Problem 80 - 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 each 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 \(\mathrm{CH}_{3}\mathrm{CH}(\mathrm{OH})\mathrm{COOH}\) can be drawn with 6 σ (sigma) bonds and 1 π (pi) bond. The shortest CO bond is in the carboxyl group, and the associated carbon atom has an \(\mathrm{sp^2}\) hybridization. Approximate bond angles around the carbon atoms are: 109.5° in the first two carbon atoms (with \(\mathrm{sp^3}\) hybridization), and 120° in the carbon atom within the carboxyl group (with \(\mathrm{sp^2}\) hybridization).

Step 1: (a) Draw the Lewis structure of \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\)

To draw the Lewis structure, we will first represent the atoms and their valence electrons: - Carbon (C): 4 valence electrons (C has four electrons in its valence shell) - Oxygen (O): 6 valence electrons - Hydrogen (H): 1 valence electron Now, we arrange these atoms in the given formula and connect them with single bonds, then complete the octet requirement around each atom by adding lone pairs or forming double bonds when necessary. The Lewis structure for lactic acid can be drawn as follows: O || C - C - OH | \ H C | O - H

Step 2: (b) Calculate the number of pi bonds and sigma bonds

In the Lewis structure, we can count the number of single and double bonds present. There are 6 single (σ) bonds and 1 double (π) bond. So, there are: - 6 σ (sigma) bonds - 1 π (pi) bond

Step 3: (c) Determine which CO bond is shortest

The shortest bond between two atoms typically occurs when there is a high number of electrons shared or a higher bond order. In this molecule, we have two different CO bonds: 1. The single bond (σ) between C and O in alcoholic group (-OH) 2. The double bond (π) between C and O in carboxyl group (-COOH) The double bond (π) will be shorter than the single bond (σ) due to increased electron density shared between the two atoms. So, the CO bond in the carboxyl group (-COOH) is the shortest CO bond in the molecule.

Step 4: (d) Identify the hybridization around each carbon atom associated with the short CO bond

To determine the hybridization of atomic orbitals around each carbon atom, we need to look at the number of electron domains (regions of electron density) around each carbon atom. The carbon atom in the carboxyl group (-COOH) has three electron domains: 1. One single (σ) bond with the adjacent carbon atom. 2. One double (π) bond with the oxygen atom in the carboxyl group. 3. One single (σ) bond with the oxygen atom, which then connects to a hydrogen atom. Given that it has three electron domains, the carbon atom's hybridization in the carboxyl group is \(\mathrm{sp^2}\).

Step 5: (e) Estimate the bond angles around each carbon atom in the molecule

We will look at the bond angles around each carbon atom by analyzing their hybridization. 1. The first carbon atom (adjacent to the two hydrogen atoms): This carbon atom is part of the methyl group and has a hybridization of \(\mathrm{sp^3}\) due to the four electron domains (3 single bonds with hydrogen atoms and 1 single bond with the adjacent carbon atom). In an \(\mathrm{sp^3}\)-hybridized atom, the bond angles are approximately 109.5°. 2. The second carbon atom (adjacent to the single-bonded oxygen atom and the carboxyl group): This carbon atom also has \(\mathrm{sp^3}\) hybridization due to its four electron domains (1 single bond with the adjacent carbon atom, 1 single bond with a hydrogen atom, 1 single bond with an oxygen atom, 1 single bond with the carboxyl group carbon atom). The bond angles around this carbon atom are also approximately 109.5°. 3. The third carbon atom (within the carboxyl group): This carbon atom has an \(\mathrm{sp^2}\) hybridization, as discussed earlier. In an \(\mathrm{sp^2}\)-hybridized atom, the bond angles are approximately 120°.

Key Concepts

Lewis Structure

A Lewis structure is a representation of a molecule that shows the arrangement of atoms and the bonds between them. In the case of lactic acid, we start by identifying the valence electrons for each atom:

• Carbon (C) has 4 valence electrons.
• Oxygen (O) has 6 valence electrons.
• Hydrogen (H) has 1 valence electron.

Lactic acid is represented as \( \text{CH}_3 \text{CH(OH)COOH} \). To draw its Lewis structure, connect the carbon atoms linearly as they are central to the structure, connecting them with single bonds. In \( \text{CH}_3 \text{CH(OH)COOH} \), carbon forms a backbone with three main parts:

• \( \text{CH}_3 \) forming the end group.
• \( \text{CHOH} \) as the middle part.
• \( \text{COOH} \) as another end group.

Oxygen atoms are attached with double and single bonds according to their positions in hydroxyl (-OH) and carboxyl (-COOH) groups, completing their octets with lone pairs.

Hybridization

Hybridization describes the mixing of atomic orbitals to form new hybrid orbitals, which determine the geometry of a molecule. For lactic acid:

• The carbon in the \( \text{CH}_3 \) group is \( \text{sp}^3 \) hybridized, implying four sigma bonds with tetrahedral geometry.
• In the \( \text{CHOH} \) region, carbon is again \( \text{sp}^3 \) hybridized, as it forms single bonds with hydrogen and oxygen.
• The carbon within the \( \text{COOH} \) group is \( \text{sp}^2 \) hybridized due to its participation in a double bond with the oxygen, which involves three electron domains resulting in a planar trigonal geometry.

This hybridization affects the molecule’s stability and reactivity, with \( \text{sp}^2 \) allowing for a shorter bond length in the carboxyl group.

Sigma and Pi Bonds

Bonds in a molecule can be classified as sigma (\( \sigma \)) or pi (\( \pi \)) bonds:

• Sigma bonds are the first bonds formed between atoms. They can be visualized like a straight line connecting two nuclei, formed by the head-on overlapping of orbitals.
• Pi bonds occur when two orbitals overlap sideways.Typically, they occur in conjunction with an existing sigma bond, providing additional strength.They are found in double and triple bonds.

In lactic acid:

• We count 6 sigma bonds, which include single bonds between carbon-carbon, carbon-hydrogen, and carbon-oxygen.
• There is also 1 pi bond, found in the C=O double bond of the carboxyl group.

These sigma and pi bonds account for the structure and stability of the molecule.

Bond Angles

Bond angles give us an idea of the spatial arrangement of atoms, influenced by hybridization:

• For \( \text{sp}^3 \)-hybridized atoms, as found in the \( \text{CH}_3 \) and \( \text{CHOH} \) parts of lactic acid, the bond angles are approximately 109.5° due to a tetrahedral shape.
• For \( \text{sp}^2 \)-hybridized atoms, as in \( \text{COOH} \), the bond angles are approximately 120° due to the planar trigonal shape.

Understanding these angles helps predict molecule reactivity. Angles reflect the arrangement where electron pair repulsions are minimized, affecting molecular interactions.

Chemical Bond Length

The chemical bond length is the distance between the nuclei of two bonded atoms. It varies based on the type of bond:

• Single bonds (sigma only) are generally longer.
• Double bonds (sigma and pi) have intermediate lengths.
• Triple bonds (one sigma and two pi) are the shortest.

In lactic acid, the shortest bond is the C=O double bond in the carboxyl group. This bond is stronger and shorter due to the pi bond, allowing more electron density to hold the atoms closer together. Understanding bond length is vital, as shorter bonds typically mean stronger connections, influencing the molecule’s overall stability.