Saccharin $\left(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S}\right)$ is sometimes dispensed in tablet form. Ten tablets with a total mass of 0.5894 g were dissolved in water. The saccharin was oxidized to convert all the sulfur to sulfate ion, which was precipitated by adding an excess of barium chloride solution. The mass of BaSO\(_{4}\) obtained was 0.5032 g. What is the average mass of saccharin per tablet? What is the average mass percent of saccharin in the tablets?

To determine the mass of saccharin in the initial state of the experiment, we need to find the amount of sulfate ion (SO₄²⁻) present in the BaSO₄ precipitate and use its stoichiometric relationship to saccharin. First, find the moles of BaSO₄ produced using its formula mass (233.43 g/mol): Moles of BaSO₄ = (mass of BaSO₄) / (formula mass of BaSO₄) = 0.5032 g / 233.43 g/mol ≈ 0.00216 mol Next, use the stoichiometric relationship between BaSO₄ and saccharin to find the moles of saccharin, which is 1:1 due to the balanced reaction: Moles of saccharin = moles of BaSO₄ = 0.00216 mol Now, find the mass of saccharin using its formula mass (183.18 g/mol): Mass of saccharin = (moles of saccharin) * (formula mass of saccharin) ≈ 0.00216 mol * 183.18 g/mol ≈ 0.3956 g

To calculate the average mass of saccharin per tablet, divide the total mass of saccharin by the number of tablets: Average mass of saccharin per tablet = mass of saccharin / number of tablets ≈ 0.3956 g / 10 tablets ≈ 0.03956 g/tablet

To calculate the mass percent of saccharin in the tablets, divide the mass of saccharin by the total mass of the tablets and then multiply by 100: Mass percent of saccharin = (mass of saccharin / total mass of tablets) * 100 ≈ (0.3956 g / 0.5894 g) * 100 ≈ 67.1 % Thus, the average mass of saccharin per tablet is approximately 0.03956 g or 39.56 mg, and the average mass percent of saccharin in the tablets is approximately 67.1%.