Problem 177 - Chemistry: An Atoms-Focused Approach

Question

Draw the Lewis structure for butane, \(\mathrm{C}_{4} \mathrm{H}_{10},\) given the structure contains four carbon atoms bonded in a row: \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}.\)

Step-by-Step Solution

Answer

Answer: The Lewis structure for butane is \(\mathrm{H_3C}\leftrightarrows(\mathrm{CH_2})\leftrightarrows(\mathrm{CH_2})\leftrightarrows(\mathrm{CH_3})\), and it does satisfy the octet rule for all carbon atoms.

Step 1: Count valence electrons

To determine the total number of valence electrons in butane, we first have to know the valence electrons of carbon (C) and hydrogen (H) atoms. Carbon has 4 valence electrons, and hydrogen has 1 valence electron. In butane, there are 4 carbon atoms and 10 hydrogen atoms. Therefore, the total number of valence electrons is: \(4 \times 4\; (C \,atoms) + 10 \times 1\; (H\, atoms) = 16 + 10 = 26\, valence\, electrons\)

Step 2: Arrange atoms and create single bonds

We know from the given information that butane has 4 carbon atoms bonded in a row: \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\). Now, let's connect these carbon atoms with single bonds. A single bond contains 2 valence electrons. Therefore, we have used \(3 \times 2 = 6\) valence electrons for the carbon bonds in the following arrangement: \(\mathrm{C}\overset{\displaystyle .}\mathrm{C}\overset{\displaystyle ..}\mathrm{C}\overset{\displaystyle .}\mathrm{C}\). We still have \(26 - 6 = 20\) valence electrons remaining for hydrogen atoms.

Step 3: Distribute remaining valence electrons and satisfy the octet rule

Now, we need to distribute the remaining 20 valence electrons among the carbon and hydrogen atoms to achieve a full octet (i.e., 8 electrons in the valence shell) for each carbon atom. Each hydrogen atom needs only 1 more electron to attain a full valence shell (2 electrons total). Since there are still 20 valence electrons remaining from our initial count of 26, the structure will be: \(\mathrm{H_3C}\leftrightarrows(\mathrm{CH_2})\leftrightarrows(\mathrm{CH_2})\leftrightarrows(\mathrm{CH_3})\) In this arrangement, there are 10 hydrogen atoms (which use up the remaining 20 valence electrons) and each carbon atom has a complete octet (with 4 single bonds).

Step 4: Check if the octet rule is satisfied

To confirm that the octet rule is satisfied, let's check for each atom in the final Lewis structure of butane: - All hydrogen atoms have two electrons, hence satisfying the duet rule. - All carbon atoms in the structure are bonded to four other atoms (either carbon or hydrogen), hence satisfying the octet rule with 8 valence electrons. In conclusion, the final Lewis structure for butane is: \(\mathrm{H_3C}\leftrightarrows(\mathrm{CH_2})\leftrightarrows(\mathrm{CH_2})\leftrightarrows(\mathrm{CH_3})\) and it satisfies both the duet rule for hydrogen and the octet rule for carbon atoms.

Key Concepts

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom. These electrons play a crucial role in chemical bonding as they are the ones that interact with other atoms. In the Lewis structure of a molecule, these are the electrons that are shared or transferred between atoms to create bonds. Understanding valence electrons helps us determine how atoms will bond and the shape of the molecule.
For example, in butane (C\(_4\)H\(_{10}\)), we calculate the total number of valence electrons by adding the valence electrons from each atom. Carbon, with the atomic number 6, has 4 valence electrons, and hydrogen, with the atomic number 1, has 1 valence electron. Thus, in butane:

• 4 carbon atoms each contribute 4 valence electrons: 4 \(\times\) 4 = 16
• 10 hydrogen atoms each contribute 1 valence electron: 10 \(\times\) 1 = 10

Adding these gives a total of 26 valence electrons for butane. These electrons will be used to create bonds in the structure, ensuring that each atom reaches its desired stable configuration.

Octet Rule

The octet rule is a key principle in chemistry that dictates that atoms tend to bond in such a way that each atom has eight electrons in its valence shell, leading to a stable electronic configuration similar to noble gases. This rule applies mostly to carbon, nitrogen, oxygen, and halogens in their bond formation.
While drawing the Lewis structure for butane, the octet rule guides us to ensure each carbon atom shares enough electrons to complete an octet. In butane, each carbon atom forms single bonds with four other atoms. This configuration results in each carbon atom having a total of 8 valence electrons, fulfilling the octet rule. Hydrogen, however, is an exception to the octet rule as it only requires 2 electrons, known as the duet rule. In the structure of butane, each hydrogen atom bonds with one carbon atom, sharing two electrons, thus achieving the duet configuration. It's critical to always check that the octet rule is satisfied when finalizing the Lewis structure of a molecule.

Butane

Butane is a simple hydrocarbon with the chemical formula C\(_4\)H\(_{10}\). It belongs to a group of compounds called alkanes, which consist of carbon and hydrogen atoms arranged in a straight or branched chain with only single bonds between carbon atoms.
The Lewis structure of butane illustrates its linear arrangement with four carbon atoms connected in a row: C-C-C-C. Each carbon atom makes single bonds with hydrogen atoms to fill the remaining available bonding sites. This arrangement ensures that each carbon atom satisfies the octet rule.

• The end carbon atoms (butane is C\(-CH_3\)CH\(_2\)CH\(_2\)CH_3) are each bonded to three hydrogen atoms and one other carbon atom, forming four covalent bonds.
• The middle carbon atoms each bond with two hydrogen atoms and two other carbon atoms.

By organizing carbon and hydrogen atoms in this way, we obtain the stable structure of butane where all atoms are appropriately bonded, with carbon atoms achieving an octet of electrons and hydrogen fulfilling the duet rule.