Question

A solution is prepared by mixing \(75.0 \mathrm{~mL}\) of \(0.020 \mathrm{M} \mathrm{BaCl}_{2}\) and \(125 \mathrm{~mL}\) of \(0.040 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4}\). What are the concentrations of barium and sulfate ions in this solution? Assume only \(\mathrm{SO}_{4}^{2-}\) ions (no \(\left.\mathrm{HSO}_{4}^{-}\right)\) are present.

Short answer

To find the final concentrations of barium and sulfate ions, we first calculate the moles of each ion in their respective solutions: moles(Ba^2+) \(= (0.020 \, M)(75.0 \, mL)(1 \, L / 1000 \, mL)\) moles(SO₄²⁻) \(= (0.040 \, M)(125 \, mL)(1 \, L / 1000 \, mL)\) Next, we find the total moles of each ion, the total volume of the mixed solution, and finally divide the total moles of each ion by the total volume to find their final concentrations: Final concentration(Ba^2+) \(= \frac{\text{Total moles(Ba}^{2+}\text{)}}{\text{Total volume}}\) Final concentration(SO₄²⁻) \(= \frac{\text{Total moles(SO}₄^{2-}\text{)}}{\text{Total volume}}\)

Step-by-step solution

Find moles of ions in each solution

First, we need to find the moles of Ba^2+ and SO₄²⁻ in each solution using the given concentrations and volumes. To do this, we will use the formula: moles = concentration × volume For Ba^2+ from BaCl₂: moles(Ba^2+) = (0.020 M) × (75.0 mL) × (1 L / 1000 mL) For SO₄²⁻ from K₂SO₄: moles(SO₄²⁻) = (0.040 M) × (125 mL) × (1 L / 1000 mL)

Calculate the total moles of each ion

Now, we will add the moles of Ba^2+ and SO₄²⁻ found in each solution to get their total moles. Total moles(Ba^2+) = moles(Ba^2+) from BaCl₂ Total moles(SO₄²⁻) = moles(SO₄²⁻) from K₂SO₄

Calculate the total volume of the mixed solution

We need to find the total volume of the mixed solution to calculate the final concentrations of the ions. To do this, simply add the individual volumes: Total volume = Volume of BaCl₂ solution + Volume of K₂SO₄ solution

Calculate the final concentrations of ions

Finally, we will divide the total moles of each ion by the total volume of the mixed solution to find their final concentrations. Final concentration(Ba^2+) = Total moles(Ba^2+) / Total volume Final concentration(SO₄²⁻) = Total moles(SO₄²⁻) / Total volume