Which of the following describes the general formula for an alcohol? (A) C𝑛H2𝑛+2, (B) C𝑛H2𝑛, (C) C𝑛H2𝑛+1 (D) C𝑛H2𝑛−2OH, or (E) C𝑛H2𝑛+1OH.
We have been given five possible general formulas. In each of the general formulas, the term 𝑛 represents the number of carbon atoms in the molecule. We need to determine which of these general formulas represents an alcohol.
Alcohols are a family of compounds that contain the same functional group: a hydroxy group. A hydroxy group consists of an oxygen atom bonded to a hydrogen atom. As all alcohol molecules must contain this functional group, the general formula must account for the presence of an oxygen atom. Looking at the answer choices, we can see that answer choices (A), (B), and (C) only contain carbon and hydrogen atoms. So these cannot be the general formula of an alcohol.
To investigate this further, let’s examine the displayed formulas of the first three alcohols of the alcohol homologous series. A homologous series is a family of compounds that has the same functional group and the same general formula with each compound differing by a structural unit. In the case of an alcohol, we know that the same functional group is a hydroxy group. And we can see from the displayed formulas that each compound in the series differs by a single CH2 unit. We can use the displayed formulas of these three alcohol molecules to determine which of the two remaining general formulas is correct.
We can see that answer choice (D) and answer choice (E) both account for the presence of the hydroxy group. If we look at the remaining portion of each of the molecules, we can see that every carbon atom in the structure is bonded to two hydrogen atoms. Therefore, for 𝑛 number of carbon atoms in the molecule there will be two times 𝑛 hydrogen atoms. But we can also see that at the end of the carbon chain, there is an additional hydrogen atom. So the number of hydrogen atoms bonded to the carbon atoms of an alcohol is two 𝑛 plus one. So the general formula of an alcohol must be C𝑛H2𝑛+1OH, which matches answer choice (E).
Just to be sure, let’s test this general formula with a third alcohol, propanol. Propanol has three carbon atoms, so we can substitute three for 𝑛 in the general formula. This gives us a molecular formula of C3H7OH. We already know that propanol contains three carbon atoms. These three carbon atoms are bonded to seven hydrogen atoms and one hydroxy group. So the general formula is correct. So the general formula for an alcohol is C𝑛H2𝑛+1OH, answer choice (E).