Question

A \(3.455-\mathrm{g}\) sample of a mixture was analyzed for barium ion by adding a small excess of sulfuric acid to an aqueous solution of the sample. The resultant reaction produced a precipitate of barium sulfate, which was collected by filtration, washed, dried, and weighed. If \(0.2815 \mathrm{~g}\) of barium sulfate was obtained, what was the mass percentage of barium in the sample?

Short answer

The mass percentage of barium in the sample can be calculated in four steps. First, find the moles of barium sulfate formed using the formula: Moles of barium sulfate = \( \frac{0.2815 \mathrm{~g}}{233.43 g/mol} \). Second, determine the moles of barium in the mixture, which are equal to the moles of barium sulfate. Third, calculate the mass of barium in the mixture using the formula: Mass of barium = Moles of barium * 137.33 g/mol. Finally, find the mass percentage of barium in the mixture using the formula: Mass percentage of barium = \( \frac{mass \ of \ barium}{3.455 \mathrm{g}} \) * 100%.

Step-by-step solution

Calculate the moles of barium sulfate

To determine the moles of barium sulfate formed, use the formula: Moles of barium sulfate = (mass of barium sulfate) / (molar mass of barium sulfate) Given the mass of barium sulfate obtained is 0.2815 g, and the molar mass of barium sulfate (BaSO4) is 137.33 g/mol (barium) + 4 * 16.00 g/mol (oxygen) + 32.07 g/mol (sulfur) = 233.43 g/mol. Therefore: Moles of barium sulfate = \( \frac{0.2815 \mathrm{~g}}{233.43 g/mol} \)

Calculate the moles of barium in the mixture

Since the ratio of barium to barium sulfate is 1:1 in the reaction, the moles of barium in the mixture are equal to the moles of barium sulfate. Thus, the moles of barium in the mixture are: Moles of barium = Moles of barium sulfate

Calculate the mass of barium in the mixture

To find the mass of barium in the mixture, use the formula: Mass of barium = (moles of barium) * (molar mass of barium) The molar mass of barium is 137.33 g/mol. Therefore: Mass of barium = Moles of barium * 137.33 g/mol

Calculate the mass percentage of barium in the mixture

Finally, calculate the mass percentage of barium in the mixture using the formula: Mass percentage of barium = \( \frac{mass \ of \ barium}{total \ mass \ of \ sample} \) * 100% The mass of the sample is given as 3.455 g. Therefore: Mass percentage of barium = \( \frac{mass \ of \ barium}{3.455 \mathrm{g}} \) * 100%