What is the molar concentration of chloride ion in the solution obtained by mixing 300 mL of 3.0 M NaCl and 200 mL of 4.0 M solution of $BaCl_{2}$?

Question

Accepted Answer

To determine the molar concentration of chloride ions in the solution obtained by mixing 300 mL of 3.0 M NaCl and 200 mL of 4.0 M BaCl₂, we need to calculate the total moles of chloride ions and the total volume of the solution.

1. **Calculate moles of chloride ions from NaCl:**
   - NaCl dissociates into Na⁺ and Cl⁻ ions. Therefore, 1 mole of NaCl gives 1 mole of Cl⁻.
   - Moles of NaCl = Molarity × Volume (in liters) = 3.0 M × 0.300 L = 0.9 moles.
   - Moles of Cl⁻ from NaCl = 0.9 moles.

2. **Calculate moles of chloride ions from BaCl₂:**
   - BaCl₂ dissociates into Ba²⁺ and 2 Cl⁻ ions. Therefore, 1 mole of BaCl₂ gives 2 moles of Cl⁻.
   - Moles of BaCl₂ = Molarity × Volume (in liters) = 4.0 M × 0.200 L = 0.8 moles.
   - Moles of Cl⁻ from BaCl₂ = 2 × 0.8 moles = 1.6 moles.

3. **Total moles of chloride ions:**
   - Total moles of Cl⁻ = Moles from NaCl + Moles from BaCl₂ = 0.9 moles + 1.6 moles = 2.5 moles.

4. **Total volume of the solution:**
   - Total volume = 300 mL + 200 mL = 500 mL = 0.500 L.

5. **Calculate molar concentration of chloride ions:**
   - Molar concentration of Cl⁻ = Total moles of Cl⁻ / Total volume in liters = 2.5 moles / 0.500 L = 5.0 M.

Therefore, the molar concentration of chloride ions in the solution is 5.0 M, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (1.8 M):** This option is incorrect because it underestimates the total moles of chloride ions. The calculation clearly shows that the total moles of chloride ions are 2.5, leading to a concentration of 5.0 M, not 1.8 M.

- **Option 3 (1.6 M):** This option is incorrect for similar reasons as Option 2. It does not account for the correct total moles of chloride ions from both NaCl and BaCl₂, which results in a higher concentration than 1.6 M.

- **Option 4 (5.0 M):** This option is actually a duplicate of Option 1 and is correct. However, since the task is to support Option 1 specifically, we focus on Option 1 as the correct choice.

In conclusion, the correct molar concentration of chloride ions in the solution is 5.0 M, as supported by the calculations, making Option 1 the correct answer.