Question

For each compound, write an equation showing how the compound dissolves in water and write an expression for \(K_{\mathrm{sp}}\). (a) \(\mathrm{CaSO}_{4}\) (b) \(\mathrm{AgCl}\) (c) CuS (d) \(\mathrm{FeCO}_{3}\)

Short answer

The equations and expressions are: (a) \(\mathrm{CaSO}_{4} \rightleftharpoons \mathrm{Ca}^{2+} + \mathrm{SO}_{4}^{2-}\), \(K_{\mathrm{sp}} = [\mathrm{Ca}^{2+}][\mathrm{SO}_{4}^{2-}]\); (b) \(\mathrm{AgCl} \rightleftharpoons \mathrm{Ag}^{+} + \mathrm{Cl}^{-}\), \(K_{\mathrm{sp}} = [\mathrm{Ag}^{+}][\mathrm{Cl}^{-}]\); (c) \(\mathrm{CuS} \rightleftharpoons \mathrm{Cu}^{2+} + \mathrm{S}^{2-}\), \(K_{\mathrm{sp}} = [\mathrm{Cu}^{2+}][\mathrm{S}^{2-}]\); (d) \(\mathrm{FeCO}_{3} \rightleftharpoons \mathrm{Fe}^{2+} + \mathrm{CO}_{3}^{2-}\), \(K_{\mathrm{sp}} = [\mathrm{Fe}^{2+}][\mathrm{CO}_{3}^{2-}]\).

Step-by-step solution

Write the Dissolution Equation for Calcium Sulfate

To describe the dissolution of \(\mathrm{CaSO}_{4}\) in water, write a balanced chemical equation for the dissociation of the compound. \(\mathrm{CaSO}_{4} \(s\) \rightleftharpoons \mathrm{Ca}^{2+} \(aq\) + \mathrm{SO}_{4}^{2-} \(aq\)\). In this reaction, solid calcium sulfate dissociates into its ions.

Write the Solubility Product Expression for Calcium Sulfate

For \(\mathrm{CaSO}_{4}\), the expression for the solubility product constant, \(K_{\mathrm{sp}}\), is the product of the molar concentrations of the ions each raised to the power of its coefficient in the balanced equation: \[K_{\mathrm{sp}} = [\mathrm{Ca}^{2+}][\mathrm{SO}_{4}^{2-}]\].

Write the Dissolution Equation for Silver Chloride

The dissolution of \(\mathrm{AgCl}\) in water is described by the balanced chemical equation: \(\mathrm{AgCl} \(s\) \rightleftharpoons \mathrm{Ag}^{+} \(aq\) + \mathrm{Cl}^{-} \(aq\)\). Here, solid silver chloride dissociates into silver and chloride ions.

Write the Solubility Product Expression for Silver Chloride

The expression for the solubility product constant for \(\mathrm{AgCl}\) is given by: \[K_{\mathrm{sp}} = [\mathrm{Ag}^{+}][\mathrm{Cl}^{-}]\].

Write the Dissolution Equation for Copper(II) Sulfide

Copper(II) sulfide dissolves in water according to the equation: \(\mathrm{CuS} \(s\) \rightleftharpoons \mathrm{Cu}^{2+} \(aq\) + \mathrm{S}^{2-} \(aq\)\). In this process, solid copper sulfide dissociates into copper(II) and sulfide ions.

Write the Solubility Product Expression for Copper(II) Sulfide

For \(\mathrm{CuS}\), the \(K_{\mathrm{sp}}\) expression is: \[K_{\mathrm{sp}} = [\mathrm{Cu}^{2+}][\mathrm{S}^{2-}]\].

Write the Dissolution Equation for Iron(II) Carbonate

Iron(II) carbonate dissolves in water as follows: \(\mathrm{FeCO}_{3} \(s\) \rightleftharpoons \mathrm{Fe}^{2+} \(aq\) + \mathrm{CO}_{3}^{2-} \(aq\)\). This shows the dissociation of solid iron(II) carbonate into iron(II) and carbonate ions.

Write the Solubility Product Expression for Iron(II) Carbonate

The solubility product constant for \(\mathrm{FeCO}_{3}\) is defined by the equation: \[K_{\mathrm{sp}} = [\mathrm{Fe}^{2+}][\mathrm{CO}_{3}^{2-}]\].

Key concepts

Dissolution Equations

Understanding dissolution equations is crucial for grasping how substances interact with water. It starts with visualizing a solid ionic compound, such as common table salt (NaCl). When this solid enters water, it dissociates into individual ions that disperse throughout the solution. For example, the dissolution of NaCl in water could be represented as follows:
\[ \mathrm{NaCl} (s) \rightleftharpoons \mathrm{Na}^{+} (aq) + \mathrm{Cl}^{-} (aq) \].
In this balanced chemical equation, the solid (s) dissociates into a positive ion or cation (Na+) and a negative ion or anion (Cl-) both in the aqueous (aq) state. This process is fundamental to the science of solutions, where water's polar nature plays a key role in separating the ions.

Chemical Equilibrium

Chemical equilibrium is a state in which the forward and reverse reactions occur at the same rate, resulting in no net change in the concentration of reactants and products over time. It's an essential concept when studying the dissolution of ionic compounds. For example, the equilibrium for the dissolution of calcium sulfate can be expressed as:
\[ \mathrm{CaSO}_{4} (s) \rightleftharpoons \mathrm{Ca}^{2+} (aq) + \mathrm{SO}_{4}^{2-} (aq) \].
The double arrows indicate that both the dissolution (forward reaction) and the precipitation (reverse reaction) are happening simultaneously. At equilibrium, the rate at which the solid dissolves equals the rate at which the ions recombine to form the solid, leading to a constant value for the concentration of the ions in solution under stable conditions.

Ionic Compounds in Water

When ionic compounds like AgCl or CuS are placed in water, their ions are surrounded by water molecules in a process called hydration. This helps stabilize the ions in solution and allows them to spread out evenly in the water. The solubility of an ionic compound in water depends on the attraction between water molecules and the ions versus the attraction the ions have for each other in the solid state. Factors such as temperature, the presence of other ions in solution, and the ionic compound's inherent properties can all affect its solubility.

Solubility and Ksp Expressions

The solubility product constant (Ksp) is an expression that relates the solubility of sparingly soluble ionic compounds to their concentration in a saturated solution at equilibrium. For instance, the Ksp for copper(II) sulfide (CuS) is given by:
\[K_{\mathrm{sp}} = [\mathrm{Cu}^{2+}][\mathrm{S}^{2-}]\].
This equilibrium expression shows that the product of the molar concentrations of the ions, each raised to the power of its stoichiometric coefficient, remains constant at a given temperature for a saturated solution. The Ksp value indicates the extent to which a compound will dissolve in water; the higher the Ksp, the more soluble the compound. Ksp expressions do not include the concentration of any solid species because it's a constant that doesn't change the equilibrium position.