(Solved): Sodium hypochlorite \( (\mathrm{NaOCl}) \) is the active ingredient in pool c ...

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Sodium hypochlorite \( (\mathrm{NaOCl}) \) is the active ingredient in pool chlorine. It completely dissolves in water to produce the hypochlorite ion \( \left(\mathrm{OCl}^{-}\right) \), which undergoes hydrolysis according to the following equilibrium. \[ \mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q) \] The equilibrium constant for this reaction at \( 25^{\circ} \mathrm{C} \) is \( 3.33 \times 10^{-7} \). For pool chlorine to be effective the \( \mathrm{pH} \) is maintained by a different buffer at \( 7.5 \) and the hypochlorous acid \( (\mathrm{HOCl}) \) concentration should be \( 1.3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \). Calculate the volume of \( 2.0 \mathrm{~mol} \mathrm{~L}^{-1} \) sodium hypochlorite solution that needs to be added to a \( 1.00 \times 10^{4} \mathrm{~L} \) pool to meet the required conditions.