Question

Write the expression for the solubility-product constant for each of the following ionic compounds: AgI, SrSO \(_{4}, \mathrm{Fe}(\mathrm{OH})_{2},\) and \(\mathrm{Hg}_{2} \mathrm{Br}_{2}\) .

Short answer

The solubility product constant expressions for the given ionic compounds are: - AgI: \(K_{sp} = [Ag^+][I^-]\) - SrSO4: \(K_{sp} = [Sr^{2+}][SO_4^{2-}]\) - Fe(OH)2: \(K_{sp} = [Fe^{2+}][OH^-]^2\) - Hg2Br2: \(K_{sp} = [Hg^{2+}]^2[Br^-]^2\)

Step-by-step solution

Dissolution Equations

Let's write the dissolution equations for each ionic compound: 1. For AgI: \(AgI \rightleftharpoons Ag^+ + I^-\) 2. For SrSO4: \(SrSO_4 \rightleftharpoons Sr^{2+} + SO_4^{2-}\) 3. For Fe(OH)2: \(Fe(OH)_2 \rightleftharpoons Fe^{2+} + 2OH^-\) 4. For Hg2Br2: \(Hg_2Br_2 \rightleftharpoons 2Hg^{2+} + 2Br^-\)

Solubility Product Constants Expressions

Now, let's write the expressions for the solubility product constants (Ksp) for each compound, using their dissolution equations: 1. For AgI: Dissolution equation: \(AgI \rightleftharpoons Ag^+ + I^-\) Ksp expression: \(K_{sp} = [Ag^+][I^-]\) 2. For SrSO4: Dissolution equation: \(SrSO_4 \rightleftharpoons Sr^{2+} + SO_4^{2-}\) Ksp expression: \(K_{sp} = [Sr^{2+}][SO_4^{2-}]\) 3. For Fe(OH)2: Dissolution equation: \(Fe(OH)_2 \rightleftharpoons Fe^{2+} + 2OH^-\) Ksp expression: \(K_{sp} = [Fe^{2+}][OH^-]^2\) 4. For Hg2Br2: Dissolution equation: \(Hg_2Br_2 \rightleftharpoons 2Hg^{2+} + 2Br^-\) Ksp expression: \(K_{sp} = [Hg^{2+}]^2[Br^-]^2\) So, the expressions for the solubility product constants for the given ionic compounds are: - AgI: \(K_{sp} = [Ag^+][I^-]\) - SrSO4: \(K_{sp} = [Sr^{2+}][SO_4^{2-}]\) - Fe(OH)2: \(K_{sp} = [Fe^{2+}][OH^-]^2\) - Hg2Br2: \(K_{sp} = [Hg^{2+}]^2[Br^-]^2\)

Key concepts

Dissolution Equation

In chemistry, a dissolution equation is essential for understanding how an ionic compound dissolves in water. When these compounds dissolve, they split into their respective ions in solution, showing how the solid compound breaks apart. This process is represented by a chemical equation called the dissolution equation.
For each ionic compound, the dissolution process is unique, depending on its chemical structure. For example:

• Silver iodide (AgI): The equation is written as \(AgI \rightleftharpoons Ag^+ + I^-\), showing that it breaks into one silver ion (\(Ag^+\)) and one iodide ion (\(I^-\)).
• Strontium sulfate (SrSO_4): Dissolves into \(Sr^{2+} + SO_4^{2-}\), releasing one strontium ion and one sulfate ion.
• Iron(II) hydroxide (Fe(OH)_2): This splits into \(Fe^{2+} + 2OH^-\), creating one iron ion and two hydroxide ions.
• Mercury bromide (Hg_2Br_2): Each unit dissociates into two mercury ions (\(2Hg^{2+}\)) and two bromide ions (\(2Br^-\)).

Understanding dissolution equations helps in predicting the behavior of these compounds when they interact with water, especially in determining their solubility.

Ionic Compounds

Ionic compounds consist of positive and negative ions held together by strong electrostatic forces called ionic bonds. These compounds typically form when metals combine with nonmetals, transferring electrons to create ions.
In the context of dissolution in water, the ionic compound dissociates into its respective ions. The strength of the ionic bond affects how readily the compound dissolves. Some ionic compounds have low solubility in water due to strong ionic attractions.
Ionic compounds like AgI and SrSO_4 are cases where the bond strength can affect the dissolution equilibrium, leading to a partially dissolved state.

• With AgI, weak dissolution results from strong ionic bonds.
• SrSO_4 is less soluble because of the strong attraction between strontium and sulfate ions.

Because these ions are either highly charged or closely packed, they sometimes form insoluble or sparingly soluble compounds in water. Hence, understanding the nature of ionic compounds is key to appreciating their dissolution behavior.

Ksp Expression

The solubility product constant, represented as \(K_{sp}\), is crucial to predicting how much of an ionic compound can be dissolved in water.
The \(K_{sp}\) expression is derived from the concentration of the ions produced during the dissolution process. It provides insight into the ionic equilibrium that occurs in a saturated solution of the compound.
Each compound's \(K_{sp}\) expression varies, based on how many ions the compound dissociates into:

• For AgI: \(K_{sp} = [Ag^+][I^-]\) depicts a simple 1:1 ratio.
• For SrSO_4: \(K_{sp} = [Sr^{2+}][SO_4^{2-}]\) also follows a direct 1:1 ion production.
• For Fe(OH)_2: \(K_{sp} = [Fe^{2+}][OH^-]^2\) indicates each formula unit provides two hydroxide ions, hence the squared term.
• For Hg_2Br_2: \(K_{sp} = [Hg^{2+}]^2[Br^-]^2\) results from the release of multiple ions requiring squared terms for both ions.

Understanding \(K_{sp}\) allows us to calculate maximum concentrations of dissolved ions and predict when a precipitate will form, making it an essential tool in chemistry.