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

Expert verified
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

01

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).
02

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 = \( 0.08 mol \)
03

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.

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