Problem 10 - Chemistry The Central Science

Question

An aqueous solution contains 1.2 \(\mathrm{mM}\) of total ions. (a) If the solution is NaCl(aq), 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

The concentration of chloride ions in the NaCl(aq) solution is 1.2 mM, while in the FeCl3(aq) solution it is 0.9 mM.

Step 1: Making sense of the given data

The exercise tells us that the aqueous solution contains 1.2 mM of total ions. That means the sum of the concentrations of each type of ion in the solution is equal to 1.2 mM.

Step 2: Determine chloride ion concentration for NaCl(aq)

In this case, the dissociation of NaCl(aq) in water is given by the following equation: \[NaCl \rightarrow Na^+ + Cl^-\] Each formula unit of NaCl dissociates into one Na+ ion and one Cl- ion. Since the total ion concentration of the solution is 1.2 mM, and NaCl gives one chloride ion per formula unit, the concentration of chloride ions will be equal to the total ion concentration. Therefore, the concentration of chloride ion in the NaCl(aq) solution is 1.2 mM.

Step 3: Determine chloride ion concentration for FeCl3(aq)

In this case, the dissociation of FeCl3(aq) in water is given by the following equation: \[FeCl_{3} \rightarrow Fe^{3+}+3 Cl^-\] Each formula unit of FeCl3 dissociates into one Fe3+ ion and three Cl- ions. Let the concentration of Fe3+ ion be x mM. Since 3 chloride ions are produced per formula unit of FeCl3, the concentration of chloride ions will be 3x mM. The sum of the concentrations of the two ions should be equal to the total ion concentration, which is 1.2 mM. So we have the following equation: \[x+3x=1.2\]

Step 4: Solve for x

Solve the equation from Step 3 for x: \[4x=1.2\] \[x=\frac{1.2}{4}\] \[x=0.3\, mM\] Finally, we can calculate the concentration of Cl- ions: Concentration of Cl- ions = 3x = 3 × 0.3 mM = 0.9 mM The concentration of chloride ions in the FeCl3(aq) solution is 0.9 mM.

Key Concepts

Aqueous Solution

An aqueous solution is a liquid mixture where water acts as the solvent. The term "aqueous" means that a substance is dissolved in water. This type of solution is very common in chemistry because water is a universal solvent. It can dissolve a wide variety of substances due to its polar nature.

In an aqueous solution:

• Solutes can be ions, molecules, or gases that dissolve in water.
• Water molecules surround solute particles, allowing them to spread evenly throughout the solution.

These solutions are integral in chemical reactions as they allow for easy interaction between dissolved substances.

Understanding how substances dissolve and dissociate in aqueous solutions is crucial for solving problems related to ion concentrations, like finding out how much of a particular ion exists in the solution.

Chloride Ions

Chloride ions (\(\text{Cl}^-\)) are negatively charged particles found in many chemical compounds. They are formed when chlorine atoms gain an extra electron. In aquatic environments, such as aqueous solutions, chloride ions commonly result from the dissociation of various salts, including sodium chloride (NaCl) and iron(III) chloride (\(\text{FeCl}_3\)).

Key points about chloride ions:

• They are important in processes such as electrical conductivity and cellular functions.
• Chloride ions maintain osmotic balance in biological systems.
• The concentration of chloride ions in a solution can affect the solution's properties, such as its electrical charge and reactivity.

In studies involving NaCl and \(\text{FeCl}_3\) solutions, calculating the chloride ion concentration allows chemists to understand and predict the behavior of these solutions in various contexts.

Dissociation Equations

Dissociation equations describe how compounds split into ions when they dissolve in water, forming an aqueous solution. These equations are essential to understanding how ions behave and interact in solutions.

Consider these dissociation examples:

• Sodium chloride (NaCl) dissociates in water as \(\text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^-\).
• Iron(III) chloride (\(\text{FeCl}_3\)) dissociates as \(\text{FeCl}_3 \rightarrow \text{Fe}^{3+} + 3\text{Cl}^-\).

For both reactions, each formula unit of the compound separates into individual ions.

These equations help determine how concentrations of ions are calculated in solutions. For example, knowing that \(\text{FeCl}_3\) produces three chloride ions per formula unit tells us that for every unit of \(\text{FeCl}_3\), three times that concentration is present in chloride ions. Understanding dissociation equations is fundamental for predicting and calculating exact ion concentrations in any given solution.