Video Transcript
A compound with the empirical formula C5H7NO2 has a molar mass of 339 grams per mole. What is the molecular formula of this compound? The molar mass of hydrogen is one gram per mole, carbon is 12 grams per mole, nitrogen, 14 grams per mole, and oxygen, 16 grams per mole.
The empirical formula is the formula of a compound with the simplest whole number ratio of atoms. For example, C4H10 would have an empirical formula of C2H5, and C3H6 would have an empirical formula of CH2. C4H8 would also have an empirical formula of CH2. If C2H5 and CH2 are the empirical formulas, then C4H10, C3H6, and C4H8 are the molecular formulas, where the molecular formula is defined as the formula with the exact number of atoms of each element in a molecule.
The question tells us that the empirical formula of the compound is C5H7NO2, and we need to work out what the molecular formula of this compound is. Our first step in finding the molecular formula is to calculate the molar mass of the empirical formula, where the molar mass is the average mass in grams per mole of substance. We know the empirical formula to be C5H7NO2. So, we need to multiply the molar mass of carbon, which we are told in the question is 12 grams per mole, by its subscript value, which is five.
We then need to add the molar mass of hydrogen, which we are told in the question is one gram per mole, multiplied by its subscript value, which is seven. We then add the molar mass of nitrogen, which is 14 grams per mole, multiplied by its subscript value. Since there is no subscript value given, we can assume it to be one. So, the molar mass of nitrogen is multiplied by one. We then need to add the molar mass of oxygen, which is 16 grams per mole, and multiply it by its subscript value, which is two. If we perform this calculation, we get a molar mass of 113 grams per mole.
The next step involves dividing the molar mass of the compound by the molar mass of the empirical formula. We have been told in the question that the compound has a molar mass of 339 grams per mole. And we’ve just calculated that the molar mass of the empirical formula is 113 grams per mole. If we perform this calculation, we get a value of three. This value indicates that the molecular formula is three times larger than the empirical formula. So, our last step involves multiplying subscripts in the empirical formula by the value we’ve just calculated, which is three.
So for carbon, we need to multiply the original subscript five by three, giving us a new subscript of 15. For hydrogen, we need to multiply seven by three, which is 21. In the empirical formula, nitrogen has a subscript value of one, so we need to multiply one by three which is three. And for oxygen, we need to multiply two by three, which is six.
So, the answer to the question “What is the molecular formula of this compound?” is C15H21N3O6.
