Hello I need help with this excersise: How many moles of NH4Cl are neccesary to add to 1 liter of solution of Co2+ 0,20 M in order to prevent the precipitation when the solution is saturated with H2S (0,1M) and the pH is 7,50. It 's known that pKbNH3=4,75 ; Kps(CoS)=2,0×10^-25 ; Ka1 (H2S)= 1,1×10^-7 ; ka2(H2S)= 10^-14 and Kc of Co (NH3)6=10^35,1

Question

Hello I need help  with this excersise: How many moles of NH4Cl are neccesary to add to 1 liter of solution of Co2+ 0,20 M in order to prevent the precipitation when the solution is saturated with H2S (0,1M) and the pH is 7,50. It 's known that pKbNH3=4,75 ; Kps(CoS)=2,0×10^-25 ; Ka1 (H2S)= 1,1×10^-7 ; ka2(H2S)= 10^-14 and Kc of Co (NH3)6=10^35,1
The reaction between NH4Cl and Co2+  is :
Co +6NH3 <----------->Co (NH3)6

I have calculated:
[S-2]= 1,1 ×10^-7 M               
[Co+2] = 1,82 ×10^-18M 
[NH3]=4,54×10^-4 M
[NH4]= 0,2551 M
Well I don't understand what to do next, in other web pages told me to do an addition:
[NH4Cl]= [NH3]+6 [Co (NH3)6]+[NH4] and then calculate the moles.
But I don't get why I have to do this addition to obtain  the molarity of the solution of NH4Cl and why they put  a 6 before the Co (NH3)6 because in the equation the coefficient of Co (NH3) is 1

DrBob222 · Answer

That [NH4Cl] = [NH3] + [NH4^+] + 6[Co(NH3)6]^2+ is a mass balance equation. You are adding all of the species in which the NH4Cl will be. You multiply that complex by 6 because it contains 6 times the NH3 found in the other species. So you add all of them together to get the total NH4Cl.