1. **State the problem:** We need to find the concentration of aqueous hydrogen peroxide (H2O2) given that 0.050 moles of MnO4- react with 400 cm³ (0.400 L) of H2O2 solution. 2. **Write the balanced chemical equation:** $$5H_2O_2(aq) + 2MnO_4^-(aq) + 6H^+(aq) \rightarrow 5O_2(g) + 2Mn^{2+}(aq) + 8H_2O(l)$$ 3. **Identify mole ratio:** From the equation, 5 moles of H2O2 react with 2 moles of MnO4-. 4. **Calculate moles of H2O2 required:** Using mole ratio, $$\text{moles H}_2O_2 = 0.050 \times \frac{5}{2} = 0.125$$ 5. **Calculate concentration of H2O2:** Concentration $C = \frac{\text{moles}}{\text{volume in liters}}$ $$C = \frac{0.125}{0.400} = 0.3125$$ 6. **Final answer:** The concentration of aqueous hydrogen peroxide needed is $0.3125$ mol/L.