Chapter 17.5, Problem 3CYU

Interpretation Introduction

Interpretation:

$\text{AgCl}$will whether precipitate out or not upon addition of $0.001\text{ M}$ silver nitrate $\left({\text{AgNO}}_3\right)$ solution to a $0.025\text{}\text{M}$ solution of hydrochloric acid $\left(\text{HCl}\right)$ has to be determined.

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.

Mixing of two solutions of different concentration will result in the change in the initial concentration of the ions as the resultant volume will change. The final concentration or the concentration after mixing for ions is to be calculated using the following relation,

  ${\text{C}}_{\text{i}}{\text{V}}_{\text{i}}={\text{C}}_{\text{f}}{\text{V}}_{\text{f}}$                                                                                        (1)

Here,

• ${\text{C}}_{\text{i}}$ is the initial concentration of the ions.
• ${\text{V}}_{\text{i}}$ is the initial volume of the solution.
• ${\text{C}}_{\text{f}}$is the final concentration of the ions.
• ${\text{V}}_{\text{f}}$ is the final volume of the solution.