Problem 93 - Chemistry The Central Science

Question

The lactic acid molecule, \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH},\) gives sour milk its unpleasant, sour taste. (a) Draw the Lewis structure for the molecule, assuming that carbon always forms four bonds in its stable compounds. (b) How many \(\pi\) and how many \(\sigma\) bonds are in the molecule? (c) Which CO bond is shortest in the molecule? (d) What is the hybridization of atomic orbitals around the carbon atom associated with that short bond? (e) What are the approximate bond angles around each carbon atom in the molecule?

Step-by-Step Solution

Answer

The Lewis structure of lactic acid is: O || H - C - C - OH | | H C - O - H | | H H It has 1 \(\pi\) bond (C=O) and 11 \(\sigma\) bonds. The shortest CO bond is the C=O double bond. The hybridization of the carbon atom associated with the C=O bond is \(sp^2\). The approximate bond angles around each carbon atom are: CH3 (109.5°), CH(OH)C (120°), and C=O (120°).

Step 1: Drawing the Lewis Structure

The molecule is CH3CH(OH)COOH, and knowing carbon forms four bonds in its stable compounds, the Lewis structure of lactic acid is: O || H - C - C - OH | | H C - O - H | | H H

Step 2: Counting the \(\pi\) and \(\sigma\) bonds

Now, count the \(π\) (pi) bonds and \(σ\) (sigma) bonds in the molecule. Pi bonds are formed due to the overlap of unhybridized p-orbitals. Since there is a double bond between C and O, there is one pi bond and one sigma bond in that C=O bond. Every single bond (like C-H, C-C, and C-O) is a sigma bond. - \(π\) (pi) bonds: 1 (in the C=O double bond) - \(σ\) (sigma) bonds: 11 (3 C-H bonds, 1 C-C bond, 1 C-O bond, 1 C=O bond, and 1 O-H bond)

Step 3: Identifying the shortest CO bond

The two CO bonds in the molecule are: 1. The single bond C-O in the CH(OH) group 2. The double bond C=O The double bond between C and O is shorter than the single bond between C and O. This is because the double bond have increased electron density between the carbon and oxygen atoms, resulting in stronger attraction and a shorter bond length. So, the shortest CO bond is the C=O double bond.

Step 4: Finding the hybridization of atomic orbitals

To determine the hybridization of atomic orbitals around the carbon atom associated with the short (double) bond, consider the number of electron groups (bonding and non-bonding electron pairs) around that carbon atom: 1. C=O double bond (1 group for sigma bond and 1 group for pi bond) 2. C-C single bond (1 group) 3. No lone pair These electron groups require 3 hybrid orbitals, so the hybridization of that carbon atom is \(sp^2\).

Step 5: Estimating the bond angles around each carbon atom

To estimate the bond angles around each carbon atom in the molecule, consider the hybridization of each carbon atom: 1. The first carbon atom (CH3) has 3 sigma bonds and is \(sp^3\) hybridized. The bond angles around an \(sp^3\) hybridized carbon are approximately 109.5 degrees. 2. The second carbon atom (CH(OH)C) has 3 sigma bonds and is \(sp^2\) hybridized. The bond angles around an \(sp^2\) hybridized carbon are approximately 120 degrees. 3. The third carbon atom (C=O) has 3 sigma bonds and is \(sp^2\) hybridized. The bond angles around an \(sp^2\) hybridized carbon are approximately 120 degrees. So, approximate bond angles around each carbon atom are: CH3 : 109.5 degrees CH(OH)C: 120 degrees C=O: 120 degrees

Key Concepts

Lewis Structures

The Lewis structure is a diagram that shows the arrangement of atoms in a molecule and the bonds between them using dots and lines. In the case of lactic acid (\(\mathrm{CH}_3\mathrm{CH}(\mathrm{OH})\mathrm{COOH} \)), drawing the Lewis structure involves representing each atom's valence electrons. The main rule to follow is that carbon typically forms four bonds. These can be a combination of single, double, or triple bonds, ensuring it is stable.

For lactic acid, the structure reveals:

• Three carbons, each engaging in four bonds.
• An OH group bonded to the middle carbon.
• A carboxyl group (COOH) attached to the terminal carbon.
• Every other bond is formed by hydrogen atoms ensuring the carbon's tetravalency.

The result is a stable Lewis structure that helps visualize how atoms are bonded.

Pi and Sigma Bonds

Sigma (\(\sigma\)) and pi (\(\pi\)) bonds are the types of covalent bonds that determine molecular structure. A sigma bond is the strongest type of covalent bond, formed by the head-on overlap of atomic orbitals. In contrast, a pi bond is formed by the side-to-side overlap of p-orbitals.

In lactic acid, the molecule forms:

• 11 sigma bonds, including single bonds like C-H, C-C, C-O, and O-H. These bonds are vital for holding the basic shape together.
• One pi bond between the carbon and oxygen in the \(\mathrm{C}=\mathrm{O} \) double bond, adding rigidity and planarity to this part of the molecule.

Understanding the number of \(\sigma\) and \(\pi\) bonds explains the molecule's stability and reactivity.

Bond Lengths

Bond length refers to the distance between two bonded atoms' nuclei in a molecule. It's influenced by the number of bonded electrons. More shared electrons generally result in shorter bonds.

In the lactic acid molecule, there are two types of C-O bonds. One is a single bond, and the other is a double bond. Typically, double bonds such as \(\mathrm{C}=\mathrm{O} \) are shorter than single bonds like \(\mathrm{C}-\mathrm{O} \). Why?

• Double bonds involve sharing more electrons, increasing the attraction and pulling the two atoms closer.
• The increased electron density results in a shorter bond length.

Thus, the \(\mathrm{C}=\mathrm{O} \) bond in lactic acid is shorter.

Hybridization

Hybridization involves mixing atomic orbitals to create new hybrid orbitals, which dictate the geometry around an atom in a molecule. Each carbon in lactic acid uses different hybrids depending on its bonds.

Examining the carbon connected to the \(\mathrm{C}=\mathrm{O} \) double bond:

• This carbon is \(sp^2\) hybridized, indicating three groups of orbitals are blended (one \(s\) and two \(p\)).
• The \(sp^2\) hybridization results in a trigonal planar shape, typical for areas involving double bonds.

Hybridization explains both the bond strength and the shape of molecules, revealing why certain bonds exist as they do.

Bond Angles

Bond angles in a molecule refer to the angle between two adjacent bonds at an atom. These angles reveal insights into the molecular shape and are influenced by hybridization.

In lactic acid:

• The \(\mathrm{CH}_3\) group's carbon, being \(sp^3\) hybridized, exhibits approximately 109.5-degree angles typical for tetrahedral shapes.
• The central carbon, connected to an \(\mathrm{OH} \) and the \(\mathrm{COOH} \), is \(sp^2\) hybridized, so bond angles are about 120 degrees, reflecting a trigonal planar arrangement.
• The third carbon, part of the \(\mathrm{C}=\mathrm{O} \) bond, also shows a 120-degree angle due to its \(sp^2\) hybridization.

Recognizing these angles assists in visualizing the 3D shape of molecules and predicting chemical behavior.