Which of the following describes
the general formula for an alkene? (A) C𝑛H2𝑛+2, (B) C𝑛H2𝑛, (C)
C𝑛H2𝑛−2, (D) C𝑛H2𝑛+1, or (E) C𝑛H2𝑛+1OH.
We have been provided with five
possible general formulas. In each of the formulas, the term
𝑛 represents the number of carbon atoms in the molecule. We need to determine which of these
general formulas represents an alkene.
Alkenes are a family of compounds
that have the same functional group, a carbon–carbon double bond. The simplest alkene will contain
two carbon atoms joined by a double bond. As carbon atoms should form a total
of four bonds, we can complete the structure by single bonding two hydrogen atoms to
each carbon atom. This is the displayed formula of
ethene. We can see from the displayed
formula that a molecule of ethene contains two carbon atoms and four hydrogen atoms
and has the molecular formula C2H4.
Now let’s look at an alkene that
contains three carbon atoms. In order for each carbon atom to
form a total of four bonds, six hydrogen atoms must be added to the structure. This is the displayed formula of
propene, which has a molecular formula of C3H6. A four-carbon alkene will have
eight hydrogen atoms. This is the displayed formula of
but-1-ene, which has the molecular formula C4H8. We can see that each of these
molecules, being that they are alkenes, contains the same functional group, a
carbon–carbon double bond.
To progressively increase the size
of an alkene, a CH2 structural unit is added. Ethene, propene, and but-1-ene
represent molecules in a homologous series. A homologous series is a family of
compounds that have the same functional group and the same general formula, with
each compound in the series differing by a structural unit.
With all of this information in
mind, we can go back to determining the general formula for an alkene. We first need to determine how the
number of carbon atoms relates to the number of hydrogen atoms. For ethene, propene, and but-1-ene,
we can see that the number of hydrogen atoms is two times larger than the number of
carbon atoms. So if there were 𝑛 number of
carbon atoms, we would expect there to be two times 𝑛 hydrogen atoms. This is the general formula for an
alkene, which matches answer choice (B). Therefore, the general formula for
an alkene is C𝑛H2𝑛, answer choice (B).