Help please! I'm still not sure how to do these!

Question

Determine the empirical formula of a compound with the following composition by mass: 48.0% C, 8.0% H, 28.0% N, and 16.0% O. If this compound has a molar mass of 200 g/mol, what is its molecular formula?

Answer 1

First, composition by mass of an element refers to how much of an element is present out of the total composition of elements in the formula. For example, take 48% C. We can imagine that out of 100 atoms, 48 of them are carbon atoms, 8 of them are hydrogen atoms, and so forth...Bottom line is that all the atoms should add up to 100, or 100%.

Next step let's pretend that the % is out of a total of 100 grams. This is just like the idea above. For example, 48% C would be 48g C, 8% H would be 8g H, and so forth. Then, using the equation for molecular weight (MW = g/mol) we can determine the number of moles of each element by re-arranging the equation: mol = g/MW. Determining the number of moles will tell us more information of the ratio of atoms to one another in the molecular formula.

Therefore:

mol C = (48 g) / (12.01 g/mol) = 4 mol C

mol H = (8 g) / (1.008 g/mol) = 8 mol H

mol N = (28 g) / (14.01 g/mol) = 2 mol N

mol O = (16 g) / (16.00 g/mol) = 1 mol O

By doing the above step, we now know how many moles of each element are present with respect to one another. However, to obtain the most simplified molecular formula, we need to divide each by the lowest number of moles. (Doing this should always give whole numbers.) For example, 1 mol O constitutes the lowest number of moles out of the other three elements and therefore we would divide each by 1 mol. In this example, the numbers will not change after dividing by 1, but note that the units will cancel out (mol/mol) and all we are left with is a "unitless" number (this is the subscript after the atom in a chemical formula!).

Therefore, the simplest way to write the formula is C₄H₈N₂O. The simplest formula is called the empirical formula. The Molecular Weight of this formula, once you add up the molecular weights of all the elements, is 100 g/mol.

MW = (4 x 12 g/mol) + (8 x 1.008 g/mol) + (2 x 14.01 g/mol) + (1 x 16.00 g/mol) = 100 g/mol

The question also asks for the molecular formula with a molecular weight of 200 g/mol. Since this is double the molecular weight of the empirical formula, all we have to do is double the quantity of each element in the formula....

C₈H₁₆N₄O₂

I hope this helps!!