Draw cyclic structures for D-ribose and D-mannose.

First, let's draw the Fischer projection for D-ribose and D-mannose (linear structure). D-ribose is an aldopentose sugar, and D-mannose is an aldohexose sugar. To draw the Fischer projection, we need to represent the carbon chain in a vertical line and the hydroxyl groups (OH) at right angles according to the following orientations: For D-ribose: D-ribose - Carbon atoms: C-1 to C-5 C-1: The carbonyl group forming an aldehyde. C-2: OH on the right side. C-3: OH on the left side. C-4: OH on the right side. C-5: CH₂OH on the right side For D-mannose: D-mannose - Carbon atoms: C-1 to C-6 C-1: The carbonyl group forming an aldehyde. C-2: OH on the left side. C-3: OH on the right side. C-4: OH on the right side. C-5: OH on the left side. C-6: CH₂OH on the right side. Now we have the linear Fischer projections for both D-ribose and D-mannose.

Now, let's convert the Fischer projection to the Haworth projection, which better represents the cyclic structure. We'll form the cyclic structures through an intramolecular hemiacetal formation which requires a reaction between the carbonyl carbon (C-1) and the hydroxyl (OH) group at the last stereogenic carbon in the Fischer projection (C-4 in D-ribose and C-5 in D-mannose). For D-ribose: 1. Rotate the -OH group on C-4 upwards, forming a bond with the C-1 carbonyl (also rotate the CH₂OH group at C-5 upwards). 2. The C-1 carbonyl carbon forms a new stereocenter, creating an anomeric carbon (C-1) with two possible configurations: alpha (α) or beta (β). In the alpha configuration, the -OH of the newly formed anomeric carbon points down while the β configuration has the -OH pointing up. 3. Draw both α and β anomers of D-ribose in the Haworth projection. For D-mannose: 1. Rotate the -OH group on C-5 upwards, forming a bond with the C-1 carbonyl (also rotate the CH₂OH group at C-6 upwards). 2. The C-1 carbonyl carbon forms a new stereocenter, creating an anomeric carbon (C-1) with two possible configurations: alpha (α) or beta (β). In the alpha configuration, the -OH of the newly formed anomeric carbon points down while the β configuration has the -OH pointing up. 3. Draw both α and β anomers of D-mannose in the Haworth projection. Now we have cyclic structures for both D-ribose and D-mannose, in α and β anomeric configurations.