Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
D-galactose has the Fischer pattern R L L R for C-2 to C-5, where R means the is on the right and L means it is on the left. Draw its β-pyranose form in a Haworth ring, with the ring oxygen at the back on the right. Count the groups that point up and the ones that point down, counting the anomeric too. Compare with β-D-glucopyranose, which has the pattern R L R R. How many ring carbons carry the on the other face?
The anomeric carbon is C-1 of an aldose. A group on the right of the Fischer projection points down in the Haworth ring and a group on the left points up. In a D sugar, the anomeric of the α form points down and that of the β form points up. The specific rotation is , with in dm and in g/mL.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Turn each letter into up or down. Then add the anomeric group.
Step 1. C-2 to C-4 of galactose. C-2 is R, so down. C-3 is L, so up. C-4 is L, so up. on C-5 is up.
Step 2. The anomeric group. In the β form, the on C-1 is up.
Step 3. Count. Up: C-1, C-3 and C-4, which is 3. Down: C-2, which is 1.
Step 4. Compare with β-D-glucopyranose. Glucose has R L R R, so its C-4 is down. The two sugars differ only at C-4, which is 1 carbon.
Answer: 3 groups up, 1 down, and 1 carbon differs from glucose. Galactose is the C-4 epimer.
Check. Glucose has 2 up and 2 down. Turning C-4 from down to up gives 3 up and 1 down.
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