Question

Caffeine, a stimulant found in coffee, tea, and energy drinks, contains C, H, O, and N.
Combustion of 1.000 mg of caffeine produces 1.813 mg CO2, 0.4639 mg H2O, and 0.2885 mg N2.
Calculate the molecular formula of caffeine, whose molar mass lies between 150 and 200 g/mol.

Answer 1

molar mass of CO2 = 44 g per mole

so 0.001813 g of CO2 has 0.001831 /44 = 0.000041 moles of CO2
there is 1 mole of C in CO2 and all the C from the compound becomes CO2 so moles of C in the compound = 0.000041 moles
mass of C = 0.000041 x 12 = 0.00049 g
% C in the compound = 0.00049 / 0.00100 = 49.4%
mass of C in 1 mole = 49.4% of 194g = 95.9 g or
moles of C in 1 mole of the compound = 8.0 moles of C

molar mass of H2O = 18 g per mole
0.0004639 g of H2O has 0.0004639 / 18 = 0.0000258 moles of H2O
there are 2 moles of H in H2O so moles of H in the compound = 0.0000515 moles
mass of H = 0.0000515 x 1.0079 = 0.0000520 g
%H in the compound = 0.0000520 / 0.0010000 = 5.2%
mass of H in 1 mole of compound = 5.2% of 194 = 10.08 g
moles of H in 1 mole of the compound = 10.00 mmoles of H

mass of sample = 0.0010 g

mass of N = 0.0002885 g
% N in the compound = 0.0002885 / 0.0010 = 28.9%
mass of N in 1 mole = 28.9% of 194g = 55.969 g or
moles of N in 1 mole of the compound = 3.997786 mmoles of N

mass of C + H + N = 0.0008g
mass of O by difference = 0.0002g
% O in the sample = 16.51%
mass of O in a mole of sample = 32.03 g or 2 mmoles of O

molecular formula is .. C8H10N4O2