Problem 10 - Chemistry The Central Science In Si Units

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? \((\mathbf{b})\) If the solution is \(\mathrm{FeCl}_{3}(a q),\) what is the concentration of chloride ion?

Step-by-Step Solution

Answer

(a) 0.6 mM Cl⁻ (b) 0.9 mM Cl⁻

Step 1: Understanding the Problem

We are given a solution that contains a total of 1.2 mM of ions. We need to determine the concentration of chloride ions in the solution when it is a solution of \( \text{NaCl} \) and \( \text{FeCl}_3 \).

Step 1: Analyze \( \text{NaCl} \) Dissociation

Sodium chloride (\( \text{NaCl} \)) dissociates in water to form sodium ions \((\text{Na}^+)\) and chloride ions \((\text{Cl}^-)\). Each formula unit of \( \text{NaCl} \) produces one \( \text{Cl}^- \). SInce \( \text{NaCl} \) contributes equally to both \( \text{Na}^+ \) and \( \text{Cl}^- \), if we have 1.2 mM total ions, each ion type (\( \text{Na}^+ \) and \( \text{Cl}^- \)) will contribute equally.

Step 2: Calculate \( \text{Cl}^- \) Concentration from \( \text{NaCl} \)

In \( \text{NaCl} \), since 1 mole of \( \text{NaCl} \) results in 1 mole of \( \text{Cl}^- \), the concentration of \( \text{Cl}^- \) is half of the total ion concentration. So, \[ [\text{Cl}^-] = \frac{1.2 \text{ mM}}{2} = 0.6 \text{ mM} \].

Step 3: Analyze \( \text{FeCl}_3 \) Dissociation

Iron(III) chloride (\( \text{FeCl}_3 \)) dissociates in water to form one \( \text{Fe}^{3+} \) ion and three \( \text{Cl}^- \) ions. This means each formula unit produces four ions total.

Step 4: Calculate \( \text{Cl}^- \) Concentration from \( \text{FeCl}_3 \)

Since each \( \text{FeCl}_3 \) unit contributes three \( \text{Cl}^- \) ions and four total ions, 1 unit of \( \text{FeCl}_3 \) produces three units of chloride ions. For \( \text{FeCl}_3 \), \[ \frac{1.2 \text{ mM}}{4} = 0.3 \text{ mM} \text{ for } \text{FeCl}_3 \]. \( \text{Cl}^- \) concentration is \( 3 \times 0.3 \text{ mM} = 0.9 \text{ mM} \).

Key Concepts

Aqueous Solution

An aqueous solution is simply a mixture where water acts as the solvent. It means that the solid, liquid, or gas component is fully dissolved in water. When substances like sodium chloride or iron(III) chloride dissolve, their ions integrate throughout the water, forming a homogenous mixture. Aqueous solutions have unique properties because water is a universal solvent, making it ideal for facilitating chemical reactions. Creating an aqueous solution involves:

• Dissolving a solute in water
• Forming a solution where compounds dissociate into ions

In these solutions, water doesn’t alter the compound structure but allows ions to disperse freely. This feature is essential for studying ionic concentrations.

Dissociation

In chemistry, dissociation refers to the process where a compound breaks down into its individual ions when dissolved in a solvent. For sodium chloride (NaCl), dissociation results in sodium (Na⁺) and chloride (Cl⁻) ions. Similarly, when iron(III) chloride (FeCl₃) dissolves, it splits into one Fe³⁺ ion and three Cl⁻ ions. This process is crucial in determining how many ions are present in a solution. Understanding dissociation is important because:

• It helps determine how many of each ion type are in a solution
• Enables calculations of ionic concentration based on formula units

The pattern of dissociation varies with each compound, impacting the total number of resulting ions.

Sodium Chloride

Sodium chloride, commonly known as table salt, is a compound made of sodium (Na) and chloride (Cl). When dissolved in water, each molecule dissociates to form one Na⁺ and one Cl⁻ ion. Thus, the concentration of each ion in a solution is directly proportional to the amount of sodium chloride dissolved. For example, if you have a total ion concentration of 1.2 mM, the concentration of Cl⁻ ions will be 0.6 mM because they contribute one Cl⁻ per Na⁺ ion. NaCl's dissociation attributes include:

• Equal Na⁺ and Cl⁻ ions in solution
• Direct correlation between dissolved NaCl and ion concentrations

This one-to-one ratio makes NaCl a straightforward compound for studying basic ionic solutions.

Iron(III) Chloride

Iron(III) chloride, or FeCl₃, is a chemical compound that dissociates into four ions. Upon dissolving in water, it produces one Fe³⁺ ion and three Cl⁻ ions. This results in multiple ions forming from a single compound unit, differing from simpler compounds like NaCl. Understanding FeCl₃'s dissociation is key to determining how many chloride ions are present in a solution. Unique aspects of FeCl₃ include:

• Dissociates into more ions than simpler salts
• Creates a solution with a distinct ion ratio

In a scenario with a total ion concentration of 1.2 mM, the concentration of Cl⁻ ions becomes 0.9 mM due to this dissociation pattern. This variety in ion production allows for more complex calculations and applications in chemistry.