Chapter 5, Problem 130RQ

A solution with a volume of 500.0 mL contained a mixture of ${\text{SO}}_{\text{3}}{}^{\text{2-}}{\text{ and S}}_{\text{2}}{\text{O}}_{\text{3}}{}^{\text{2-}}.\text{ A 100}\text{.0 mL}$ portion of the solution was found to react with 80.00 mL of $0.0500M{\text{ 2CrO}}_{\text{4}}{}^{\text{2-}}$ in a basic solution to give ${\text{CrO}}_{\text{2}}{}^{\text{-}}$. The only sulfur-containing product was ${\text{SO}}_{\text{4}}{}^{\text{2-}}$. After the reaction, the solution was treated with excess $\text{0}\text{.200 }M{\text{ BaCl}}_{\text{2}}$ solution, which precipitated ${\text{BaSO}}_{\text{4}}$. This solid was filtered from the solution, dried, and found to weigh 0.9336 g. Explain in detail how you can determine the molar concentrations of ${\text{SO}}_{\text{3}}{}^{\text{2-}}{\text{ and S}}_{\text{2}}{\text{O}}_{\text{3}}{}^{\text{2-}}$ in the original solution.