Which one of the following is the general formula of Alkenes?

Question

Prepp Team · Accepted Answer

Let's break down the general formula for alkenes. Alkenes are a type of hydrocarbon, which means they are organic compounds made up entirely of hydrogen and carbon atoms.

Understanding Alkenes and Their Structure

The defining feature of an alkene is the presence of at least one carbon-carbon double bond ($C=C$). This double bond affects the number of hydrogen atoms present compared to alkanes, which only have single bonds.

Hydrocarbons can be classified into different homologous series based on their structure and functional groups. Alkenes form a homologous series.

General Formula for Alkenes

In a homologous series, members have a general formula that relates the number of carbon atoms ($n$) to the number of hydrogen atoms. For alkenes with only one double bond ( acyclic or open-chain alkenes), the general formula is:

C$_{n}$H$_{2n}$

Here, $n$ represents the number of carbon atoms in the molecule. The smallest alkene has two carbon atoms ($n=2$) because you need at least two carbons to form a double bond.

Examples of Alkenes

Let's look at a few simple alkenes and see how their formulas fit the general formula C$_{n}$H$_{2n}$:

When $n=2$, the formula is C$_{2}$H$_{2 \times 2}$ = C$_{2}$H$_{4}$. This is ethene (also known as ethylene).
When $n=3$, the formula is C$_{3}$H$_{2 \times 3}$ = C$_{3}$H$_{6}$. This is propene (also known as propylene).
When $n=4$, the formula is C$_{4}$H$_{2 \times 4}$ = C$_{4}$H$_{8}$. This can be but-1-ene or but-2-ene.

In each case, the number of hydrogen atoms is exactly double the number of carbon atoms.

Analyzing the Given Options

Let's compare the provided options with the correct general formula for alkenes:

C$_{n}$H$_{n}$:

This formula does not represent simple alkenes. For example, if $n=2$, it would be C$_{2}$H$_{2}$, which is ethyne (acetylene), an alkyne with a triple bond.
C$_{n}$H$_{2n}$:

As discussed, this is the correct general formula for alkenes with one carbon-carbon double bond.
C$_{n}$H$_{2n+1}$:

This formula represents alkyl radicals (like methyl, ethyl, etc.), which are formed by removing one hydrogen atom from an alkane.
C$_{n}$H$_{2n+2}$:

This is the general formula for alkanes, which are saturated hydrocarbons with only single bonds (e.g., methane CH$_{4}$, ethane C$_{2}$H$_{6}$, propane C$_{3}$H$_{8}$).

Therefore, the option that correctly represents the general formula of alkenes is C$_{n}$H$_{2n}$.

Revision Table: Hydrocarbon General Formulas

Hydrocarbon Type	Bond Type	General Formula	Example ($n=2$)
Alkanes	Single Bonds only	C$_{n}$H$_{2n+2}$	C$_{2}$H$_{6}$ (Ethane)
Alkenes (one double bond)	At least one Double Bond	C$_{n}$H$_{2n}$	C$_{2}$H$_{4}$ (Ethene)
Alkynes (one triple bond)	At least one Triple Bond	C$_{n}$H$_{2n-2}$	C$_{2}$H$_{2}$ (Ethyne)

Additional Information: Alkenes and Hydrocarbons

Alkenes are unsaturated hydrocarbons because they contain a double bond, allowing them to add more atoms (like hydrogen, halogens, water) across the double bond. This reactivity makes alkenes important starting materials in many industrial processes, such as the production of polymers (e.g., polythene from ethene).

The C=C double bond consists of one sigma ($\sigma$) bond and one pi ($\pi$) bond. The pi bond is weaker and more reactive than the sigma bond, which is why alkenes undergo addition reactions easily.

Cycloalkenes are cyclic hydrocarbons containing a double bond. Their general formula is C$_{n}$H$_{2n-2}$ for one double bond in a ring, similar to alkynes. However, the question asks for the general formula of "Alkenes" without specifying cyclic, implying the simple acyclic ones which follow C$_{n}$H$_{2n}$.

Homologous series have members with similar chemical properties and gradually changing physical properties as the molecular weight increases. The difference between consecutive members in a homologous series like alkenes is a -CH$_{2}$- group.