Final answer:
The Fischer projection of (2R, 3S)-2,3-dibromopentane is drawn with the longest chain vertically, bromines at C2 and C3 according to R and S configurations, chiral centers at C2 and C3, and the IUPAC name of the compound is 2,3-dibromopentane.
Step-by-step explanation:
To draw the Fischer projection for (2R, 3S)-2,3-dibromopentane, follow these rules: Place the longest carbon chain vertically with the most oxidized carbon at the top. The two bromine atoms will be on carbon 2 and 3. For the chiral centers, carbon 2 (C2) will have the Br on the left and H on the right, whereas carbon 3 (C3) will have the Br on the right and H on the left, assuming the lowest priority groups are projecting backwards (vertical line).
The chiral centers in the compound are the second and third carbon atoms, as they are bonded to four different groups.
The IUPAC name for (2R, 3S)-2,3-dibromopentane is 2,3-dibromopentane, as it is a five-carbon alkane (pentane) with bromine substituents on the second and third carbons.
Regarding the stereochemistry of the bromine substituents, the (2R) configuration means that the substituents on the second carbon are arranged in a clockwise manner, and the (3S) configuration means those on the third carbon are arranged in a counterclockwise manner, considering the priority of the groups attached to each chiral carbon.