Step 1: Understanding the Question:
The question describes an artificial sweetener, X, which is composed of two specific chlorinated sugar units: $4\text{-chloro-}4\text{-deoxy-}\alpha\text{-D-galactopyranose}$ and $1,6\text{-dichloro-}1,6\text{-dideoxy-}\beta\text{-D-fructofuranose}$. This compound is commercially known as Sucralose.
Step 2: Key Formula or Approach:
To identify the correct structure, we must evaluate the stereochemistry of each sugar unit and their linkage based on standard Haworth projection rules:
1. Galactose configuration: Galactose is the C-4 epimer of glucose. In the provided Fischer projection of D-galactose, the hydroxyl at C-4 is on the left. In a Haworth projection, this translates to the C-4 substituent pointing "up". Thus, the chlorine atom at C-4 must be oriented "up".
2. Fructose configuration: The fructose unit is a $\beta$-anomer, meaning the glycosidic oxygen at C-2 points "up". Substitutions are at C-1 and C-6 with chlorine atoms. In a $\beta\text{-D-fructofuranoside}$, the $\text{CH}_2\text{Cl}$ group at C-1 points "down", and the $\text{CH}_2\text{Cl}$ group at C-6 points "up".
3. Glycosidic Bond: The linkage is a $1,2'$-glycosidic bond, connecting the anomeric C-1 of the galactose unit to the anomeric C-2 of the fructose unit.
Step 3: Detailed Explanation:
Comparing the options:
- Options (A) and (B) show incorrect linkages where the oxygen bridge is not directly between the two anomeric carbons of the sugar rings. Instead, it involves an external methylene group.
- Option (C) shows the correct glycosidic linkage, but the chlorine atom at C-4 of the galactose ring is pointing "down", which would actually represent a chlorinated glucose derivative.
- Option (D) correctly shows the $1,2'$-glycosidic linkage. The galactose ring has the chlorine at C-4 pointing "up", and the fructose ring correctly displays the $\beta$-orientation for the glycosidic bond and the correct placement of the chlorine atoms at C-1 and C-6.
Step 4: Final Answer:
Structure (D) perfectly matches the stereochemical and constitutional requirements of Sucralose.