Chapter 17.5, Problem 2CYU

a)

Interpretation Introduction

Interpretation:

The minimum concentration of ${\text{I}}^{-}$ at which precipitation of ${\text{PbI}}_2$ starts from a given concentration solution of $\text{Pb}{\left({\text{NO}}_3\right)}_2$ is to be calculated.

Concept introduction:

Solubility product constant, ${\text{K}}_{\text{sp}}$, 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 ${\text{K}}_{\text{sp}}$ of a salt is given as,

$\begin{array}{l}{\text{A}}_x{\text{B}}_y\left(\text{s}\right)\rightleftharpoons x{\text{A}}^{y+}\left(\text{aq}\right)+y{\text{B}}^{-x}\left(\text{aq}\right)\\ {\text{K}}_{\text{sp}}={\left[{\text{A}}^{y+}\right]}^x{\left[{\text{B}}^{-x}\right]}^y\end{array}$

Here,

• $\left[{\text{A}}^{y+}\right]$ and $\left[{\text{B}}^{-x}\right]$ are equilibrium concentration.

Reaction quotient, $\text{Q}$, 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 $\text{Q}$ of a salt is given as,

$\begin{array}{l}{\text{A}}_x{\text{B}}_y\left(\text{s}\right)\rightleftharpoons x{\text{A}}^{y+}\left(\text{aq}\right)+y{\text{B}}^{-x}\left(\text{aq}\right)\\ {\text{K}}_{\text{sp}}={\left[{\text{A}}^{y+}\right]}^x{\left[{\text{B}}^{-x}\right]}^y\end{array}$

Here,

• $\left[{\text{A}}^{y+}\right]$ and $\left[{\text{B}}^{-x}\right]$ are the concentration at any time except equilibrium.

1. 1. If $\text{Q}={\text{K}}_{\text{sp}}$, this implies that the solution is saturated solution and the concentration of the ions have reached their maximum limit.
2. 2. If $\text{Q}<{\text{K}}_{\text{sp}}$, 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 $\text{Q}>{\text{K}}_{\text{sp}}$, this implies that the solution is oversaturated and precipitation of salt will occur.

b)

Interpretation Introduction

Interpretation:

The left concentration of ${\text{Pb}}^{2+}$ ions in the solution of $\text{Pb}{\left({\text{NO}}_3\right)}_2$ when the concentration of ions added to the solution is increased to cause precipitation of ${\text{PbI}}_2$ is to be calculated.

Concept introduction:

Solubility product constant, ${\text{K}}_{\text{sp}}$, 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 ${\text{K}}_{\text{sp}}$ of a salt is given as,

$\begin{array}{l}{\text{A}}_x{\text{B}}_y\left(\text{s}\right)\rightleftharpoons x{\text{A}}^{y+}\left(\text{aq}\right)+y{\text{B}}^{-x}\left(\text{aq}\right)\\ {\text{K}}_{\text{sp}}={\left[{\text{A}}^{y+}\right]}^x{\left[{\text{B}}^{-x}\right]}^y\end{array}$

Here,

• $\left[{\text{A}}^{y+}\right]$ and $\left[{\text{B}}^{-x}\right]$ are equilibrium concentration.