Caffeine has a molar mass of 195 grams per mole. the percent composition of its component elements is:

carbon: 49.5 percent

hydrogen: 5.1 percent

nitrogen: 28.9 percent

oxygen: 16.5 percent

find the empirical and molecular formulas of caffeine.

Assuming that you have 100 grams of sample, each of the values is the grams of each atom. 

first we need to convert each grams to moles using their molar mass

carbon-> 49.5 grams (1 mol/ 12.0 g)= 4.13 moles

hydrogen-> 5.1 grams (1 mol/ 1.01 g)= 5.05 moles

nirogen-> 28.9 grams (1 mol/ 14.0 g)= 2.06 moles

oxygen->16.5 grams (1 mol/ 16.0 g)= 1.03 moles

then you need to divide each value by the smallest, and if you don't get the whole number, you need to multiply

carbon-> 4.13/1.03= 4

hydrogen->5.05/ 1.03= 5

nitrogen-> 2.06/ 1.03= 2

oxygen-> 1.03/ 1.03= 1

empirical formula-> C4H5N2O

to find the molecular formula, you can find the molar mass of the empirical formula and see what is the ratio of the given molar mass by the question.

molar mass of C4H5N2O = 97.1 g/ mol

195/ 97.1= 2

the molecular formula is twice the empirical-> C8H10N4O2