Do complexes of a metal distribute in between the water and an organic compound layer?

Question

My original question is one that is stated in the title, and I also have some side questions too.

I came across this question where you have a CuSO4 aqueous solution. Then you take an Ammonia aqueous solution and mix those two solutions. Then you take some Trichloromethane, and you mix it with the above mixed solution. The objective of the question is to determine the ratio of Cu²⁺ : NH₃ in the formed complex.

So, for example, my assumption is that when CuSO₄ and NH₃ aqueous solutions are mixed, the Cu²⁺ ions form complex with Ammonia as [Cu(NH₃)₄(H2O)₂]²⁺. According to the question there is excess Ammonia so, when you put Trichloromethane, Ammonia distributes between Trichloromethane and Water.

My first question is, does Cu²⁺ ions also distribute in between Trichloromethane and water? If it is, are there [Cu(NH₃)₄(H2O)₂]²⁺ distributed between these two layers? (more precisely, are there [Cu(NH₃)₄(H2O)₂]²⁺ or Cu²⁺ ions in Trichloromethane layer?)

For my second question consider following equilibrium.

\begin{align} \ce{[Cu(H2O)_6]^2+ + 2NH3 &<=> [Cu(OH)_2(H2O)_6] + 2NH4^+}\\ \ce{[Cu(OH)_2(H2O)_4] + 4NH3 &<=> [Cu(NH3)_4(H2O)_2]^2+ +2OH- +2H2O}\\ \end{align}

In the question, it uses titration to measure the NH₃ amount dissolved in each layer. It uses HCl for the titration. So, as these are equilibriums, is it OK to use this titration, because when HCl react with NH₃, the above equilibriums reverse bias their equilibrium to release more Ammonia into the system?

A guide with the thought process about this question would be helpful.

Sorry in advance if my English is hard to understand. I couldn't find the English version of this question. I will a post photo of the original question, which is written in Sinhala, so if you need you can translate it from Google.

Also, below is a slightly modified accurate translation than Google translate that I made.

25.0 cm³ of an aqueous ammonia solution was mixed with 25.0 cm³ of a solution of 0.10 mol dm^-3 CuSO₄. The resulting deep blue solution was stirred well with about 50 cm³ of trichloromethane and allowed to equilibrate at a certain temperature. 31.9 cm³ of 0.02 mol dm^-3 HCl solution was required to neutralize the ammonia at 25.0 cm³ of the organic layer. 20.8 cm³ of 1.00 mol dm^-3 HCl solution was required to neutralize 25.0 cm³ of the dark blue aqueous ammonia layer. Calculate the Cu²⁺: NH₃ ratio of the complex formed by molecular association of NH₃ and Cu²⁺.

The distribution constant for NH₃, between water and organic layer is 25.

Answer 1

[OP] My first question is, does $\ce{Cu^2+}$ ions also distribute in between Trichloromethane and water?

No, the charged species will stay in the aqueous layer.

[OP] So, as these are equilibriums, is it OK to use this titration, because when $\ce{HCl}$ react with $\ce{NH3}$, the above equilibriums reverse bias their equilibrium to release more Ammonia into the system?

Yes, that is the point of the titration of the aqueous layer. There is some free ammonia, and some ammonia released from the complex as you titrate with HCl.

[Instructions] The distribution constant for NH3, between water and organic layer is 25.

The titration of the organic layer with HCl gives you the concentration of ammonia in the organic layer. The concentration of (free) ammonia in water will be 25-times higher. You have to subtract the amount of free ammonia in water from the measured amount in the aqueous layer to figure out the amount that was complexed with copper.