Creating stereochemically correct ring structures for D-Altrose can be challenging without graphical representations. However, I can describe the general structures and provide some information on the alpha and beta forms and mutarotation.
Furanose Ring (Five-Membered Ring):
In a furanose ring structure, you would typically have five carbons forming a ring.
The OH groups on carbon 2 and 4 would determine the stereochemistry, and they should be cis to each other (on the same side) for D-Altrose.
Pyranose Ring (Six-Membered Ring):
For a pyranose ring, you would have six carbons forming a ring.
The OH group on carbon 2 and 3 should be cis to each other, as should the OH group on carbon 4 and 5.
In the pyranose form, the OH on carbon 2 can be either "up" or "down." The "up" form is the beta form, and the "down" form is the alpha form. This can be represented using the Haworth projection.
To show the mutarotation, the alpha and beta forms interconvert through the open-chain structure. In this process, the OH group on carbon 2 switches from "up" (alpha) to "down" (beta) or vice versa. The other OH groups also adjust their positions accordingly. This change occurs when the hemiacetal bond between the anomeric carbon (carbon 1) and the oxygen in the ring opens and then reforms.
For the specific graphical representations, you may want to use a chemical drawing software or consult a chemistry textbook or resource with structural diagrams. This will give you a more precise visualization of D-Altrose's ring structures and how they undergo mutarotation.