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\(M \mathrm{NaCl} ?\)

Short answer

The 100.0 mL of 0.30 M AlCl3 solution contains the largest number of moles of Cl- ions, with 0.09 mol of Cl-.

Step-by-step solution

Calculate the moles of AlCl3

To find the moles of AlCl3 in the first solution, we multiply the volume of the solution (100.0 mL) by its concentration (0.30 M): moles of AlCl3 = Volume * Concentration = 100.0 mL * 0.30 mol/L Since 1 L = 1000 mL, we can convert mL to L: moles of AlCl3 = 0.100 L * 0.30 mol/L = 0.03 mol

Calculate the moles of MgCl2

To find the moles of MgCl2 in the second solution, we multiply the volume of the solution (50.0 mL) by its concentration (0.60 M): moles of MgCl2 = Volume * Concentration = 50.0 mL * 0.60 mol/L Converting mL to L: moles of MgCl2 = 0.050 L * 0.60 mol/L = 0.03 mol

Calculate the moles of NaCl

To find the moles of NaCl in the third solution, we multiply the volume of the solution (200.0 mL) by its concentration (0.40 M): moles of NaCl = Volume * Concentration = 200.0 mL * 0.40 mol/L Converting mL to L: moles of NaCl = 0.200 L * 0.40 mol/L = 0.08 mol #Step 2: Calculate the moles of chloride ions in each solution#

Calculate the moles of Cl- from AlCl3

One mole of AlCl3 dissociates into 3 moles of Cl- ions when dissolved in water. Therefore, to find the moles of Cl- ions from AlCl3, we multiply the moles of AlCl3 by 3: moles of Cl- from AlCl3 = 3 * moles of AlCl3 = 3 * 0.03 mol = 0.09 mol

Calculate the moles of Cl- from MgCl2

One mole of MgCl2 dissociates into 2 moles of Cl- ions when dissolved in water. Therefore, to find the moles of Cl- ions from MgCl2, we multiply the moles of MgCl2 by 2: moles of Cl- from MgCl2 = 2 * moles of MgCl2 = 2 * 0.03 mol = 0.06 mol

Calculate the moles of Cl- from NaCl

One mole of NaCl dissociates into 1 mole of Cl- ions when dissolved in water. Therefore, the moles of Cl- ions from NaCl are equal to the moles of NaCl: moles of Cl- from NaCl = moles of NaCl = 0.08 mol #Step 3: Compare the moles of chloride ions to find the largest#

Determine the largest number of moles of Cl-

Now compare the moles of Cl- ions in each solution: 0.09 mol (from AlCl3) > 0.06 mol (from MgCl2) and 0.09 mol (from AlCl3) > 0.08 mol (from NaCl) Since the moles of Cl- ions from AlCl3 (0.09 mol) are greater than those from MgCl2 and NaCl, the 100.0 mL of 0.30 M AlCl3 solution contains the largest number of moles of Cl- ions.

Key concepts

Moles Calculation

Understanding how to calculate moles is a fundamental concept in chemistry, which is essential for solving problems related to electrolyte solutions. Moles measure the amount of substance, and it's calculated using the formula:

• \(\text{Moles} = \text{Volume} \times \text{Concentration}\)

This means, to find the number of moles, you multiply the volume of the solution by its molarity (concentration).
This concept is key when dealing with chemical solutions and reactions.

For example, if you have a solution with a volume of 100.0 mL and a concentration of 0.30 M, the calculation goes as follows:

• Convert the volume from milliliters to liters: 100.0 mL = 0.100 L
• Multiply by the concentration: \(\text{Moles} = 0.100 \text{ L} \times 0.30 \text{ mol/L} = 0.03 \text{ mol}\)

This calculation is repeated for each solution you encounter, allowing you to compare how many moles of a given solute you have.

Chloride Ions

Chloride ions (

• \(\text{Cl}^-\)

) are essential components in many chemical reactions and solutions. When you dissolve a compound containing chloride in water, it dissociates to release these ions.
In this context, it's crucial to consider not just the moles of the compound—but the number of chloride ions yielded.

For instance, aluminum chloride (AlCl3) dissociates completely in water to produce:

• 1 mole of AlCl3 releases 3 moles of Cl-
• \(\text{Moles of } \text{Cl}^- = 3 \times \text{moles of } \text{AlCl}_3\)

Similarly, magnesium chloride (MgCl2) dissociates to yield:

• 1 mole of MgCl2 releases 2 moles of Cl-
• \(\text{Moles of } \text{Cl}^- = 2 \times \text{moles of } \text{MgCl}_2\)

Sodium chloride (NaCl) dissociates in a simpler 1:1 ratio:

• 1 mole of NaCl releases 1 mole of Cl-

This understanding allows you to accurately compute the actual number of chloride ions present in each solution.

Chemical Dissociation

Chemical dissociation is the process where a compound breaks down into its constituent ions when dissolved in water. Electrolytes, including strongly dissociating compounds like AlCl3, MgCl2, and NaCl, undergo this when in solution.

Here’s a simple breakdown:

• For AlCl3: Dissociates to confer 1 Al^3+ and 3 Cl^- ions per molecule.
• For MgCl2: Dissociates to confer 1 Mg^2+ and 2 Cl^- ions per molecule.
• For NaCl: Dissociates to confer 1 Na^+ and 1 Cl^- ion per molecule.

Understanding this principle is crucial because it influences the concentration of ions in a solution.
More ions means greater electrical conductivity, which is why these solutions are known as strong electrolytes.

When comparing solutions, it’s important to calculate how many ions of interest—like chloride ions—are produced through dissociation. This requires analyzing each electrolyte compound for the number of ions it releases.