Problem 37 - Chemistry and Chemical Reactivity

Question

For each of the following insoluble salts, (i) write a balanced equation showing the equilibrium occurring when the salt is added to water and (ii) write the \(K_{\mathrm{sp}}\) expression. (a) AgCN (b) \(\mathrm{NiCO}_{3}\) (c) \(\mathrm{AuBr}_{3}\)

Step-by-Step Solution

Answer

For AgCN: Equation - \(\text{AgCN (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{CN}^- (aq)\), \(K_{\mathrm{sp}} = [\text{Ag}^+][\text{CN}^-]\). For NiCO3: \(\text{NiCO}_3 (s) \rightleftharpoons \text{Ni}^{2+} (aq) + \text{CO}_3^{2-} (aq)\), \(K_{\mathrm{sp}} = [\text{Ni}^{2+}][\text{CO}_3^{2-}]\). For AuBr3: \(\text{AuBr}_3 (s) \rightleftharpoons \text{Au}^{3+} (aq) + 3\text{Br}^- (aq)\), \(K_{\mathrm{sp}} = [\text{Au}^{3+}][\text{Br}^-]^3\).

Step 1: Understanding the Problem

The problem asks us to represent the equilibrium of the dissolution of each insoluble salt in water as a balanced chemical equation, and then to write the corresponding solubility product constant (\(K_{\mathrm{sp}}\)) expression.

Step 2: Write Balanced Equation for AgCN Dissolution

When \(\text{AgCN}\) dissolves in water, it dissociates into silver ions (\(\text{Ag}^+\)) and cyanide ions (\(\text{CN}^-\)). The balanced dissolution equation is: \[ \text{AgCN (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{CN}^- (aq) \]

Step 3: Write Ksp Expression for AgCN

The solubility product expression, \(K_{\mathrm{sp}}\), for \(\text{AgCN}\) is given by the product of the concentrations of the ions in solution: \[ K_{\mathrm{sp}} = [\text{Ag}^+][\text{CN}^-] \]

Step 4: Write Balanced Equation for NiCO3 Dissolution

\(\text{NiCO}_3\) dissociates into nickel ions (\(\text{Ni}^{2+}\)) and carbonate ions (\(\text{CO}_3^{2-}\)) in water. The balanced equation is: \[ \text{NiCO}_3 (s) \rightleftharpoons \text{Ni}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]

Step 5: Write Ksp Expression for NiCO3

The \(K_{\mathrm{sp}}\) expression for \(\text{NiCO}_3\) is: \[ K_{\mathrm{sp}} = [\text{Ni}^{2+}][\text{CO}_3^{2-}] \]

Step 6: Write Balanced Equation for AuBr3 Dissolution

When \(\text{AuBr}_3\) dissolves in water, it dissociates into gold ions (\(\text{Au}^{3+}\)) and bromide ions (\(\text{Br}^-\)). The balanced dissolution equation is: \[ \text{AuBr}_3 (s) \rightleftharpoons \text{Au}^{3+} (aq) + 3\text{Br}^- (aq) \]

Step 7: Write Ksp Expression for AuBr3

The \(K_{\mathrm{sp}}\) expression for \(\text{AuBr}_3\) involves the stoichiometry of the ions: \[ K_{\mathrm{sp}} = [\text{Au}^{3+}][\text{Br}^-]^3 \]

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a state where the rate of the forward reaction equals the rate of the reverse reaction.
In the context of dissolution, this means the rate at which an insoluble salt dissolves equals the rate at which it precipitates.
This balance allows us to understand how salt behaves in water.
In a dissolution process, the solid salt dissociates into its ions in an aqueous solution. As these ions spread out, they can also recombine to form the solid.
When these two processes balance, we reach equilibrium.

• The system is dynamic, meaning even at equilibrium, these processes are still happening.
• Equilibrium doesn't necessarily mean equal concentrations of reactants and products, but rather constant concentrations over time.

Understanding equilibrium helps us predict how much of the salt can dissolve in a given amount of water.

Insoluble Salts

Insoluble salts are salts that do not dissolve well in water.
However, even insoluble salts have a small degree of dissolution that can be described using the solubility product constant, or \(K_{\mathrm{sp}}\).
In chemistry, solubility is not a black-and-white concept.
Most "insoluble" salts actually dissolve slightly, leading to an equilibrium of ions in solution.
These salts dissociate into their component ions. For example:

• \(\text{AgCN} \rightarrow \text{Ag}^+ + \text{CN}^-\)
• \(\text{NiCO}_3 \rightarrow \text{Ni}^{2+} + \text{CO}_3^{2-}\)
• \(\text{AuBr}_3 \rightarrow \text{Au}^{3+} + 3\text{Br}^-\)

The idea here is that each dissociation is governed by its own \(K_{\mathrm{sp}}\), allowing us to quantify the equilibrium of an insoluble salt's slight solubility.

Dissolution Equation

A dissolution equation shows how a salt dissolves and what ions it forms.
It provides a visual representation of dissolving.
For example, the dissolution equation for an insoluble salt like \(\text{NiCO}_3\) can be written as:\[ \text{NiCO}_3 (s) \rightleftharpoons \text{Ni}^{2+} (aq) + \text{CO}_3^{2-} (aq) \]This equation illustrates the solid salt breaking into ions.
The double arrow indicates that it reaches a state of dynamic equilibrium.
Using these equations in tandem with \(K_{\mathrm{sp}}\) expressions:

• \([\text{Ni}^{2+}][\text{CO}_3^{2-}]\) describes how the concentration of ions relates to the salt's dissolving power.
• The stoichiometry in the dissolution equation helps explain the \(K_{\mathrm{sp}}\) expression.

Understanding dissolution equations helps in identifying the amount of salt that can actually dissolve, even if it is labeled "insoluble."