### Video Transcript

What is the number of carbon atoms in one molecule of a hydrocarbon that is 16 percent hydrogen by mass and has a molar mass of 86 grams per mole? A) Two, B) Four, C) Five, D) Six, or E) Seven.

The focus of the question is on a molecule of a hydrocarbon, meaning a substance made up of carbon and hydrogen only. And we’re told that of the mass of the hydrocarbon molecule, 16 percent is due to hydrogen, and that would have been measured by some form of elemental analysis. And lastly, we’ve been told that the molar mass of the substance is 86 grams per mole. What this means is one mole’s worth of molecules of the hydrocarbon will have a mass of 86 grams. We can use this to our advantage because it means that a single molecule of this hydrocarbon has a mass of 86 unified atomic mass units.

You might see amu, meaning atomic mass unit, in place of u, the unified atomic mass unit. These have slightly different definitions, but will produce the same answer in this circumstance. So, let’s imagine the mass of the hydrocarbon as a big circle. 16 percent of the mass is due to hydrogen, which means that an entire 84 percent of the mass is due to carbon. However, the atomic mass of carbon is 12 times that of hydrogen. So, each atom of carbon contributes 12 times as much to the mass of hydrocarbon than each atom of hydrogen.

So, what we can do, if we want to work out the number of carbon atoms in one molecule of the hydrocarbon, is work out what mass of the hydrocarbon is made up of carbon and then divide that by the atomic mass. That’s equal to 84 percent of 86 unified atomic mass units. So in the next step, we divide by the atomic mass of carbon. So, the number of carbon atoms per molecule is equal to the percentage of the mass due to carbon multiplied by the mass of the molecule divided by the atomic mass of carbon, which evaluates to seven percent of 86.

The easiest way to do this calculation is to convert seven percent into seven 100s. Meaning, all we need to do is multiply 86 by seven and then divide by 100. Which gives us 602 divided by 100. Which gives us 6.02 carbon atoms per molecule of hydrocarbon. But we can only have whole numbers of carbon atoms. So, 6.02 can be rounded to six. So, our answer for the number of carbon atoms in one molecule of a hydrocarbon that is 16 percent hydrogen by mass and has a molar mass of 86 grams per mole is six.