Question 3.8: Determine the empirical formula of a compound that is 30.45 ...
Determine the empirical formula of a compound that is 30.45 percent nitrogen and 69.55 percent oxygen by mass.
Strategy Assume a 100-g sample so that the mass percentages of nitrogen and oxygen given in the problem statement correspond to the masses of N and O in the compound. Then, using the appropriate molar masses, convert the grams of each element to moles. Use the resulting numbers as subscripts in the empirical formula, reducing them to the lowest possible whole numbers for the final answer.
Setup The empirical formula of a compound consisting of N and O is NxOy. The molar masses of N and O are 14.01 and 16.00 g/mol, respectively. One hundred grams of a compound that is 30.45 percent nitrogen and 69.55 percent oxygen by mass contains 30.45 g N and 69.55 g O.
30.45 \cancel{g N} × \frac{1 mol N}{14.01 \cancel{g N}} = 2.173 mol N
69.55 \cancel{g O} × \frac{1 mol O}{16.00 \cancel{g O}} = 4.347 mol O
This gives a formula of N2.173O4.347. Dividing both subscripts by the smaller of the two to get the smallest possible whole numbers (2.173/2.173 = 1, 4.347/2.173 ≈ 2) gives an empirical formula of NO2. This may or may not be the molecular formula of the compound because both NO2 and N2O4 have this empirical formula. Without knowing the molar mass, we cannot be sure which one it is.