Chapter 15, Problem 107CP

Sodium tripolyphosphate (Na₅P₃O₁₀) is used in many synthetic detergents. Its major effect is to soften the water by complexing Mg²⁺ and Ca²⁺ ions. It also increases the efficiency of surfactants, or wetting agents that lower a liquid’s surface tension. The K value for the formation of MgP₃O₁₀³⁻ is 4.0 × 10⁸ The reaction is ${\text{Mg}}^{2+}\left(aq\right)+{\text{P}}_3{\text{O}}_{10}{}^{5-}\left(aq\right)\rightleftharpoons {\text{MgP}}_3{\text{O}}_{10}{}^{3-}\left(aq\right)$. Calculate the concentration of Mg²⁺ in a solution that was originally 50. ppm Mg²⁺ (50. mg/L of solution) after 40. g Na₅P₃O₁₀ is added to 1.0 L of the solution.