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 100.0 mL of 0.30 M AlCl3 solution has the largest number of moles of chloride ions with 0.09 mol.

Step-by-step solution

Analyzing each solution

For each of the three solutions, we need to find the number of moles of chloride ions: 1. AlCl3: This compound has 3 chloride ions for each aluminum ion (3 Cl- ions for each formula unit). 2. MgCl2: This compound has 2 chloride ions for each magnesium ion (2 Cl- ions for each formula unit). 3. NaCl: This compound has 1 chloride ion for each sodium ion (1 Cl- ion for each formula unit).

Calculate moles of Cl- ions in each solution

Now, we need to calculate the moles of chloride ions in all of the solutions: 1. For AlCl3 solution: Moles of AlCl3 = Volume (L) × Molarity Moles of AlCl3 = \( 100.0 \times 10^{-3}L \times 0.30M \) Moles of AlCl3 = \( 0.03 mol \) Moles of Cl- ions = Moles of AlCl3 × Number of Cl- ions in AlCl3 Moles of Cl- ions = \( 0.03 mol \times 3 \) Moles of Cl- ions = \( 0.09 mol \) 2. For MgCl2 solution Moles of MgCl2 = Volume (L) × Molarity Moles of MgCl2 = \( 50.0 \times 10^{-3} L \times 0.60 M \) Moles of MgCl2 = \( 0.03 mol \) Moles of Cl- ions = Moles of MgCl2 × Number of Cl- ions in MgCl2 Moles of Cl- ions = \( 0.03 mol \times 2 \) Moles of Cl- ions = \( 0.06 mol \) 3. For NaCl solution Moles of NaCl = Volume (L) × Molarity Moles of NaCl = \( 200.0 \times 10^{-3} L \times 0.40 M \) Moles of NaCl = \( 0.08 mol \) Moles of Cl- ions = Moles of NaCl × Number of Cl- ions in NaCl Moles of Cl- ions = \( 0.08 mol \times 1 \) Moles of Cl- ions = \( 0.08 mol \)

Compare the moles of Cl- ions in each solution

Now let's compare the moles of chloride ions in each solution: 1. AlCl3 solution: \( 0.09 \ mol \) of Cl- ions 2. MgCl2 solution: \( 0.06 \ mol \) of Cl- ions 3. NaCl solution: \( 0.08 \ mol \) of Cl- ions From the comparison, we can conclude that the 100.0 mL of 0.30 M AlCl3 solution has the largest number of moles of chloride ions with 0.09 mol.