Question

Which of the following molecular formulas represents an alkene? (a) \(\mathrm{C}_{10} \mathrm{H}_{22}\) (b) \(\mathrm{C}_{10} \mathrm{H}_{20}\)

Short answer

The molecular formula \( ext{C}_{10} ext{H}_{20}\) (option b) represents an alkene.

Step-by-step solution

Understand Alkene General Formula

Alkenes are hydrocarbons that contain at least one carbon-to-carbon double bond. The general formula for alkenes is given by \( ext{C}_{n} ext{H}_{2n}\), where \(n\) is the number of carbon atoms in the molecule.

Compare Given Molecular Formulas to Alkene Formula

Let's compare the given options to the formula for alkenes:- (a) \( ext{C}_{10} ext{H}_{22}\) doesn't match the alkene formula \( ext{C}_{n} ext{H}_{2n}\) because \(22 eq 2 \times 10\).- (b) \( ext{C}_{10} ext{H}_{20}\) does match because \(20 = 2 \times 10\), fitting the general formula for alkenes.

Identify the Correct Option

From the comparison, option (b) \( ext{C}_{10} ext{H}_{20}\) fits the general alkene formula \( ext{C}_{n} ext{H}_{2n}\). Therefore, it correctly represents an alkene.

Key concepts

Molecular Formulas

Molecular formulas are essential for understanding the composition of a molecule. They show the elements present and their quantities. For instance, a molecule with the formula \(\mathrm{C}_{10}\mathrm{H}_{20}\) indicates it contains 10 carbon atoms and 20 hydrogen atoms. This formula provides insights into the molecule's potential class, like whether it might be an alkene or not.
The general formula for alkenes, \(\mathrm{C}_{n}\mathrm{H}_{2n}\), explains a lot about their structure. Alkenes will always have twice as many hydrogen atoms as carbon atoms. Calculating molecular formulas accurately can help distinguish between different molecular classes such as alkanes, alkenes, and alkynes.
Given examples illustrate the point:

• \(\mathrm{C}_{10}\mathrm{H}_{22}\) does not fit the alkene formula because 22 is not twice 10.
• \(\mathrm{C}_{10}\mathrm{H}_{20}\), however, matches perfectly because 20 equals two times 10.

The alignment or mismatch of molecular formulas with the general alkene formula helps to classify them correctly.

Carbon-to-Carbon Double Bond

The defining feature of alkenes is the carbon-to-carbon double bond. Unlike single bonds, double bonds involve two pairs of shared electrons. This makes the molecule more rigid and introduces distinctive chemical properties.
In alkenes, such double bonds contribute to reactivity patterns such as addition reactions. The double bond's presence is also responsible for the reduced number of hydrogen atoms in molecules compared to single bonded (alkane) structures.
The double bond in alkenes is influential in the molecular geometry. It restricts the rotation around the bond, making the molecule planar around this region. This rigidity can affect how molecules interact with each other, contributing to their physical properties and interaction with light.

Hydrocarbons

Hydrocarbons are organic compounds composed entirely of hydrogen and carbon atoms. They form the backbone of organic chemistry and come in different types such as alkanes, alkenes, and alkynes.
Alkenes, a type of hydrocarbon, are distinguishable by their carbon-to-carbon double bonds as seen in molecules like \(\mathrm{C}_{10}\mathrm{H}_{20}\). Hydrocarbons are broadly classified based on the type of bonding and saturation state.
Alkanes have only single bonds and are saturated, meaning they have the maximum number of hydrogen atoms. Alkenes, having double bonds, are unsaturated and have fewer hydrogen atoms.

• They play vital roles as fuels, precursors for plastics, and in the production of many chemical products.
• Understanding hydrocarbons helps in comprehending larger biological and synthetic structures.

This classification based on bonds and hydrogen content forms the basis of studying hydrocarbon chemistry.