How to Find Empirical and Molecular Formulas

Alright, so I’m going to explain, as seen by the title, how to find empirical and molecular formulas from experimental data. Often when solving a problem, you’re given the percent composition of a compound, or the percent of each element in the compound, so that’s how we’re going to start.

1. Because you’re typically not given the mass of the sample of the compund, just assume it’s a 100 g sample. Your first task is to find the mass of each element in the compound. With a 100 g sample, 20% Hydrogen would become 20 g of H, etc.
2. Using the mass of each element, convert all the elements to moles (see past posts if you don’t remember how to do this). You’ll probably get a bunch of messy decimals, which is okay. If you’re writing out each step on a piece of paper, don’t necessarily round. It would be in your best interest to right out every digit that your calculator gives you.
3. From here is where it gets a little confusing (it’ll make more sense in the example problem below). Divide each mole amount by the smallest amount there. If your amounts are 2, 4, 6, and 8 (they would never be this nice, fyi), then you would divide each number by 2, including 2 itself, getting 1, 2, 3, and 4, respectively.
4. Like I said before, you’re going to get a bunch of messy decimals. Take another mole amount (not the one you divided by itself) after you divide it by the smallest amount and multiply it by 2, then 3, then 4, etc. until you reach a whole number. For instance if you have 1.666, you would multiply it by 2 and find that it produced 3.333–not a whole number. Go back to 1.666 and multipy it by 3–it equals 5. This whole number will become the subscript for whatever element it corresponds to, so make sure you keep track of each element throughout the problem. TIP: Yes, of course you can round, but 7.8 doesn’t count as a whole number. 7.99 or 8.001 would be preferable.
5. The rest of the elements should multiply by the same number and produce whole numbers. Each respective whole number becomes the subscript for that element. Obviously the element that you divided by itself will equal 1. 1 multiplied by the common multiplier (let’s say 3) will equal the multiplier. So in this case, that element’s subscript would be 3.
6. Once you know all the subscripts you have found the empirical formula. The empirical formula just means that all the subscripts are in lowest terms, but it doesn’t tell us much about the structure of the compound, as opposed to a molecular formula. Finding the molecular formula is simple. If the problem is asking you to find the molecular formula as well, it will give you the mass of the compound’s molecular formula. You would simply find the mass of the empirical formula (if your formula was CH2, you would find the atomic mass of C and add it to the atomic mass of H, which is multiplied by 2 to account for the 2 H’s in the formula). Compare the empirical formula’s mass to that of the molecular formula by dividing the emp. mass by the mol. mass. Often the mol. mass will simply be twice that of the emp. mass, in which case you would just multiply the subscripts by 2 to get the mol. formula.

EXAMPLE PROBLEM (this should clear up all your questions)

Given: A compound consists of 40.00% C, 6.72% H, and 53.29% O. The molecular compound’s mass is 180 g/mol.

1. 40g H, 6.72g C, 53.29g O

2.   40/12.01=3.330557868 moles C

6.72/1.01= 6.653465347 moles H

53.29/16= 3.330625 moles O

3. Divide all numbers by smallest amount (moles of C)

Carbon: 3.330557868/3.330557868= 1

Hydrogen: 6.653465347/3.330557868= 1.997702971

Oxygen: 3.330625/3.330557868= 1.000020156

4. In this case the numbers are all close enough to whole numbers, so you don’t have to worry about multiplying the values to get whole numbers. Therefore, the empirical formula would be CH2O. The empirical mass is 30.03 g. We know that the mol. mass is 180 g. 180 divided by 30.03 is about 6, so you just multiply all the subscripts by 6. Therefore the molecular formula is C6H12O6.

Alright, so that’s how to find the empirical and molecular formulas. Sorry that was so long-winded, but I hope you understand it better now. If anyone finds any areas I missed, please comment and let me know so we all have a full understanding of this topic. Thanks guys!