How to calculate the [Cu2^+] in a solution that was initially 1.0 M NH3 and 0.10 M Cu2^+ ?
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
wondering what you mean by Kf
Kf = the formation constant, sorry if i wrongly wrote it, sir
........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.
To calculate the concentration of [Cu2+] in the given solution, you first need to determine the equilibrium concentration of [Cu(NH3)4]^2+ by applying the equilibrium constant expression. The equilibrium constant (Kf) for the formation of [Cu(NH3)4]^2+ from Cu2+ and NH3 is given as 2.1 x 10^13.
Let's follow a step-by-step approach to solve the problem:
Step 1: Write the balanced equation for the formation of [Cu(NH3)4]^2+:
Cu2+ + 4NH3 ⇌ [Cu(NH3)4]^2+
Step 2: Set up the equilibrium expressions using the concentrations of the species:
Kf = [Cu(NH3)4]^2+ / ([Cu2+] * [NH3]^4)
Step 3: Substitute the given initial concentrations into the equilibrium expression:
Kf = (x) / (0.10 * (1 - x)^4)
Note: 'x' represents the equilibrium concentration of [Cu(NH3)4]^2+ and is the same as [Cu2+].
Step 4: Solve for 'x':
Rearrange the equation to isolate 'x':
(x) = Kf * 0.10 * (1 - x)^4
Solve the equation for 'x' using numerical methods or trial and error.
Note: Calculating this equation manually is difficult due to the high value of Kf. You may need to use computational methods or a graphing calculator to find the solution.
Step 5: Once you find the value of 'x', use it to calculate the concentration of [Cu2+] in the solution.
For example, if 'x' is found to be 0.05 M, then the concentration of [Cu2+] in the solution would be 0.05 M.
Remember, if 'x' is small compared to the initial concentration of Cu2+ (0.10 M in this case), you can assume that [Cu2+] is approximately equal to the initial concentration.
So, in this case, the concentration of [Cu2+] would be approximately 0.10 M.
Keep in mind that this approximation is only valid if 'x' is significantly smaller than the initial concentration.
That's it! You have calculated the concentration of [Cu2+] in the given solution.