Introduction:
In this scenario, we have a 0.05 M solution of ammonium hydroxide (NH4OH) and a 0.001 M solution of ammonium chloride (NH4Cl). We need to determine the concentration of hydroxide ions (OH-) in the resulting solution when these two solutions are mixed together.

Ammonium Hydroxide (NH4OH):
Ammonium hydroxide is a weak base that partially dissociates in water. It reacts with water to produce ammonium ions (NH4+) and hydroxide ions (OH-).

NH4OH ⇌ NH4+ + OH-

The equilibrium constant for this reaction is given by the equilibrium expression:

Kw = [NH4+][OH-]

Ammonium Chloride (NH4Cl):
Ammonium chloride is a salt that completely dissociates in water. It breaks down into ammonium ions (NH4+) and chloride ions (Cl-).

NH4Cl → NH4+ + Cl-

Formation of NH4+ and OH- Ions:
When we mix the ammonium hydroxide solution with the ammonium chloride solution, the ammonium ions (NH4+) from both solutions will remain in solution. However, the hydroxide ions (OH-) from the ammonium hydroxide will react with the hydrogen ions (H+) from the dissociation of water to form water molecules.

NH4OH + H2O ⇌ NH4+ + OH- + H2O

The concentration of hydroxide ions (OH-) in the resulting solution will depend on the concentration of ammonium hydroxide and the extent of its dissociation. Since ammonium hydroxide is a weak base, it will only partially dissociate, leading to a smaller concentration of hydroxide ions compared to the concentration of ammonium hydroxide.

Calculating the OH- Ion Concentration:
To calculate the OH- ion concentration, we need to consider the initial concentration of ammonium hydroxide and the extent of its dissociation. Since the concentration of ammonium hydroxide is given as 0.05 M, we can assume that the concentration of NH4+ ions is also 0.05 M.

Since ammonium hydroxide is a weak base, we can assume that its dissociation is negligible compared to the concentration of NH4+. Therefore, the concentration of OH- ions can be approximated as the same as the concentration of NH4+ ions, which is 0.05 M.

Conclusion:
In conclusion, when a 0.05 M ammonium hydroxide solution is dissolved in a 0.001 M ammonium chloride solution, the concentration of hydroxide ions (OH-) in the resulting solution is approximately 0.05 M. This is because the weak base ammonium hydroxide partially dissociates to produce ammonium ions (NH4+) and hydroxide ions (OH-), and the concentration of OH- ions can be approximated as the same as the concentration of NH4+ ions.