Textbook Problem M.19

[Rachel Bartley 2B]

A stimulant in coffee and tea is caffeine, a substance of molar mass 194 g/mol. When 0.376 g of caffeine was burned, 0.682 g of carbon dioxide, 0.174 g of water, and 0.110 g of nitrogen were formed. Determine the empirical and molecular formulas of caffeine, and write the equation for its combustion.

I know that I need to start with finding the amount of moles of each element, which I was able to do for C, H, and N, but because O appears in both H2O and CO2, I am confused on how to find the amount of moles of O and then use this to find the empirical formula. What am I supposed to do?

[Rio Gagnon 1G]

In order to find the moles of O, you must first calculate the grams of each element (C, N, and H). Then, subtract each of those values from the given mass of caffeine and you are left with the grams of O (.06 g O). Convert this number to moles (0.0038). In order to find the empirical formula, you divide the smallest moles by the amount of moles of each individual element (you should get 4 mol C:5 mol H:1 mol N2:1 mol O). In order to find the molecular formula, you must find the molar mass of the empirical formula you just got and divide it from the molar mass of the given substance (194/97.09 = 2), so you multiply each subscript by 2.

[Jennifer Huynh 3I]

To find the moles of O, we know that the total mass of caffeine is 0.376 and we can find the masses of each element (C, H, and N) using the given masses of carbon dioxide, water, and nitrogen. Then, subtract the masses of C, H, and N from the total mass of caffeine to obtain the mass of O. After calculating the mass of O, find the moles of O and then divide the moles of each element by the mole with the smallest value. Lastly, you will be left with the ratio of the atoms in the empirical formula.