Problem 51 - Chemistry The Molecular Science

Question

Write a balanced chemical equation for the equilibrium occurring when each of these solutes is added to water, then write the \(K_{\mathrm{sp}}\) expression for each solute. (a) \(\mathrm{BaCrO}_{4}\) (b) \(\mathrm{Mn}(\mathrm{OH})_{2}\) (c) Lead(II) carbonate (d) Nickel(II) hydroxide (e) Strontium phosphate (f) Mercury(I) sulfate

Step-by-Step Solution

Answer

Balanced equations and \(K_{\mathrm{sp}}\) expressions are provided for each compound.

Step 1: Understanding the Problem

We need to write balanced chemical equations for the dissociation of the given compounds in water and then find the solubility product expressions (\(K_{\mathrm{sp}}\)).

Step 2: Dissociation of Barium Chromate

(a) \(\text{BaCrO}_4 \) dissociates in water as follows: \[ \text{BaCrO}_4(s) \rightleftharpoons \text{Ba}^{2+}(aq) + \text{CrO}_4^{2-}(aq) \]The \(K_{\mathrm{sp}}\) expression is: \[ K_{\mathrm{sp}} = [\text{Ba}^{2+}][\text{CrO}_4^{2-}] \]

Step 3: Dissociation of Manganese(II) Hydroxide

(b) \(\text{Mn(OH)}_2 \) dissociates in water as follows: \[ \text{Mn(OH)}_2(s) \rightleftharpoons \text{Mn}^{2+}(aq) + 2\text{OH}^-(aq) \]The \(K_{\mathrm{sp}}\) expression is: \[ K_{\mathrm{sp}} = [\text{Mn}^{2+}][\text{OH}^-]^2 \]

Step 4: Dissociation of Lead(II) Carbonate

(c) Lead(II) carbonate, \(\text{PbCO}_3\), dissociates as follows: \[ \text{PbCO}_3(s) \rightleftharpoons \text{Pb}^{2+}(aq) + \text{CO}_3^{2-}(aq) \]The \(K_{\mathrm{sp}}\) expression is: \[ K_{\mathrm{sp}} = [\text{Pb}^{2+}][\text{CO}_3^{2-}] \]

Step 5: Dissociation of Nickel(II) Hydroxide

(d) Nickel(II) hydroxide, \(\text{Ni(OH)}_2\), dissociates as follows: \[ \text{Ni(OH)}_2(s) \rightleftharpoons \text{Ni}^{2+}(aq) + 2\text{OH}^-(aq) \]The \(K_{\mathrm{sp}}\) expression is: \[ K_{\mathrm{sp}} = [\text{Ni}^{2+}][\text{OH}^-]^2 \]

Step 6: Dissociation of Strontium Phosphate

(e) Strontium phosphate, \(\text{Sr}_3(\text{PO}_4)_2\), dissociates as follows: \[ \text{Sr}_3(\text{PO}_4)_2(s) \rightleftharpoons 3\text{Sr}^{2+}(aq) + 2\text{PO}_4^{3-}(aq) \]The \(K_{\mathrm{sp}}\) expression is: \[ K_{\mathrm{sp}} = [\text{Sr}^{2+}]^3[\text{PO}_4^{3-}]^2 \]

Step 7: Dissociation of Mercury(I) Sulfate

(f) Mercury(I) sulfate, \(\text{Hg}_2\text{SO}_4\), dissociates as follows: \[ \text{Hg}_2\text{SO}_4(s) \rightleftharpoons \text{Hg}_2^{2+}(aq) + \text{SO}_4^{2-}(aq) \]The \(K_{\mathrm{sp}}\) expression is: \[ K_{\mathrm{sp}} = [\text{Hg}_2^{2+}][\text{SO}_4^{2-}] \]

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a core concept in chemistry that describes a balance between opposing processes. When a chemical reaction reaches equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. As a result, the concentrations of products and reactants remain constant. The key point to note is that equilibrium doesn't mean the reactions stop; rather, they continue to occur at the same rate. This steady state can be described by an equilibrium constant, such as the solubility product, often denoted by \(K_{sp}\). This constant is unique to each reaction and indicates how much of the solute can dissolve in the solvent to form a saturated solution. When dealing with solubility, the \(K_{sp}\) helps us understand at what point the substance can no longer dissolve in the solvent, pointing to the maximum concentration of ions present in the solution.

Dissociation Reactions

Dissociation reactions involve the separation of an ionic compound into its individual ions. These reactions are crucial when understanding how substances dissolve in water. When a solid compound, such as a salt, is added to water, it breaks down into ions. For instance, when barium chromate (\(\text{BaCrO}_4\)) is placed in water, it dissociates into barium ions (\(\text{Ba}^{2+}\)) and chromate ions (\(\text{CrO}_4^{2-}\)).

• The dissociation reaction can be written as \(\text{BaCrO}_4(s) \rightleftharpoons \text{Ba}^{2+}(aq) + \text{CrO}_4^{2-}(aq)\).
• Dissociation reactions are often reversible, especially in equilibrium conditions, meaning they can proceed forward and backward until equilibrium is achieved.

Understanding the dissociation process is fundamental to writing balanced chemical equations and formulating the \(K_{sp}\).

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They illustrate how reactants transform into products, showing stoichiometry, which is the quantitative relationship between them. For equilibrium, writing accurate chemical equations is essential when calculating or understanding the solubility product.

• The equation must be balanced, meaning the number of each type of atom is the same on both sides of the equation.
• For the dissociation of lead(II) carbonate (\(\text{PbCO}_3\)), the equation is \(\text{PbCO}_3(s) \rightleftharpoons \text{Pb}^{2+}(aq) + \text{CO}_3^{2-}(aq)\).

Balanced chemical equations help us in formulating the \(K_{sp}\) expressions which determine the solubility behavior of compounds in water.

Aqueous Solutions

Aqueous solutions are mixtures where water acts as the solvent. When substances dissolve in water, they interact with water molecules. This process is crucial in solubility studies as water's unique properties make it an excellent solvent for many substances.
Water's polar nature allows it to dissolve ionic compounds effectively, leading them to dissociate into their respective ions.

• This results in an equilibrium state where the dissolved and undissolved substances reach a balance.
• In the case of nickel(II) hydroxide (\(\text{Ni(OH)}_2\)), when dissolved in water, it forms \(\text{Ni}^{2+}\) and \(\text{OH}^-\) ions according to the equation \(\text{Ni(OH)}_2(s) \rightleftharpoons \text{Ni}^{2+}(aq) + 2\text{OH}^- (aq)\).

Understanding aqueous solutions and their properties is fundamental in studying how ions distribute and interact in water-based environments.