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

Expert verified
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

01

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: \(moles~BaSO4 = \frac{mass~BaSO4}{M_{BaSO4}}\)
02

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. \(moles~S = moles~BaSO4\)
03

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: \(average~mass~per~tablet = \frac{mass~saccharin}{10}\)
04

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.

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