Question

Arrange the alkanes in each set in order of increasing boiling point. (a) 2-Methylbutane, 2,2-dimethylpropane, and pentane (b) 3,3 -Dimethylheptane, 2,2,4-trimethylhexane, and nonane

Short answer

Question: Arrange the following alkanes in order of increasing boiling point: (a) 2-Methylbutane, 2,2-dimethylpropane, and pentane (b) 3,3-Dimethylheptane, 2,2,4-trimethylhexane, and nonane Answer: (a) 2,2-dimethylpropane < 2-methylbutane < Pentane (b) 2,2,4-trimethylhexane < 3,3-dimethylheptane < Nonane

Step-by-step solution

Write down the molecular formulas of the alkanes

Using the given names, we can determine the molecular formulas of the alkanes as follows: 2-methylbutane: \(\text{C}_{5}\text{H}_{12}\) 2,2-dimethylpropane: \(\text{C}_{5}\text{H}_{12}\) Pentane: \(\text{C}_{5}\text{H}_{12}\)

Examine the size and branching of each alkane

Now let's look at the size and branching of each alkane. 2-methylbutane: This alkane has one branch at position 2. 2,2-dimethylpropane: This alkane has two branches at position 2. Pentane: This is a linear alkane with no branches.

Arrange alkanes by boiling point

Based on the analysis of size and branching, we can arrange the alkanes by boiling point as follows: 2,2-dimethylpropane (highest branching) < 2-methylbutane (less branching) < Pentane (linear) (b) 3,3-Dimethylheptane, 2,2,4-trimethylhexane, and nonane

Write down the molecular formulas of the alkanes

Using the given names, we can determine the molecular formulas of the alkanes as follows. 3,3-dimethylheptane: \(\text{C}_{9}\text{H}_{20}\) 2,2,4-trimethylhexane: \(\text{C}_{9}\text{H}_{20}\) Nonane: \(\text{C}_{9}\text{H}_{20}\)

Examine the size and branching of each alkane

Let's look at the size and branching of each alkane. 3,3-dimethylheptane: This alkane has two branches at position 3. 2,2,4-trimethylhexane: This alkane has three branches, two at position 2, and one at position 4. Nonane: This is a linear alkane with no branches.

Arrange alkanes by boiling point

Based on the branching and size of the alkanes, we can arrange the alkanes by boiling point as follows: 2,2,4-trimethylhexane (highest branching) < 3,3-dimethylheptane (less branching) < Nonane (linear)

Key concepts

Alkane Structure

Alkanes, often referred to as paraffins, are hydrocarbon molecules made up of carbon and hydrogen atoms. They are characterized by single bonds between carbon atoms and have the general formula \( C_nH_{2n+2} \). The simplest alkane is methane \( CH_4 \), which consists of a single carbon atom bonded to four hydrogen atoms.

As the carbon chain gets longer, the complexity of the alkane increases. Alkanes can be either straight-chained or branched. A straight-chain alkane has a continuous chain of carbon atoms with hydrogen atoms filling the remaining valences. For example, pentane \( C_5H_{12} \) is a straight-chain alkane with five carbon atoms in a row.

In contrast, branched alkanes have one or more carbons attached to the main chain, creating a 'branch'. These branches can greatly affect the physical properties of the molecule. An example is 2-methylbutane, where a methyl group (CH3) is attached to the second carbon of butane, giving it a branching structure.

The structure of alkanes plays a crucial role in their physical properties, including melting points, boiling points, and solubility.

Molecular Branching

Molecular branching refers to the presence of alkyl groups that are attached to the main carbon chain of an organic molecule. In the context of alkanes, branches occur when carbon atoms bond in such a way that there are side chains attached to the main carbon backbone.

For instance, 2,2-dimethylpropane has a more complex branching pattern, with two methyl groups attached to the same carbon atom, creating a highly branched structure.

The degree of branching impacts the way molecules pack together in the liquid state, which influences the boiling points of the substance. Highly branched molecules are not able to pack as tightly as linear ones, which means there are fewer intermolecular forces to overcome when the substance is heated. As such, branched alkanes typically have lower boiling points than their unbranched counterparts.

Comparing Boiling Points

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. In alkanes, boiling points can be directly affected by the structure and branching of the molecule.

To compare the boiling points of alkanes, consider the molecular mass and the degree of branching. Longer, straight-chain alkanes have higher boiling points because they have more surface area for van der Waals forces, which are the attractive forces between molecules. For example, the linear structure of nonane allows for more contact between molecules, resulting in higher boiling points than its branched counterparts.

Pentane possesses a longer straight-chain compared to 2-methylbutane and 2,2-dimethylpropane, thus it can pack more closely with other molecules, leading to stronger intermolecular van der Waals forces which require more energy to break. As a result, pentane has the highest boiling point among the three.

As seen in the given exercise solutions, more branched alkanes have lower boiling points even if they share the same molecular formula. 2,2,4-trimethylhexane has a lower boiling point compared to 3,3-dimethylheptane and nonane due to its greater degree of branching which hinders the efficient packing of molecules.