Final answer:
To find the percent sodium by mass in the original mixture, the stoichiometry of the reactions between sodium, zinc, and sulfuric acid and between barium chloride and the sulfates must be considered. The moles of barium sulfate precipitated indicate the total moles of sulfate ions, which can be used to calculate the mass and thus the percentage of sodium in the mixture.
Step-by-step explanation:
To determine the percent sodium by mass in the original mixture, we need to understand the stoichiometry of the chemical reaction between sodium, zinc, and sulfuric acid, and then relate it to the reaction of barium chloride with the sulfate that is formed. First, sodium and zinc react with sulfuric acid to form sodium sulfate (Na2SO4) and zinc sulfate (ZnSO4), both of which will react with barium chloride (BaCl2) to produce barium sulfate (BaSO4). The amount of BaSO4 precipitated will be directly proportional to the amount of sulfate ions present from the sodium and zinc sulfate.
Since barium sulfate is produced from the sulfate ions, the moles of BaSO4 precipitated is equal to the moles of sulfate ions in the reaction. With the given molarity and volume of BaCl2, we can calculate the moles of BaSO4 and hence, the moles of sulfate ions, which represent the total sulfate ions from both Na2SO4 and ZnSO4. Knowing the mole ratio of sodium to sulfate in Na2SO4, we can convert the moles of sulfate ions to moles of sodium, and from there, calculate the mass of sodium in the original mixture. Using the original mixture mass, we can then calculate the percent by mass of sodium in the original mixture.
The steps involve using molar masses, stoichiometry, and the concept of limiting reactant where necessary. The final percentage is obtained by dividing the mass of sodium by the total mass of the mixture and multiplying by 100.