### Video Transcript

What is the general formula for the
group of the compounds to which the following displayed formula is related?

In this question, we are given the
displayed formula of a molecule. A displayed formula is a
representation of a molecule showing all the atoms and bonds, and the bonds are
drawn as lines. When looking at the provided
displayed formula, we can see that the molecule contains only carbon and hydrogen
atoms. Therefore, we can classify this
molecule as a hydrocarbon. We also notice that the molecule
contains one carbon-to-carbon triple bond. Hydrocarbons that contain at least
one double or triple bond between carbon atoms are classified as unsaturated
hydrocarbons. And the type of unsaturated
hydrocarbon that contains one or more triple carbon-to-carbon bonds is called an
alkyne.

So weβve determined that the
molecule belongs to a class of hydrocarbons called alkynes. At this point, it would be helpful
for us to write a molecular formula for the given molecule. A molecular formula is a chemical
formula expressing the exact number and type of atoms of each element in a
molecule. To write a molecular formula, we
will need to count up the total number of carbon and hydrogen atoms in the
molecule. According to the displayed formula,
there are a total of six carbon atoms in the molecule and there are a total of 10
hydrogen atoms. In a molecular formula, the
subscripts to the right of each chemical symbol represent the number of that type of
atom in the molecule. Therefore, the molecular formula of
the given molecule is C6H10.

Now, the question is asking us to
find a general formula for the group of compounds that the given molecule belongs
to. So we need to know the general
formula of an alkyne. The general formula of an alkyne is
CπH2πβ2. In this formula, π represents the
number of carbon atoms in the alkyne molecule. The alkyne given in the problem
contains six carbon atoms. Therefore, when using the general
formula, π is equal to six. After substitution, we get
C6H2(6)β2. After simplifying, we get the
expected molecular formula, C6H10. The general formula of an alkyne
represents the molecular formula of any alkyne, such as the one in this problem.

Letβs demonstrate this relationship
by looking at the two simplest alkynes: ethyne, or acetylene, and propyne. According to the displayed formula,
the ethyne molecule contains two carbon atoms. Therefore, we will need to
substitute two for π in the general formula. After substitution, we get
C2H2(2)β2. After simplification, we get C2H2,
which is the correct molecular formula for ethyne. The propyne molecule contains three
carbon atoms. Therefore, we will need to
substitute three for π in the general formula for an alkyne. This gives us C3H2(3)β2. After simplification, we get C3H4,
which is the correct molecular formula for the propyne molecule.

In conclusion, the general formula
for the group of the compounds to which the following displayed formula is related
is CπH2πβ2.