### Video Transcript

A compound with a relative formula mass of 84.2 is composed only of hydrogen and carbon. The compound is found to contain 85.6 percent carbon and 14.4 percent hydrogen by mass. What is the formula of this compound? The relative atomic mass of hydrogen is one, and the relative atomic mass of carbon is 12.

This is a question about percentage composition. Our goal is to find the chemical formula of the compound with the information given. The mystery compound has a relative formula mass of 84.2. While relative formula mass is a unitless measure, we can say that one molecule of the compound has a mass of 84.2 unified atomic mass units. We also know that the compound is 85.6 percent carbon by mass and 14.4 percent hydrogen by mass. If we multiply these percentages by the total mass of the molecule, we can find the mass of the carbon atoms in the compound and the mass of the hydrogen atoms in the compound. Carrying out this arithmetic, we get 72.1 unified atomic mass units of carbon and 12.1 unified atomic mass units of hydrogen.

The relative atomic mass gives us the average mass of an atom of that element. If we divide the mass of that element in the molecule by the mass per atom, we can end up with a number of atoms of that element. 72.1 divided by 12 rounds to six atoms. Here, we wanna round our answer to a whole number, since the final formula will have a whole number of carbon atoms and a whole number of hydrogen atoms. It’s okay to round these numbers here because the other numbers in the problem may be rounded as well, especially the atomic masses. If we used more precise values, our calculated answers would get closer and closer to the whole number. Carrying out the second division gives us an answer of 12 atoms of hydrogen. Combining these numbers of atoms in a chemical formula gives us the final answer C6H12, the correct answer.

As a review, to solve this problem, we took the percent by mass and multiplied it by the mass of the molecule, which gave us a total mass of all of the atoms of that element in the molecule. Dividing this number by the mass per atom gives us the number of atoms in the formula of the compound. So what is the formula of the compound in the question? That’s C6H12.