Question

Write structural formulas for the normal (straightchain) alkanes with a. seven carbon atoms. b. eleven carbon atoms. c. sixteen carbon atoms.

Short answer

The structural formulas for the straight-chain alkanes with the given number of carbon atoms are: a. Seven carbon atoms: \(C_7H_{16}\) - CH3-CH2-CH2-CH2-CH2-CH2-CH3 b. Eleven carbon atoms: \(C_{11}H_{24}\) - CH3-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3 c. Sixteen carbon atoms: \(C_{16}H_{34}\) - CH3-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3

Step-by-step solution

Construct the Alkane with Seven Carbon Atoms

The general formula for alkanes is \(C_nH_{2n+2}\), allowing calculation of the number of hydrogen atoms for an alkane with seven carbon atoms. Substituting \(n = 7\) into the formula will give \(C_7H_{16}\), meaning that there are 16 hydrogen atoms. The structural notation would represent these atoms as follows: CH3-CH2-CH2-CH2-CH2-CH2-CH3 This chemical structure indicates that each carbon atom (C) is attached to at least two hydrogen atoms (H), except the two end carbons which are attached to three.

Construct the Alkane with Eleven Carbon Atoms

Following the same method, substituting \(n = 11\) into the general formula \(C_nH_{2n+2}\) for alkanes gives \(C_{11}H_{24}\), meaning that the alkane with eleven carbon atoms has 24 hydrogen atoms. Its structural notation would be as follows: CH3-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3 As it can be seen, in the straight-chain alkane, each carbon atom (C) is attached to two hydrogen atoms (H), except for the two end carbons that are bonded to three hydrogen atoms.

Construct the Alkane with Sixteen Carbon Atoms

Finally, substituting \(n = 16\) into the formula \(C_nH_{2n+2}\) gives \(C_{16}H_{34}\), meaning that the alkane with sixteen carbon atoms has 34 hydrogen atoms. The alkane with sixteen carbon atoms can be represented with the following structural formula: CH3-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH2-CH3 Again, in this straight-chain alkane, each carbon atom (except for the ones at the extremities) is bonded to two hydrogen atoms, while the two end carbon atoms are each attached to three hydrogen atoms.

Key concepts

The Alkane General Formula

Understanding the general formula of alkanes is a fundamental aspect of organic chemistry. Alkanes are a class of hydrocarbons that consist only of the elements carbon (C) and hydrogen (H), and they are known for having single bonds between carbon atoms. The general formula for alkanes is expressed as \(C_nH_{2n+2}\).

This formula indicates that for every 'n' number of carbon atoms, an alkane will have '2n+2' hydrogen atoms. To find the specific number of hydrogen atoms in an alkane, simply plug the number of carbon atoms into 'n' in the formula. For instance, if an alkane has seven carbon atoms (n=7), as shown in the exercise, we substitute 7 into the formula to give us \(C_7H_{16}\).

The reason why this formula works is due to the tetrahedral geometry of carbon atoms in alkanes. Each carbon atom can form a maximum of four bonds. In a straight-chain alkane, every carbon atom is bonded to two other carbon atoms (except for the ends of the chain) and to enough hydrogen atoms to fulfill the four bonds, thus resulting in the \(C_nH_{2n+2}\) general formula.

Hydrocarbon Chain Representation

How we represent hydrocarbon chains, particularly alkanes, is crucial for visualizing their structure and understanding chemical reactions they may undergo. The most basic representation is the straight-chain, or 'normal', structure.

In a straight-chain alkane, each carbon atom is connected to the adjacent carbon atoms by single bonds and to hydrogen atoms to satisfy the four bonds that carbon can form. At the beginning and end of the chain, carbon atoms bond with three hydrogen atoms, while all other carbons in the chain bond with two hydrogen atoms. Thus, a straight-chain alkane looks like a successive chain of CH2 units, capped with CH3 at both ends.

For example, to visualize an alkane with seven carbon atoms, we would write the formula starting and ending with CH3 (methyl groups), and connecting CH2 (methylene groups) in between: CH3-CH2-CH2-CH2-CH2-CH2-CH3. This elongates the chain by one CH2 group for each additional carbon. The representation grows systematically as we increase the number of carbon atoms, showing the repetitive, scaffold nature of alkane structures.

Organic Chemistry Nomenclature

Nomenclature, or the system of naming, in organic chemistry is essential for clear and accurate communication. It allows chemists to systematically name compounds based on their structure, ensuring that each name conveys precise information about the molecular composition of the compound.

The naming of alkanes is governed by rules set out by the International Union of Pure and Applied Chemistry (IUPAC). The root of an alkane's name indicates the number of carbon atoms in the chain. For example, 'meth-' implies one carbon, 'eth-' two carbons, followed by 'prop-' for three, 'but-' for four, and so on. To signify that the compound is an alkane (all single bonds between carbons), the ending '-ane' is added to the root.

As a result, an alkane with one carbon atom is methane (CH4), with two is ethane (C2H6), and with three is propane (C3H8). The nomenclature becomes more complex with branched or substituted alkanes, but the straight-chain alkanes follow this straightforward pattern. Using these rules, students can confidently name alkanes of varying lengths and understand the structure behind each name.