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 \(\boldsymbol{\sigma}\) 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?

Short answer

The Lewis structure for lactic acid is: O=C-C-OH │ OH The molecule has 11 σ bonds and 2 π bonds. The shortest CO bond is the C=O double bond. The carbon atom associated with this bond has sp^2 hybridization. The approximate bond angles around this sp^2 hybridized carbon atom are 120°, and around the sp^3 hybridized carbon atom are 109.5°.

Step-by-step solution

a) Drawing the Lewis structure

The Lewis structure is a diagram that shows the distribution of electrons in a molecule. First, find the number of valence electrons: - Carbon (C): 4 valence electrons - Hydrogen (H): 1 valence electron - Oxygen (O): 6 valence electrons There are two Carbon atoms, six Hydrogen atoms, and three Oxygen atoms in the lactic acid molecule. Total valence electrons = 2(4) + 6(1) + 3(6) = 8 + 6 + 18 = 32 Now, draw the Lewis structure by connecting the atoms with shared pairs of electrons (covalent bonds) and distributing the remaining electrons around each atom to fulfill the octet rule (2 electrons for Hydrogen and 8 electrons for Carbon and Oxygen). The Lewis structure for lactic acid is: O=C-C-OH │ OH

b) Determining the number of π and σ bonds

In a molecule, there are two types of covalent bonds: σ (sigma) bonds and π (pi) bonds. σ bonds are formed by the overlap of atomic orbitals along the axis between two atoms, whereas π bonds are formed from parallel P orbitals. We can determine the number of π and σ bonds from the Lewis structure. - One C=C double bond (containing 1 σ bond and 1 π bond) - Two C-C single bonds (containing 2 σ bonds) - Two C-O single bonds (containing 2 σ bonds) - One C=O double bond (containing 1 σ bond and 1 π bond) - Three C-H single bonds (containing 3 σ bonds) - Two O-H single bonds (containing 2 σ bonds) In total, there are 1+2+2+1+3+2 = 11 σ bonds and 1+1 = 2 π bonds in the lactic acid molecule.

c) Identifying the shortest CO bond

Double bonds are shorter than single bonds due to greater electron density between the bonded atoms. Therefore, the shortest CO bond in the lactic acid molecule is the C=O double bond.

d) Determining the hybridization of atomic orbitals

To determine the hybridization of the carbon atom associated with the shortest CO bond (C=O), count the number of electron domains around the carbon atom: 1 double bond, 1 single bond, and no lone pairs. The carbon atom has 3 electron domains, meaning it undergoes sp^2 hybridization.

e) Approximating bond angles around each carbon atom

The approximate bond angles around each carbon atom depend on the hybridization: - sp^2 hybridized carbon (associated with the C=O bond): The geometry around an sp^2 hybridized carbon is trigonal planar, with bond angles of approximately 120°. - sp^3 hybridized carbon (associated with the C-C bond): The geometry around an sp^3 hybridized carbon is tetrahedral, with bond angles of approximately 109.5°. In conclusion, the approximate bond angles around the sp^2 hybridized carbon atom are 120°, and around the sp^3 hybridized carbon atom are 109.5° in the lactic acid molecule.

Key concepts

Hybridization

Hybridization is a concept used to explain the bonding within molecules through the mixing of atomic orbitals to create new hybrid orbitals. These hybrid orbitals help predict the geometry of molecules and how atoms in a molecule bond. In the case of lactic acid, which contains carbon atoms forming different bonds, understanding the hybridization helps explain the molecule's shape and bond angles.

Each carbon atom in the lactic acid molecule can undergo different types of hybridization depending on its bonding environment:

• sp² Hybridization: This occurs in carbon atoms that have one double bond, like the carbon in the C=O bond. It involves mixing one s orbital with two p orbitals to form three equivalent sp² hybrid orbitals, which are arranged in a trigonal planar shape with bond angles of approximately 120°.
• sp³ Hybridization: This is seen in carbon atoms bonded with four single bonds, such as the carbon atoms forming C-H and C-C bonds in lactic acid. An s orbital mixes with three p orbitals to form four sp³ hybrid orbitals which arrange themselves in a tetrahedral shape, resulting in bond angles of roughly 109.5°.

Sigma and Pi Bonds

In the world of chemistry, sigma and pi bonds are the building blocks of molecular structure. They describe how atoms share electrons to form molecules. In the lactic acid molecule, which you might recognize by its sour contribution to milk, these bonds define its chemical framework.

- **Sigma ( \( \sigma \) ) Bonds** are the primary form of covalent bonding, formed by the direct overlap of atomic orbitals along the axis between two bonded nuclei. In lactic acid, these bonds make up the single bonds found between carbon and hydrogen (C-H), carbon and carbon (C-C), and carbon and oxygen (C-O). Since these bonds overlap directly between the nuclei, sigma bonds are generally stronger than pi bonds. In total, lactic acid contains 11 sigma bonds.

• 3 C-H bonds
• 2 C-C bonds
• 2 O-H bonds

- **Pi ( \( \pi \) ) Bonds**, on the other hand, arise from the sideways overlap of p orbitals. These are present when atoms are connected by double bonds or triple bonds. In lactic acid, the pi bonds are found in the C=O double bond, adding additional electron density parallel to the sigma bond. Lactic acid has 2 pi bonds.

Understanding the distribution and nature of these bonds helps chemists predict molecule stability, reactivity, and physical properties.

Valence Electrons

Valence electrons are the electrons available in the outermost shell of an atom and are crucial for understanding how atoms bond and form molecules. They determine an atom's chemical properties and its ability to bond with other atoms.

In forming lactic acid, knowing the count of valence electrons from each participating atom allows you to build the molecule's Lewis structure. For example:

• Carbon, with an atomic number of 6, has 4 valence electrons in its outer shell.
• Hydrogen, which has an atomic number of 1, contributes 1 valence electron.
• Oxygen, with its 8 electrons, provides 6 valence electrons.

To correctly draw a molecule's Lewis structure, sum all valence electrons from each atom in the molecule. In lactic acid (\(\text{CH}_3\text{CH}(\text{OH})\text{COOH}\)) , we find a total of 32 valence electrons.

• 2 carbons: 2 × 4 = 8 electrons
• 6 hydrogens: 6 × 1 = 6 electrons
• 3 oxygens: 3 × 6 = 18 electrons

The distribution of these electrons informs us on how the atoms will bond together, forming a stable molecule with all atoms achieving a complete outer shell, according to the octet rule for main group elements (Hydrogen being the exception with a duet).

Bond Angles

Bond angles offer insight into the spatial orientation of bonded atoms within a molecule, revealing the overall shape and structural characteristics of the molecule. They are fundamentally determined by the arrangement of hybrid orbitals and the repulsion between electron pairs.

In lactic acid, two primary regions dictate the bond angles due to different hybridizations of carbon atoms:

• Trigonally Planar around sp² Hybridized Carbon: For the carbon atom involved in the C=O double bond, the bond angle is about 120°. This setup results from the plane formed by the three sp² hybrid orbitals, which aim to minimize repulsion between the electron pairs.
• Tetrahedral around sp³ Hybridized Carbon: For carbon atoms connected to the single bonds (like C-C and C-H bonds in lactic acid), the bond angles are approximately 109.5° due to the four sp³ hybridized orbitals, which form a tetrahedral shape maximizing the distance between each bond pair.

Understanding the bond angles helps explain both the two-dimensional (on paper) and three-dimensional (in space) molecular geometries, illuminating how we perceive molecular motion and reaction pathways.