[mlesniewski]

I have a homework problem for which part of the answer is stumping me.  The problem is as follows and I have shown my work so far.  Any help would be greatly appreciated.  Thank you. 

Am I forgetting that Ag2(S2O3)2 would precipitate before forming Ag(S2O3)3-?
If so, I was not given a Ksp for this process.

PROBLEM:
What is [Ag+] when 25.8 mL of 0.22M Ag(NO3) and 0.80M Na2S2O3 are mixed? Kf  =  4.7 x 10^13

1.   Find the actual initial molar concentrations of each ion based on amounts mixed:
         For Ag:  0.0258 x 0.22 =  0.0057 M
         For S2O3:  0.0258 x 0.80 =  0.0206 M

2.   Ksp does not factor into this calculation since all nitrates are soluble and nitrate appears on both sides of the equation as a spectator ion.  (Or does it??)

3.   The reaction for Kf looks like:

Ag+  +  2S2O32-  à  Ag(S2O3)2^3-

Kf  =  4.7 x 10^13 = [Ag(S2O3)2]/([ Ag+  ][ S2O32]^2)



4.  Set up the ice table to look like:
          Ag             +           2S2O3       à       Ag(S2O3)2  3-
I     0.0057 M               0.0206 M                    0 M
C        -X                            -2X                      +X
E   0.0057- X               0.0206 - 2X                X


Kf  =  4.7 x 10^13  =  [X/(0.0057)(0.0206)^2]

X = conc. of complex ion =  4.7 x 10^13  x (.2.4 x 10^-6)  = a large number that does not make sense

[Borek]

         For Ag:  0.0258 x 0.22 =  0.0057 M
         For S2O3:  0.0258 x 0.80 =  0.0206 M

Haven't you forgot to divide by the final volume?

E   0.0057- X               0.0206 - 2X                X


Kf  =  4.7 x 10^13  =  [X/(0.0057)(0.0206)^2]

X/(0.0057-X)(0.0206-2X)^2

But I bet you may safely assume reaction goes to completion and calculate concentrations of everything but Ag⁺ from simple stoichiometry (hint: find limiting reagent).