What is the minimum concentration of I⁻ that can cause precipitation of Pbl₂ from a 0.050 M solution of PWNO₃)₂? K_sp for Pbl₂ is 9.8 × 10⁻⁹. What concentration of Pb²⁺ ions remains in solution when the concentration of I⁻ is 0.0015 M?

Interpretation:

The minimum concentration of I− at which precipitation of PbI2 starts from a given concentration solution of Pb(NO3)2 is to be calculated.

Concept introduction:

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.

The expression for Ksp of a salt is given as,

AxBy(s)⇌xAy+(aq)+yB−x(aq)Ksp=[Ay+]x[B−x]y

Here,

• [Ay+] and [B−x] are equilibrium concentration.

Reaction quotient, Q, for a reaction is defined as the product of the concentration of the ions at any time of the reaction (other than equilibrium time ) of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Q of a salt is given as,

AxBy(s)⇌xAy+(aq)+yB−x(aq)Ksp=[Ay+]x[B−x]y

Here,

• [Ay+] and [B−x] are the concentration at any time except equilibrium.

1. 1. If Q=Ksp, this implies that the solution is saturated solution and the concentration of the ions have reached their maximum limit.
2. 2. If Q<Ksp, this implies that the solution is not saturated and more salt can be added to the solution or the salt present in the solution already will dissolve more until the precipitation starts.
3. 3. If Q>Ksp, this implies that the solution is oversaturated and precipitation of salt will occur.

The minimum concentration required to cause the precipitation of PbI2 is calculated below.

Given:

The concentration of Pb(NO3)2 solution is 0.050​​ M.

The value of solubility product constant,Ksp, for PbI2 is 9.8×10−9.

Pb(NO3)2 is a strong electrolyte and therefore undergoes complete dissociation in water  as follows,

Pb(NO3)2(s)⇌Pb2+(aq)+2NO3−(aq)

The concentration of Pb2+ and NO3− will be equal to the initial concentration of the Pb(NO3)2 solution.

[Pb2+]=0.05​ M

[NO3−]=0.05 M

PbI2 when dissolved in water dissociates as follows,

PbI2(s)⇌Pb2+(aq)+2I−(aq)

The expression of Ksp for PbI2 is as follows,

Ksp=[Pb2+][I−1]2

Rearrange for [I−1].

[I−1]2=Ksp[Pb2+][I−1]=Ksp[Pb2+]2

Substitute 0

Interpretation:

The left concentration of Pb2+ ions in the solution of Pb(NO3)2 when the concentration of ions added to the solution is increased to cause precipitation of PbI2 is to be calculated.

Concept introduction:

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.

The expression for Ksp of a salt is given as,

AxBy(s)⇌xAy+(aq)+yB−x(aq)Ksp=[Ay+]x[B−x]y

Here,

• [Ay+] and [B−x] are equilibrium concentration.