Problem 10 - Chemistry: The Central Science in SI Units, Global Edition

Question

An aqueous solution contains \(1.2 \mathrm{~m} M\) of total ions. (a) If the solution is \(\mathrm{NaCl}(a q),\) what is the concentration of chloride ion? (b) If the solution is \(\mathrm{FeCl}_{3}(a q),\) what is the concentration of chloride ion? [Section 4.5\(]\)

Step-by-Step Solution

Answer

(a) In the NaCl(aq) solution, the concentration of chloride ions (Cl⁻) is 0.6 M. (b) In the FeCl₃(aq) solution, the concentration of chloride ions (Cl⁻) is 0.36 M.

Step 1: Case (a): Sodium chloride (NaCl) solution

In NaCl(aq) solution, sodium chloride dissociates into its constituent ions: sodium ions (Na⁺) and chloride ions (Cl⁻). The dissociation of one mole of NaCl produces one mole of Na⁺ and one mole of Cl⁻ ions, so the ratio between NaCl and Cl⁻ is 1:1. Given the total ion concentration in the solution is 1.2 M, we can write this as the sum of the concentrations of Na⁺ and Cl⁻ ions: \[1.2 ~\text{M} = [Na^+] + [Cl^-]\] Since the ratio between NaCl and Cl⁻ is 1:1, their concentrations are equal: \[[Na^+] = [Cl^-]\] Substituting this back into the equation, we can determine the concentration of chloride ions: \[1.2 ~\text{M} = 2[Cl^-]\] Now, solve for [Cl⁻]: \[[Cl^-] = \frac{1.2 ~\text{M}}{2} = 0.6 ~\text{M}\] So, the concentration of chloride ions in the NaCl(aq) solution is 0.6 M.

Step 2: Case (b): Iron(III) chloride (FeCl₃) solution

In FeCl₃(aq) solution, iron(III) chloride dissociates into its constituent ions: iron(III) ions (Fe³⁺) and chloride ions (Cl⁻). The dissociation of one mole of FeCl₃ produces one mole of Fe³⁺ and three moles of Cl⁻ ions, so the ratio between FeCl₃ and Cl⁻ is 1:3. Given the total ion concentration in the solution is 1.2 M, we can write this as the sum of the concentrations of Fe³⁺ and Cl⁻ ions: \[1.2 ~\text{M} = [Fe^{3+}] + 3[Cl^-]\] Since the ratio between FeCl₃ and Cl⁻ is 1:3, their concentrations are related as: \[[Fe^{3+}] = \frac{1}{3}[Cl^-]\] Substituting this back into the equation, we can determine the concentration of chloride ions: \[1.2 ~\text{M} = \frac{1}{3}[Cl^-] + 3[Cl^-]\] Combine the Cl⁻ terms: \[1.2 ~\text{M} = \frac{10}{3}[Cl^-]\] Now, solve for [Cl⁻]: \[[Cl^-] = \frac{1.2 ~\text{M}}{\frac{10}{3}} = \frac{1.2 ~\text{M} \cdot 3}{10} = 0.36 ~\text{M}\] So, the concentration of chloride ions in the FeCl₃(aq) solution is 0.36 M.

Key Concepts

Sodium Chloride

Sodium chloride, commonly known as table salt, is an iconic example when exploring ionic compounds and their behaviors in solutions. When sodium chloride (\(\mathrm{NaCl}\)) is dissolved in water, it dissociates completely into its constituent ions: sodium ions (\(\mathrm{Na^+}\)) and chloride ions (\(\mathrm{Cl^-}\)).
The process of dissociation is straightforward as each molecule of sodium chloride splits to produce one sodium ion and one chloride ion, creating an equal proportion of ions in the solution.

• The dissociation equation: \(\mathrm{NaCl (s)} → \mathrm{Na^+ (aq)} + \mathrm{Cl^- (aq)}\)
• The ratio of sodium ions to chloride ions is 1:1.
• This makes calculating concentrations in solution quite simple: if you know the total ionic concentration is 1.2 M, you can split it equally.

In this example, because the total ion concentration equals the sum of both ions, we divide by two to find that the concentration of chloride ions is 0.6 M.

Iron(III) Chloride

Iron(III) chloride, or ferric chloride (\(\mathrm{FeCl_3}\)), provides a fascinating look into ionic compounds with multiple ions per molecule. When dissolved, each unit of \(\mathrm{FeCl_3}\) separates into one iron(III) ion (\(\mathrm{Fe^{3+}}\)) and three chloride ions (\(\mathrm{Cl^-}\)).
This 1:3 dissociation ratio means there are significantly more chloride ions than ferric ions in a solution.

• The dissociation equation: \( \mathrm{FeCl_3 (s)} → \mathrm{Fe^{3+} (aq)} + 3 \mathrm{Cl^- (aq)} \)
• This shows for every mole of \( \mathrm{FeCl_3} \) in the solution, there are three moles of chloride ions.

Knowing the total ionic concentration (1.2 M), we identify the contribution of each type of ion considering the dissociation ratio. The chloride ions are significantly abundant, hence needing careful calculation. The concentration of chloride ions in this example is calculated to be 0.36 M, illustrating their prolific quantity in the solution relative to the iron(III) ions.

Dissociation in Aqueous Solutions

Dissociation in aqueous solutions is a fundamental chemical concept that describes how ionic compounds dissolve in water. This process occurs when a solid ionic compound separates into its individual ions.
The solvent molecules, usually water, surround and isolate these ions, allowing them to drift apart and interact freely in the solution.

• Ionic compounds dissociate according to fixed stoichiometric ratios determined by their chemical formulas.
• For example, sodium chloride splits into equal parts, whereas iron(III) chloride releases three chloride ions for every one ferric ion.
• This dissociation influences the resulting ion concentrations in a solution, affecting various properties, such as conductivity and reactivity.

Understanding dissociation is key to mastering how aqueous solutions behave, helping to predict how ions will affect chemical reactions in solutions. It's crucial when calculating ionic concentrations, often determining the stoichiometry needed to achieve desired concentrations in practical and experimental chemistry.