Question

Which of the following solutions of strong electrolytes contains the largest number of moles of chloride ions: \(100.0 \mathrm{~mL}\) of \(0.30 \mathrm{M} \mathrm{AlCl}_{3}, 50.0 \mathrm{~mL}\) of \(0.60 \mathrm{M} \mathrm{MgCl}_{2}\), or \(200.0 \mathrm{~mL}\) of \(0.40 \mathrm{M} \mathrm{NaCl} ?\)

Short answer

The solution with the largest number of moles of chloride ions is \(100.0 \mathrm{~mL}\) of $0.30 \mathrm{M} \mathrm{AlCl}_{3}$, which contains 0.09 moles of Cl⁻.

Step-by-step solution

Identify the dissociation of the strong electrolytes

Each of the strong electrolytes given will dissociate completely in the solution, producing respective ions. We can write the dissociation reaction as: AlCl₃ ↔ Al³⁺ + 3Cl⁻ MgCl₂ ↔ Mg²⁺ + 2Cl⁻ NaCl ↔ Na⁺ + Cl⁻

Calculate the moles of chloride ions produced by each electrolyte

To find the moles of chloride ions produced by each electrolyte, we'll follow this formula: moles of Cl⁻ = [concentration (M) * volume (L)] * (moles of Cl⁻ / moles of electrolyte) Make sure to convert the given volume from mL to L by dividing the volume by 1000.

Calculate the moles of chloride ions in the AlCl₃ solution

Using the given concentration and volume of AlCl₃ solution: moles of Cl⁻ = [0.30 M * (100.0 mL / 1000)] * 3 moles of Cl⁻ = 0.09 moles

Calculate the moles of chloride ions in the MgCl₂ solution

Using the given concentration and volume of MgCl₂ solution: moles of Cl⁻ = [0.60 M * (50.0 mL / 1000)] * 2 moles of Cl⁻ = 0.06 moles

Calculate the moles of chloride ions in the NaCl solution

Using the given concentration and volume of NaCl solution: moles of Cl⁻ = [0.40 M * (200.0 mL / 1000)] * 1 moles of Cl⁻ = 0.08 moles

Compare the moles of chloride ions for each solution

Now that we've calculated the moles of chloride ions for each electrolyte solution, we can compare them to see which one has the highest value. AlCl₃: 0.09 moles Cl⁻ MgCl₂: 0.06 moles Cl⁻ NaCl: 0.08 moles Cl⁻ Out of these values, the AlCl₃ solution contains the largest number of moles of chloride ions (0.09 moles). Therefore, \(100.0 \mathrm{~mL}\) of $0.30 \mathrm{M} \mathrm{AlCl}_{3}$ contains the largest number of moles of chloride ions.

Key concepts

Moles Calculation

When dealing with chemical solutions, calculating the number of moles is fundamental. It involves understanding concentrations and volumes of solutes to derive the quantity of ions or molecules present. Here’s how you can simplify this calculation:

• First, convert the volume of the solution from milliliters (mL) to liters (L) by dividing by 1000. This is crucial as molarity is defined in terms of liters.
• Next, use the molarity (M), which indicates how many moles of solute are present in one liter of solution.
• The formula for number of moles is: \[ \text{Moles} = \text{Molarity (M)} \times \text{Volume (L)} \]

For instance, to find the moles of chloride ions in a solution: \[ 0.30 \text{ M} \times \left( \frac{100.0 \text{ mL}}{1000} \right) = 0.03 \text{ moles of } \text{AlCl}_3 \] Applying stoichiometry further helps in calculating the moles for the ions produced after dissociation.

Dissociation Reaction

Strong electrolytes like sodium chloride (NaCl), aluminum chloride (AlCl₃), and magnesium chloride (MgCl₂) fully dissociate in water. This means they split into their constituent ions completely. Understanding this reaction is key to analyzing solutions:

• For NaCl, it dissociates into \[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
• In AlCl₃, each molecule produces three chloride ions:\[ \text{AlCl}_3 \rightarrow \text{Al}^{3+} + 3\text{Cl}^- \]
• MgCl₂ dissociates yielding:\[ \text{MgCl}_2 \rightarrow \text{Mg}^{2+} + 2\text{Cl}^- \]

Each initial electrolyte molecule results in multiple ions forming in the solution, contributing to the total chloride ion count.

Chloride Ions

Chloride ions (\[ \text{Cl}^- \]) are commonly found in solutions of strong electrolytes. They play a significant role in determining properties like conductivity. When it comes to calculating these from strong electrolytes, always consider the dissociation pattern:

• Identify how many chloride ions are generated per mole of the compound. For example, AlCl₃ produces three times as many, whereas NaCl provides only one per formula unit.
• Use the dissociation formula to understand the stoichiometry; multiply the moles of compound by the number of Cl⁻ ions per mole of compound.

From the given examples:- AlCl₃ solution in the exercise results in the highest production of chloride ions.- The calculation shows 0.09 moles of Cl⁻ ions from AlCl₃, 0.06 from MgCl₂, and 0.08 from NaCl.Thus, understanding chloride ion production helps compare electrolytic solutions efficiently.