Sodium tripolyphosphate \(\left(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}ight)\) is used in many synthetic detergents. Its major effect is to soften the water by complexing \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid's surface tension. The \(\mathrm{p} K\) value for the formation of \(\mathrm{MgP}_{3} \mathrm{O}_{10}{ }^{3-}\) is -8.60 . The reaction is \(\mathrm{Mg}^{2+}+\mathrm{P}_{3} \mathrm{O}_{10}{ }^{5-} ightleftharpoons \mathrm{MgP}_{3} \mathrm{O}_{10}{ }^{3-}\). Calculate the concentration of \(\mathrm{Mg}^{2+}\) in a solution that was originally 50.

\(\mathrm{ppm} \mathrm{Mg}^{2+}\) (50. \(\mathrm{mg} / \mathrm{L}\) of solution) after \(40 . \mathrm{g}\) of \(\mathrm{Na}_{5} \mathrm{P}_{3} \mathrm{O}_{10}\) is added to \(1.0 \mathrm{~L}\) of the solution.