1. Calculate the moles of each reactant:

* Na₂SO₄:

- Moles = (Volume in L) * (Molarity)

- Moles = (0.015 L) * (0.260 mol/L) = 0.0039 mol Na₂SO₄

* KCl:

- Moles = (Volume in L) * (Molarity)

- Moles = (0.0272 L) * (0.200 mol/L) = 0.00544 mol KCl

2. Calculate the moles of each ion:

* Na₂SO₄:

- Na⁺: 0.0039 mol Na₂SO₄ * (2 mol Na⁺ / 1 mol Na₂SO₄) = 0.0078 mol Na⁺

- SO₄²⁻: 0.0039 mol Na₂SO₄ * (1 mol SO₄²⁻ / 1 mol Na₂SO₄) = 0.0039 mol SO₄²⁻

* KCl:

- K⁺: 0.00544 mol KCl * (1 mol K⁺ / 1 mol KCl) = 0.00544 mol K⁺

- Cl⁻: 0.00544 mol KCl * (1 mol Cl⁻ / 1 mol KCl) = 0.00544 mol Cl⁻

3. Calculate the total volume of the solution:

* Total volume = 15.0 mL + 27.2 mL = 42.2 mL = 0.0422 L

4. Calculate the concentration of each ion:

* Na⁺:

- Concentration = (Moles of Na⁺) / (Total volume in L)

- Concentration = (0.0078 mol) / (0.0422 L) = 0.185 M

* SO₄²⁻:

- Concentration = (Moles of SO₄²⁻) / (Total volume in L)

- Concentration = (0.0039 mol) / (0.0422 L) = 0.0924 M

* K⁺:

- Concentration = (Moles of K⁺) / (Total volume in L)

- Concentration = (0.00544 mol) / (0.0422 L) = 0.129 M

* Cl⁻:

- Concentration = (Moles of Cl⁻) / (Total volume in L)

- Concentration = (0.00544 mol) / (0.0422 L) = 0.129 M

Therefore, the concentrations of the ions in the solution are:

* [Na⁺] = 0.185 M

* [SO₄²⁻] = 0.0924 M

* [K⁺] = 0.129 M

* [Cl⁻] = 0.129 M