Video Transcript
What is the general formula for the group of the compounds to which the following displayed formula is related?
The compound shown contains three carbon atoms and eight hydrogen atoms. So this molecule has the molecular formula C3H8. But the question does not ask us for the molecular formula of this compound. Instead, we need to determine a general formula that will work for all compounds related to the one shown.
The compound shown only contains carbon and hydrogen atoms that are joined by single covalent bonds. Therefore, this molecule can be classified as an alkane, a saturated hydrocarbon that only consists of single covalent bonds. As alkanes are hydrocarbons, we know that the general formula will contain both carbon and hydrogen atoms. It’s our job to determine how many of each.
To do this, let’s take a look at the displayed formula of the two simplest alkanes: methane and ethane. Looking at the three molecular formulas, it might be difficult to see how the number of carbon and hydrogen atoms are related, but the displayed formula can help. Looking at the displayed formulas, we can see that each carbon atom forms a bond with two hydrogen atoms. In addition, at each end of the alkane chain, there is one additional hydrogen atom. So we can say that the number of hydrogen atoms in an alkane is two times the number of carbon atoms plus two. If an alkane contained 𝑛 number of carbon atoms, then the molecule must contain two times 𝑛 plus two hydrogen atoms.
To verify that this is the correct general formula for an alkane, let’s set 𝑛 equal to four. This molecule must contain four single-bonded carbon atoms. Each carbon atom in the alkane must form a total of four single covalent bonds. So we can complete the structure by single bonding each carbon atom to the appropriate number of hydrogen atoms. We can see that this molecule does contain four carbon atoms and 10 hydrogen atoms. This tells us that the general formula is correct.
So the general formula for the group of compounds to which the provided displayed formula is related is C𝑛H2𝑛+2.
