Problem 17 - General Chemistry

Question

Which of the following compounds would produce the highest concentration of \(\mathrm{Cl}^{-}\) ions when \(0.10 \mathrm{~mol}\) of each is placed in separate beakers containing equal volumes of water? a. \(\mathrm{NaCl}\) b. \(\mathrm{PbCl}_{2}\) c. \(\mathrm{HClO}_{4}\) d. \(\mathrm{MgCl}_{2}\) e. \(\mathrm{HCl}\)

Step-by-Step Solution

Answer

\( \mathrm{MgCl}_2 \) produces the highest concentration of \( \mathrm{Cl}^- \) ions.

Step 1: Identify the Ionic Compounds

First, identify which of the given compounds are ionic. Compounds like \( \mathrm{NaCl} \), \( \mathrm{PbCl}_2 \), \( \mathrm{MgCl}_2 \), and \( \mathrm{HCl} \) are ionic and will dissociate in water to produce \( \mathrm{Cl}^{-} \) ions.

Step 2: Determine the Disassociation of Compounds

Check the dissociation of the compounds in water: \( \mathrm{NaCl} \rightarrow \mathrm{Na}^+ + \mathrm{Cl}^- \), \( \mathrm{PbCl}_2 \rightarrow \mathrm{Pb}^{2+} + 2\mathrm{Cl}^- \), \( \mathrm{MgCl}_2 \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{Cl}^- \), and \( \mathrm{HCl} \rightarrow \mathrm{H}^+ + \mathrm{Cl}^- \). Note that \( \mathrm{HClO}_4 \) is a strong acid, dissociating as \( \mathrm{HClO}_4 \rightarrow \mathrm{H}^+ + \mathrm{ClO}_4^- \), not releasing \( \mathrm{Cl}^- \) ions.

Step 3: Analyze Cl^- Ion Production

Calculate the relative number of \( \mathrm{Cl}^- \) ions produced by each: \( \mathrm{NaCl} \) and \( \mathrm{HCl} \) each provide \( 0.10 \) mol of \( \mathrm{Cl}^- \), \( \mathrm{PbCl}_2 \) produces \( 0.20 \) mol (because of the \( 2 \mathrm{Cl}^- \) ions), and \( \mathrm{MgCl}_2 \) also produces \( 0.20 \) mol of \( \mathrm{Cl}^- \).

Step 4: Identify the Compound with Highest Cl^- Production

Since both \( \mathrm{PbCl}_2 \) and \( \mathrm{MgCl}_2 \) result in \( 0.20 \) mol of \( \mathrm{Cl}^- \) ions, compared to only \( 0.10 \) mol from other compounds, they would produce the highest concentration of \( \mathrm{Cl}^- \) ions. However, \( \mathrm{MgCl}_2 \) is more soluble than \( \mathrm{PbCl}_2 \), making it the compound that will produce the highest soluble concentration of \( \mathrm{Cl}^- \).

Key Concepts

Ionic Compounds

Ionic compounds are substances formed from the combination of positive and negative ions. These compounds arise when atoms transfer electrons to attain a full outer shell of electrons, leading to the formation of ions. Metals usually become positively charged ions by losing electrons, while non-metals become negatively charged ions by gaining electrons. When an ionic compound is formed, these oppositely charged ions attract each other, forming a stable structure through ionic bonds.

Ionic compounds have distinctive characteristics:

• They have high melting and boiling points due to the strong bonds between ions.
• They conduct electricity when dissolved in water, as the ions are free to move.
• They are usually solid at room temperature.

In the context of our exercise, identifying which compounds are ionic helps determine which ones will disassociate in water to produce specific ions, like the chloride ions we are examining.

Dissolution in Water

When ionic compounds dissolve in water, they dissociate into their individual ions. This process allows for the ions to separate from the solid lattice and interact with water molecules, creating a solution with distinct ionic properties. Water, being a polar solvent, is exceptionally effective at dissolving ionic compounds.

In our exercise, when each compound is dissolved, dissociation occurs as follows:

• For NaCl: It dissociates into one sodium ion ( \(\mathrm{Na}^+\) ) and one chloride ion ( \(\mathrm{Cl}^-\) ).
• For PbCl₂: It dissociates into one lead ion ( \(\mathrm{Pb}^{2+}\) ) and two chloride ions ( \(2\mathrm{Cl}^-\) ).
• For MgCl₂: It dissociates into one magnesium ion ( \(\mathrm{Mg}^{2+}\) ) and two chloride ions ( \(2\mathrm{Cl}^-\) ).
• For HCl: This compound is a hydrogen chloride that dissociates into one hydrogen ion ( \(\mathrm{H}^+\) ) and one chloride ion ( \(\mathrm{Cl}^-\) ).

Understanding dissolution is crucial to predicting how many chloride ions each compound will contribute to the solution.

Chloride Ion Concentration

Chloride ion concentration is a crucial measurement when evaluating the dissolution impact of ionic compounds. In an aqueous solution, how much a compound contributes to the total chloride ion (\(\mathrm{Cl}^-\)) concentration depends on its dissociation properties. Some compounds produce more chloride ions than others due to their chemical formula and their dissociation pattern.

In our exercise:

• Both \(\mathrm{NaCl}\) and \(\mathrm{HCl}\) provide \(0.10\) mol of \(\mathrm{Cl}^-\) ions, aligning one chloride ion per formula unit.
• \(\mathrm{PbCl}_2\) and \(\mathrm{MgCl}_2\) release \(0.20\) mol of chloride ions due to their contribution of two chloride ions per formula unit.

Ultimately, the compound with the highest soluble chloride ion concentration is \(\mathrm{MgCl}_2\), due to its greater solubility compared to \(\mathrm{PbCl}_2\), providing more available \(\mathrm{Cl}^-\) ions for interaction in water.