Use the structure of d-galactose in Problem 6.15 to answer the following: 
(b) Draw the Fischer projection of l-galactose.

Verified step by step guidance

1. Understand the structure of D-galactose: D-galactose is an aldohexose, which means it is a six-carbon sugar with an aldehyde group. In its Fischer projection, the hydroxyl groups (OH) are arranged in a specific pattern along the carbon chain.
2. Identify the stereochemistry of D-galactose: In the Fischer projection of D-galactose, the hydroxyl groups on the chiral centers (C2, C3, C4, and C5) are arranged as follows: C2 - OH on the right, C3 - OH on the left, C4 - OH on the right, C5 - OH on the right.
3. Convert D-galactose to L-galactose: To convert D-galactose to L-galactose, invert the configuration at every chiral center. This means that for L-galactose, the hydroxyl groups will be: C2 - OH on the left, C3 - OH on the right, C4 - OH on the left, C5 - OH on the left.
4. Draw the Fischer projection for L-galactose: Start with the aldehyde group at the top (C1), then draw the carbon chain vertically. Place the hydroxyl groups according to the L-galactose configuration determined in the previous step.
5. Verify the structure: Ensure that the drawn Fischer projection correctly represents L-galactose by checking that the hydroxyl groups are placed as determined and that the overall structure is consistent with the L-configuration.

Key Concepts

Fischer Projection

The Fischer projection is a two-dimensional representation of a molecule that shows the configuration of its stereocenters. In this format, vertical lines represent bonds that go behind the plane of the page, while horizontal lines represent bonds that come out of the page. This method is particularly useful for visualizing carbohydrates and amino acids, allowing for easy identification of their stereochemistry.

D-Galactose vs. L-Galactose

D-galactose and L-galactose are stereoisomers, differing in the configuration around one or more of their chiral centers. The 'D' and 'L' designations refer to the orientation of the hydroxyl group on the penultimate carbon (the second to last carbon) in the Fischer projection. Understanding this distinction is crucial for accurately drawing the Fischer projection of L-galactose based on the structure of D-galactose.

Stereochemistry

Stereochemistry is the study of the spatial arrangement of atoms in molecules and how this affects their chemical properties and reactions. In carbohydrates like galactose, the specific arrangement of hydroxyl groups and hydrogen atoms around chiral centers determines the molecule's identity and function. A solid grasp of stereochemistry is essential for accurately representing and manipulating molecular structures in organic chemistry.