Question

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 \(0.5894 \mathrm{~g}\) 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 \(\mathrm{BaSO}_{4}\) obtained was \(0.5032 \mathrm{~g}\). What is the average mass of saccharin per tablet? What is the average mass percent of saccharin in the tablets?

Short answer

The average mass of saccharin per tablet is \(0.0522~g\), and the average mass percent of saccharin in the tablets is \(88.56\%\).

Step-by-step solution

Calculate the moles of BaSO4 obtained

First, we need to find the moles of BaSO4 obtained from the given mass. The molar mass of BaSO4 is: \(M_{BaSO_4} = (137.33 + 32.07 + (4 × 16))~g/mol\) Moles of BaSO4 can be calculated as: \(moles~BaSO4 = \frac{mass~BaSO4}{M_{BaSO4}}\)

Find the moles of sulfur present in the saccharin tablets

Since all the sulfur in saccharin is converted to sulfate ions in the obtained BaSO4, we can determine the moles of sulfur present in the saccharin tablets. \(moles~S = moles~BaSO4\)

Determine the mass of saccharin and calculate its average mass per tablet

Now that we have the moles of sulfur, we can calculate the mass of saccharin (C7H5NO3S). The molar mass of saccharin is: \(M_{saccharin} = (7 × 12.01 + 5 × 1.01 + 1 × 14.01 + 3 × 16 + 1 × 32.07)~g/mol\) Mass of saccharin can be found by: \(mass~saccharin = moles~S × M_{saccharin}\) Then we can find the average mass of saccharin per tablet as: \(average~mass~per~tablet = \frac{mass~saccharin}{10}\)

Calculate the average mass percent of saccharin in the tablets

Finally, we can calculate the average mass-percent of saccharin in the tablets using the formula: \(mass~percent = \frac{average~mass~saccharin~per~tablet}{average~mass~per~tablet} × 100\) Where "average mass per tablet" refers to the total mass of the tablets divided by 10.

Key concepts

Moles of BaSO4

In any chemistry problem involving a precipitate, such as barium sulfate (BaSO4), one key step is calculating the moles of the compound formed. To find the moles of BaSO4, we first need its molar mass. This is calculated by summing the atomic weights of barium (Ba), sulfur (S), and four oxygen atoms (O):

• Barium (Ba): 137.33 g/mol
• Sulfur (S): 32.07 g/mol
• Oxygen (4 O): 4 × 16 g/mol = 64 g/mol

Adding these together gives us the molar mass of BaSO4: 233.4 g/mol. Given the mass of the BaSO4 precipitate is 0.5032 g, we calculate the moles of BaSO4 using the formula: \[ moles~BaSO_4 = \frac{mass~BaSO_4}{M_{BaSO_4}} = \frac{0.5032~g}{233.4~g/mol} \] This measures the amount of barium sulfate formed and equivalently represents the moles of sulfur originally present in the saccharin tablets, since each BaSO4 contains exactly one sulfur atom.

Average Mass Per Tablet

Once the moles of sulfur are established, determining the mass of saccharin in the tablets, and subsequently the average mass per tablet, is our next step. Since the sulfur in saccharin is now part of BaSO4, we can take these moles to find the saccharin's mass. The molar mass of saccharin, calculated as:

• 7 Carbons (C): 7 × 12.01 g/mol = 84.07 g/mol
• 5 Hydrogens (H): 5 × 1.01 g/mol = 5.05 g/mol
• 1 Nitrogen (N): 14.01 g/mol
• 3 Oxygens (O): 3 × 16 g/mol = 48 g/mol
• 1 Sulfur (S): 32.07 g/mol

Adding these gives us: 183.18 g/mol. We multiply the moles of sulfur (or BaSO4) by the molar mass of saccharin to find its total mass. The average mass per saccharin tablet is then calculated by dividing this total mass by the number of tablets (10 in this case): \[ average~mass~per~tablet = \frac{mass~saccharin}{10} \] This gives us the mass of saccharin in each tablet, essential for further calculations like mass percent.

Mass Percent Calculation

The mass percent of saccharin in the tablets is an expression of purity or concentration. This is found by comparing the saccharin content against the total mass of a tablet, represented as a percentage. Recall from initial problem data: the total mass of ten tablets is 0.5894 g, making the mass of one tablet: \[ average~mass~per~tablet = \frac{0.5894~g}{10} \] The mass percent is then calculated using: \[ mass~percent = \frac{average~mass~saccharin~per~tablet}{average~mass~per~tablet} \times 100 \] This provides insight into how much of the tablet is active ingredient (saccharin), a useful measure when evaluating product composition or compliance with dietary regulations. Remember to carefully execute each step to ensure your final answer is accurate and reflects true composition.