Problem 25 - Chemistry The Molecular Nature of Matter

Question

Write the \(K_{\mathrm{sp}}\) expressions for each of the following compounds: (a) \(\mathrm{Hg}_{2} \mathrm{Cl}_{2},\) (b) \(\mathrm{AgBr}\), (c) \(\mathrm{PbBr}_{2}\), (d) \(\mathrm{CuCl}\), (e) \(\mathrm{HgI}_{2}\)

Step-by-Step Solution

Answer

The solubility product constant \(K_{\mathrm{sp}}\) expressions are: (a) \(K_{\mathrm{sp}} = [\mathrm{Hg}_{2}^{2+}][\mathrm{Cl}^{-}]^{2}\), (b) \(K_{\mathrm{sp}} = [\mathrm{Ag}^{+}][\mathrm{Br}^{-}]\), (c) \(K_{\mathrm{sp}} = [\mathrm{Pb}^{2+}][\mathrm{Br}^{-}]^{2}\), (d) \(K_{\mathrm{sp}} = [\mathrm{Cu}^{+}][\mathrm{Cl}^{-}]\), (e) \(K_{\mathrm{sp}} = [\mathrm{Hg}^{2+}][\mathrm{I}^{-}]^{2}\).

Step 1: Identifying the Ions in Each Compound

Start by identifying the cations and anions that make up each ionic compound. For example, \(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\) consists of \(\mathrm{Hg}_{2}^{2+}\) and \(\mathrm{Cl}^{-}\) ions.

Step 2: Determining the Dissociation

Write down the dissociation of each compound into its constituent ions. For instance, \(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\) dissociates into \(\mathrm{Hg}_{2}^{2+}\) and \(\mathrm{Cl}^{-}\) ions.

Step 3: Expression for Solubility Product (Ksp)

For each compound, write the expression for the solubility product constant \(K_{\mathrm{sp}}\), which is the product of the concentrations of the ions each raised to the power of their coefficients in the balanced dissociation equation.

Step 4: Write Ksp for Hg2Cl2

For \(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\), \(K_{\mathrm{sp}} = [\mathrm{Hg}_{2}^{2+}][\mathrm{Cl}^{-}]^{2}\).

Step 5: Write Ksp for AgBr

For \(\mathrm{AgBr}\), \(K_{\mathrm{sp}} = [\mathrm{Ag}^{+}][\mathrm{Br}^{-}]\).

Step 6: Write Ksp for PbBr2

For \(\mathrm{PbBr}_{2}\), \(K_{\mathrm{sp}} = [\mathrm{Pb}^{2+}][\mathrm{Br}^{-}]^{2}\).

Step 7: Write Ksp for CuCl

For \(\mathrm{CuCl}\), \(K_{\mathrm{sp}} = [\mathrm{Cu}^{+}][\mathrm{Cl}^{-}]\).

Step 8: Write Ksp for HgI2

For \(\mathrm{HgI}_{2}\), \(K_{\mathrm{sp}} = [\mathrm{Hg}^{2+}][\mathrm{I}^{-}]^{2}\).

Key Concepts

Chemical Equilibrium

Understanding chemical equilibrium is essential when studying the behavior of reactions, including those involving ionic compounds and their solubility in water. Chemical equilibrium refers to a state in which the rate of the forward reaction equals the rate of the reverse reaction, leading to no net change in the concentration of reactants and products over time. It is a dynamic process where reactions continue to occur, but the system is in balance.

In the context of the solubility product constant, or \(K_{\text{sp}}\), equilibrium is reached when a saturated solution is formed, and there's a constant concentration of dissolved ions. This state happens because the rate at which the ionic compounds dissolve in water is equal to the rate at which they precipitate out. \(K_{\text{sp}}\) is a special type of equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is used to predict whether a precipitate will form in a given solution and to calculate the maximum concentration of ions that can exist in a solution before precipitation occurs.

Ionic Compounds

Ionic compounds are substances composed of charged ions, with at least one metal and one non-metal element. They are held together by strong electrostatic forces known as ionic bonds. The formation of these compounds is often driven by the complete transfer of electrons from one atom to another, leading to the creation of positive and negative ions.

For example, in the compound \(\text{AgBr}\), silver (\text{Ag}) loses an electron, becoming a positively charged cation (\text{Ag}^+), and bromine (\text{Br}) gains an electron, becoming a negatively charged anion (\text{Br}^-). The solubility of these compounds in water can vary considerably, and this property is important for predicting reaction outcomes, such as the formation of a precipitate, or for understanding various biochemical processes.

Dissociation of Compounds

The dissociation of compounds into their constituent ions is a critical concept in solubility and chemical equilibrium. When ionic compounds dissolve in water, they dissociate, meaning they separate into the ions that comprise them. This process is influenced by the compound's solubility and the nature of its ions.

For instance, when the compound \(\text{PbBr}_{2}\) is placed in water, it begins to dissociate into \(\text{Pb}^{2+}\) ions and \(\text{Br}^{-}\) ions. The degree to which this dissociation occurs can be represented by the solubility product constant, \(K_{\text{sp}}\), which is unique for each substance. In the solution to our textbook exercise, when the compound is fully dissociated, \(K_{\text{sp}}\) is calculated by multiplying the concentrations of the resulting ions, each raised to the power of its stoichiometric coefficient, reflecting the number of ions generated from the solid compound.