Video: Calculating the Percentage Composition of Ethanol

Ethanol has the formula C₂H₅OH. a) As a percentage by mass, what is the oxygen content of the ethanol molecule, to 2 significant figures? b) As a percentage by mass, what is the carbon content of the ethanol molecule, to 2 significant figures? c) As a percentage by mass, what is the hydrogen content of the ethanol molecule, to 2 significant figures?

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Video Transcript

Ethanol has the formula C₂H₅OH. a) As a percentage by mass, what is the oxygen content of the ethanol molecule to two significant figures? b) As a percentage by mass, what is the carbon content of the ethanol molecule to two significant figures? And c) As a percentage by mass, what is the hydrogen content of the ethanol molecule to two significant figures?

On the surface, it looks like this question isn’t looking for percentage composition. But it does ask for the mass percentage of all the elements in our formula. The first thing we should do is condense down the formula into its chemical formula listing the number of atoms of each element only. From the formula, we can see that an ethanol molecule contains only carbon, hydrogen, and oxygen. And each molecule contains two carbon atoms, six hydrogen atoms, and one oxygen atom. The percentage by mass or mass percentage is equal to the mass of the element divided by the mass of the sample all multiplied by 100 percent.

In this case, the sample is one molecule of ethanol. And the mass of the element is the mass of either two carbon atoms, six hydrogen atoms, or one oxygen atom. We can work out the mass of an atom of each element by looking up the relative atomic mass on our periodic table. The relative atomic mass of carbon is 12.011. The relative atomic mass of hydrogen is 1.008. And the relative atomic mass of oxygen is 15.999. By multiplying the number of atoms of each element per molecule by the relative atomic mass of that element, we’ll get the mass of each element in the molecule. This means that for a molecule of ethanol, carbon contributes 24.022 to the mass, hydrogen contributes 6.048, and oxygen contributes 15.999. If we sum all these contributions together, we’ll get the relative formula mass of an ethanol molecule.

We now have all the information we need to answer all three questions. For part a), we take the contribution for oxygen per molecule of ethanol as 15.999 and divide it by the relative formula mass of ethanol 46.069 and then multiply everything by 100 percent. This gets us 34.7283 percent which we round to 35 percent as our answer to two significant figures. Doing the same working for carbon where we use it’s mass contribution of 24.022, we get a mass percentage of 52 percent to two significant figures. And lastly for hydrogen, we get a mass percentage of 13 percent. To find the mass percentage for hydrogen, we could’ve taken away the percentage for oxygen and carbon from 100 percent. However, that would mean that any mistake in our oxygen or carbon calculation would make our hydrogen calculation incorrect. Doing it this way gives us better odds of a correct answer.

So using the process for figuring out the percentage composition of ethanol, we’ve demonstrated that oxygen has a mass percentage of 35 percent. Carbon has a mass percentage of 52 percent. And hydrogen has a mass percentage of 13 percent in the ethanol molecule.

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