[plankk]

I have a task:

How many times solubility of AgSCN is bigger in the solution of 1 M KSCN than in distilled water?

This is my solution:
Firstly I calculated the solubity of AgSCN in distilled water.
K_so=10^-12=[Ag][SCN]=S²
S=10^-6 mol/l

Then I attempted to calculate the solubilty in KSCN:
[Ag]=S*L
[SCN]=1+S

Where L is: L=1/(1+B₁[SCN]+B₂[SCN]²+B₃[SCN]³+B₄[SCN]⁴)
I've got such value of stability constants of complexes:
B₁=10^4,6
B₂=10^7,6
B₃=10^9,1
B₄=10^10,1

I did aproximation: [SCN]=1
L=7,2*10^-11

After all I could calculated S: K_so=[SCN]*L*S
S=K_so/([SCN]*L)=0,0139 mol/l

So my anwser was: 0,0139/10^-6=13900

In the key the answer is 12600. I found that such solution is possible if we assume that the only Ag(SCN)₄^3- is made. I understand that KSCN is in excess, so such assumption can be correct. But it means that I did this task wrong or only that I'm too precise?

[Borek]

Don't bother, as long as you are sure you know what you are doing. Answers to such questions are almost always approximate, and set of approximations used determines the answer. As long as your answer is in correct ballpark it should be accepted.

[SCN]=1+S

Care to elaborate?

[plankk]

The whole concentration of SCN^- is the sum of the concentration of KSCN and the concentration of salt (AgSCN), which can be dissolved.

[Borek]

Ah, OK. No idea what I was thinking about 

[plankk]

I'm still doing exercises with metal complexes and I'm still having problems. I think that making new topic isn't necassary, so I will continue in this.

How many times will change the concentration of Ag⁺, if we add to 0,01 M AgNO₃ the same volume of 0,1 M KCN?

I did it like that:
The beginning concentration of Ag⁺ is the concentration of AgNO₃ so [Ag⁺]₀=c_AgNO3=0,01 mol/l

The concentration of Ag⁺ after adding KCN will be: [Ag⁺]₁=L*c

The concentration of AgNO₃ will change because the solution will be dilluted: c=1/2*c_AgNO3

Where L is: L=1/(1+B₂[CN]²+B₃[CN]³+B₄[CN]⁴)

Where B_x is the stability constant of complex. I've got such value:
B₂=10^21,1
B₃=10^21,8
B₄=10^20,7

I assume that the concentration of CN^- is: [CN]=0,05 mol/l (the same reason as with the AgNO₃)

After all [Ag⁺]₁=1,27*10^-21

So [Ag⁺]₀/[Ag⁺]₁=7,87*10¹⁸

In the key I've got the answer: 4,8*10¹³

Very big divergence indeed. I suppose that I have something wrong. I have thought about hydrolysis of CN^-. I have calculated new concentration of CN^- from K_b=10^-4. [CN]=0,04781 and in the end [Ag⁺]₀/[Ag⁺]₁=7,14*10¹⁷. Still isn't even close to answer from key. Where have I made mistake?

[Borek]

Seems like your result is pretty close to the exact value calculated numerically. Note: slightly different value of dissociation constant for HCN.

What book do you use?

W zbiorze zadań Galusa w niektórych podrozdziałach co druga odpowiedź nie ma wiele wspólnego z rzeczywistością

[plankk]

Thanks a lot. You're right - it is Galus.

Chyba właśnie trafiłam na jeden z tych działów.