How to calculate the [Cu2^+] in a solution that was initially 1.0 M NH3 and 0.10 M Cu2^+ ?

Question

Kf value for Cu(NH3)4 ^ 2+ = 2.1*10^13

Please give me a detailed way of doing this problem. Thank you very much

Answer 1

wondering what you mean by Kf

Answer 2

Kf = the formation constant, sorry if i wrongly wrote it, sir

Answer 3

........Cu^2+ + 4NH3 ==> Cu(NH3)4^++
I.......0.1M....1.0M.......0M
C......-0.1M...-0.4M......+0.1M
E........0?.....0.6M.......0.1M

What I usually do is to recognize that with a Kf of 2.1E13 the reaction goes far to the right and you have formed essentially all of the complex and little of the Cu^2+ is left(that zero isn't quite right and that's what you want to determine). So if we make that assumption, we have a new problem which says that we are starting with Cu complex of 0.1M and 0.6M NH3 and we want to know (Cu^2+). I have drawn a line below the E line of the previous work and we work backwards with the new numbers.
........Cu^2+ + 4NH3 ==> Cu(NH3)4^++
I.......0.1M....1.0M.......0M
C......-0.1M...-0.4M......+0.1M
E........0?.....0.6M.......0.1M
--------------------------------
I........0......0.6M.......0.1M
C.......+x.....+4*x.........-x
E........x.....0.6+4x.....0.1-x

Then Substitute the E line into the Kf expression for Cu(NH3)4^2+ and solve for x = (Cu^2+).
Post your work if you get stuck.