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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)\(\mathrm{HCl}\)

Short Answer

Expert verified
\(\mathrm{MgCl}_{2}\) produces the highest \(\mathrm{Cl}^{-}\) ion concentration (0.20 M).

Step by step solution

01

Identify the Dissociation Formulas

Write down the dissociation reaction for each compound in water: 1. NaCl dissolves completely into Na鈦 and Cl鈦 ions: \[ \mathrm{NaCl} \rightarrow \mathrm{Na}^{+} + \mathrm{Cl}^{-} \]2. PbCl鈧 slightly dissolves into Pb虏鈦 and more precisely releases 2 Cl鈦 ions: \[ \mathrm{PbCl}_{2} \rightarrow \mathrm{Pb}^{2+} + 2\mathrm{Cl}^{-} \]3. HClO鈧 dissociates completely releasing ClO鈧勨伝: \[ \mathrm{HClO}_{4} \rightarrow \mathrm{H}^{+} + \mathrm{ClO}_{4}^{-} \]4. MgCl鈧 dissociates fully to form Mg虏鈦 and 2 Cl鈦 ions: \[ \mathrm{MgCl}_{2} \rightarrow \mathrm{Mg}^{2+} + 2\mathrm{Cl}^{-} \]5. HCl dissociates completely into H鈦 and Cl鈦 ions: \[ \mathrm{HCl} \rightarrow \mathrm{H}^{+} + \mathrm{Cl}^{-} \]
02

Determine the Number of Cl鈦 Ions Produced

Evaluate the number of \(\mathrm{Cl}^{-}\) ions produced per formula unit: 1. \(\mathrm{NaCl}\) yields 1 \(\mathrm{Cl}^{-}\) ion. 2. \(\mathrm{PbCl}_{2}\) yields 2 \(\mathrm{Cl}^{-}\) ions but its solubility is low. 3. \(\mathrm{HClO}_{4}\) doesn't yield any \(\mathrm{Cl}^{-}\) ions. 4. \(\mathrm{MgCl}_{2}\) yields 2 \(\mathrm{Cl}^{-}\) ions. 5. \(\mathrm{HCl}\) yields 1 \(\mathrm{Cl}^{-}\) ion.
03

Calculate Total Cl鈦 Ion Concentrations

Calculate the concentration of \(\mathrm{Cl}^{-}\) ions:1. For \(\mathrm{NaCl}\), concentration is 0.10 M of \(\mathrm{Cl}^{-}\).2. \(\mathrm{PbCl}_{2}\) has low solubility, contributing negligibly to \(\mathrm{Cl}^{-}\)'s concentration.3. \(\mathrm{HClO}_{4}\) has 0.00 M of \(\mathrm{Cl}^{-}\).4. For \(\mathrm{MgCl}_{2}\), concentration is 0.20 M of \(\mathrm{Cl}^{-}\).5. For \(\mathrm{HCl}\), concentration is 0.10 M of \(\mathrm{Cl}^{-}\).
04

Identify the Compound with Maximum Cl鈦 Ions

Among these, \(\mathrm{MgCl}_{2}\) yields 0.20 M, the highest concentration of \(\mathrm{Cl}^{-}\) ions due to dissociating completely and producing two \(\mathrm{Cl}^{-}\) ions per formula unit.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ionic Compounds
Ionic compounds are types of chemical compounds composed of ions held together by electrostatic forces termed ionic bonding. These compounds generally form between metals and non-metals. When placed in water, they tend to dissociate into their constituent ions.
For instance, in our exercise, compounds like sodium chloride (NaCl) and magnesium chloride (MgCl鈧) are ionic. When sodium chloride dissolves, it produces sodium ions (Na鈦) and chloride ions (Cl鈦) in equal amounts. Similarly, magnesium chloride releases magnesium ions (Mg虏鈦) and twice the amount of chloride ions (2 Cl鈦) due to the presence of two chlorine atoms in its formula.
Understanding ionic compounds and their behavior in water is crucial in predicting how many chloride ions will be present in solution when a compound dissociates.
Solubility Rules
Solubility rules help us determine whether an ionic compound will dissolve in water and how much it will dissociate. These rules are guidelines that predict the solubility of different ionic compounds in water.
For example, according to solubility rules, compounds like sodium chloride (NaCl) are highly soluble in water, meaning they dissociate completely to release ions. On the other hand, compounds like lead(II) chloride (PbCl鈧) are not as soluble. Even though PbCl鈧 can technically release two chloride ions per formula unit, its low solubility means that it won't significantly contribute to the chloride ion concentration in a solution.
Knowing the solubility of a compound allows us to understand how many of its constituent ions can actually contribute to the ion concentration in a solution, which was essential in solving our textbook problem.
Chloride Ion Concentration
Chloride ion concentration is a measure of the amount of chloride ions (\( \mathrm{Cl}^- \)) present in a solution. Understanding how different compounds produce these ions when dissolved is important for this concept.
In the given exercise, determining which compound yields the highest chloride ion concentration involves looking at both the dissociation equations and solubility. For instance, although both magnesium chloride (MgCl鈧) and lead(II) chloride (PbCl鈧) can theoretically produce two chloride ions per unit, MgCl鈧 is fully soluble, resulting in a higher effective concentration of chloride ions.
Thus, to find which compound yields the greatest amount of chloride ions, the assessment hinges on knowing both the formula's dissociation profile and its solubility in water. Specifically, MgCl鈧, due to its ability to dissociate completely and release two chloride ions for every formula unit, results in a higher chloride ion concentration compared to other options like NaCl or HCl, each contributing a smaller concentration of Cl鈦 ions.

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