What concentration of NH₃ must be present in 0.1M AgNO₃ solution to prevent AgCl from precipitation when 5.85g of NaCl are added to 250ml of this solution.

To determine the concentration of ammonia (NH3) needed to prevent the precipitation of silver chloride (AgCl) when sodium chloride (NaCl) is added to a silver nitrate (AgNO3) solution, we need to consider the solubility product constant (Ksp) of AgCl and the chemistry involved in complex ion formation with ammonia.

Understanding the Reaction Dynamics

When NaCl is added to the AgNO3 solution, silver ions (Ag+) react with chloride ions (Cl-) to form AgCl, which is a sparingly soluble salt. The Ksp for AgCl is approximately 1.77 x 10^-10 at room temperature. To prevent AgCl from precipitating, we need to ensure that the product of the concentrations of Ag+ and Cl- does not exceed this Ksp value.

Calculating Chloride Ion Concentration

First, we need to calculate the concentration of Cl- ions that will be introduced by adding 5.85 g of NaCl to 250 mL of the AgNO3 solution.

• Molar mass of NaCl = 58.44 g/mol
• Moles of NaCl = 5.85 g / 58.44 g/mol ≈ 0.100 mol
• Since NaCl dissociates completely, moles of Cl- = moles of NaCl = 0.100 mol
• Volume of solution = 250 mL = 0.250 L
• Concentration of Cl- = 0.100 mol / 0.250 L = 0.400 M

Determining Silver Ion Concentration

Next, we need to find the concentration of Ag+ ions in the solution. The initial concentration of AgNO3 is 0.1 M, which means there are 0.1 moles of Ag+ in 1 L of solution. In 250 mL, the concentration remains 0.1 M until Cl- is added.

Applying the Solubility Product Constant

To prevent AgCl from precipitating, we must ensure that:

[Ag+][Cl-] < Ksp

Substituting the known values:

[Ag+][Cl-] < 1.77 x 10^-10

Given that [Cl-] is 0.400 M, we can rearrange the equation to find the maximum allowable concentration of Ag+:

[Ag+] < Ksp / [Cl-]

Substituting the values:

[Ag+] < 1.77 x 10^-10 / 0.400 ≈ 4.425 x 10^-10 M

Role of Ammonia in Complex Formation

Ammonia can form a complex with silver ions, which effectively reduces the free Ag+ concentration in the solution. The formation of the complex ion [Ag(NH3)2]+ shifts the equilibrium, allowing more Ag+ to remain in solution without precipitating AgCl.

Calculating Required NH3 Concentration

To find the concentration of NH3 needed, we can use the stability constant (Kf) for the complex formation. The Kf for [Ag(NH3)2]+ is approximately 1.7 x 10^7. The equilibrium expression for the formation of this complex is:

Kf = [Ag(NH3)2+] / ([Ag+][NH3]^2)

Rearranging this gives us:

[NH3]^2 = [Ag+] / (Kf * [Ag(NH3)2+])

Assuming that all Ag+ is complexed, we can set [Ag(NH3)2+] equal to the initial concentration of Ag+, which is 0.1 M. Thus, we can substitute [Ag+] with the maximum concentration we calculated earlier:

[NH3]^2 = 4.425 x 10^-10 / (1.7 x 10^7 * 0.1)

Calculating this gives:

[NH3]^2 = 4.425 x 10^-10 / 1.7 x 10^6 ≈ 2.60 x 10^-16

Taking the square root to find [NH3]:

[NH3] ≈ 1.61 x 10^-8 M

Final Thoughts

In summary, to prevent the precipitation of AgCl when adding 5.85 g of NaCl to a 0.1 M AgNO3 solution, you would need a concentration of ammonia of approximately 1.61 x 10^-8 M. This concentration ensures that the free Ag+ ions remain below the threshold necessary for AgCl precipitation, thanks to the formation of the [Ag(NH3)2]+ complex.