In the open-chain Fischer projection of D-galactose, the -OH groups at C2, C3, and C4 are located on the right, left, and left sides of the carbon chain, respectively. When D-galactose forms a cyclic -pyranose ring, what are the relative orientations (up or down) of the -OH groups at C1, C2, C3, and C4 in its standard Haworth projection?

Step-by-step solution

In the Fischer projection of D-galactose, the -OH groups at C2, C3, and C4 are on the right, left, and left, respectively. When converting to a standard Haworth projection, groups on the right side of the Fischer projection point 'down', and groups on the left side point 'up'. Therefore, at C2 the -OH points down, at C3 the -OH points up, and at C4 the -OH points up. For the -anomer of a D-sugar, the anomeric -OH group at C1 is cis to the terminal -CH₂OH group (which points up). Thus, the -OH at C1 must point up. T