a sketch of an idea---I don't know if you can actually make the calculation work out (you may be missing some info you'll need along the way). – chipbuster Jan 4 '16 at 8:02
• This is no way an answer but it is only a vague guess. I am guessing both Ag10 and Ag5 has surface charges(+ve, -ve or Zero). In low Ph there will be lots of H+ ions which will react with negatively charged silver cluster and make it neutral and at high Ph -OH ions will react with positively charged Ag cluster – Eka Jan 10 '16 at 18:18