What is the solubility of AgCl (a) in pure water and (b) in 1.0 M NH₃?

Interpretation:

Solubility of AgCl in pure water has to be calculated using Ksp value of AgCl.

Concept introduction:

The solubility of a salt is defined as the maximum amount of salt that can be dissolved in definite amount of solvent. It is expressed in moles per liter or grams per liter. Solubility in terms of moles per liter is called molar solubility and is defined as the number of moles of solute (salt) dissolved in per liter of solution.

Solubility product constant Ksp is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

For example, general salt AxBy when dissolved in water dissociates as,

AxBy(s)⇌xAy+(aq)+yB−x(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[B−x]y (1)

The ICE table (1) for salt AxBy, which relates the equilibrium concentration of ions in the solution is given as follows,

EquationAxBy⇌xAy++yB−xInitial(M)00Change(M)+xs+ysEquilibrium(M)xsys

From the table,

[Ay+]=xs[B−x]=ys

Substitute xs for [Ay+] and ys for [B−x] in equation (1).

Ksp=(xs)x(ys)y=xxyy(s)x+y

Rearrange for s.

s=(Kspxxyy)1/(x+y)

Here,

• x is the coefficient of the cation A+y.
• y is the coefficient of the anion B−x.
• s is the molar solubility.

Given:

Refer to the Table 17.2 in the textbook for the value of Ksp.

The value of solubility product constant,Ksp of AgCl is 1.8×10−10.

The balanced chemical reaction for the dissolution of AgCl in water is,

  AgCl(s)⇌ Ag+(aq) + Cl−(aq)

The ICE table (2) is as follows,

EquationAgCl(s)⇌Ag+(aq)+Cl−(aq)Initial (M)00Change (M)+s+sEquilibrium (M) s s

The Ksp expression for AgCl is,

Ksp = [Ag+][Cl−1] (2)

From the table,

[Ag+]=s[Cl−1]=s

Substitute s for [Ag+] and [Cl−1] in equation (2)

Interpretation:

The solubility of AgCl in presence of 1 M NH3  has to be calculated.

Concept introduction:

Some metal ions when present in an aqueous solution containing anions or neutral species called Lewis base or ligands having a tendency to donate electron pairs to metal ions then complex ion formation will take place. Complex ions are stable and thus formation of these increase the solubility of the salt containing the metal ions same as in complex ions.

Example of metal ions that form complex ions includes Ag+,Cd2+,Fe2+,Zn2+,Ni2+ etc.

Example of Lewis bases includes,NH3,OH− etc.

The complex ion remains in equilibrium with the metal ion and the ligand called complex ion formation equilibrium and the equilibrium constant is called as formation constant Kf.

A larger value of Kf implies that the complex ion formed is more stable. Kf is the measure of the strength of the interaction between the metal ions and the Lewis base to form the complex ion.

Kd is the dissociation constant of the complex ion and its value is equal to the inverse of the formation constant value of the same complex because dissociation of a complex is just reverse of the formation of the complex. A larger value of Kd implies less stable complex ion.

Kf=1Kd

For example for general complex ion formation reaction,

  xM+yL⇌[MxLy]

Kf and Kd can be given as,

Kf=1Kd=[MxLy][M]x[L]y

 Here,

• [MxLy] is the equilibrium concentration of complex ion.
• [M] is the equilibrium concentration of metal ion.
• [L] is the equilibrium concentration of the ligand.
• x and y are the coefficients of metal ion and ligand respectively.

Complex ions are stable and thus formation of these increases the solubility of the salt containing the metal ions same as in complex ions.