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# Equilibrium problem watch

1. The formation constants of the [Au(NH3)4]2+ and [Au(S2O3)2]3- species are 1.00*1026 and 1.00*1028, respectively. Consider a leeching solution, in which the equilibrium concentrations of the species are as follows:

[S2O32-]=0.100 M; [NH3]=0.100 M; total concentration of gold (I) species = 5.50*10-5 M

Calculate the percentage of gold (I) ions that are complexed with thiosulphate.

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My attempt:

I have to calculate [[Au(S2O3)2]3-] and if I can do that then [[Au(S2O3)2]3-]/CAu will bring me my percentage (CAu=5.50*10-5 M given).

So first we write down the reactions:

Au+ + 4NH3 -> [Au(NH3)4]+
Au+ + 2S2O32- -> [Au(S2O3)2]3-

Now I'll try to get some equilibrium out of here which contains only concentrations I have or can express in terms of constants I have and the one variable I want - [[Au(S2O3)2]3-].

So there's the trouble. My initial instincts would be "get rid of the [Au+] - you're not given it anywhere" and then regard CAu with CAu=[[Au(S2O3)2]3-]+[[Au(NH3)4]+] being the Au mass balance in terms of the total concentration, which is known. Then rearrange this so that it is an expression in terms of just the one variable we want: CAu-[[Au(S2O3)2]3-]=[[Au(NH3)4]+].

Then I could subtract the first reaction from the second (K(overall)=K2*K1-1, removing the Au+ which I don't know, and solve for just [[Au(S2O3)2]3-].

Only one hitch. I can remove Au+ from consideration of the equilibrium by eliminating it through my reaction combination - that is why I chose to subtract - but I cannot remove it from the problem, because it is also present in CAu. My original expression was wrong: it must be CAu=[[Au(S2O3)2]3-]+[[Au(NH3)4]+]+[Au+] to note that there might be some uncomplexed gold (I) ions.

So how do I do this then?

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Updated: April 12, 2013
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