Step 1: Understanding the Question:
The question asks to identify the reagent 'R' capable of reducing glucose entirely to a continuous six-carbon straight-chain alkane (n-hexane). This reaction is historically significant as structural proof for the open-chain architecture of glucose.
Step 2: Key Formula or Approach:
Prolonged heating of a carbohydrate with hydroiodic acid (HI) and red phosphorus (often indicated simply as $\text{HI}, \Delta$) functions as a powerful reducing system that replaces all hydroxyl ($-\text{OH}$) and carbonyl ($\gt \text{C=O}$) groups with hydrogen atoms.
Step 3: Detailed Explanation:
Glucose is an aldohexose with the formula $\text{C}_6\text{H}_{12}\text{O}_6$. When glucose undergoes a prolonged reaction with concentrated hydroiodic acid (HI) at elevated temperatures ($\Delta$), all six carbon atoms are stripped of their oxygen-containing functional groups and completely saturated with hydrogen atoms:
$$\text{CHO-(CHOH)}_4\text{-CH}_2\text{OH} \xrightarrow{\text{HI},\ \Delta} \text{CH}_3\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-CH}_2\text{-CH}_3 \quad (\text{n-hexane})$$
The formation of n-hexane confirms that all six carbon atoms in a glucose molecule are linked in a straight, unbranched chain.
Step 4: Final Answer:
The reagent required is $\text{HI}, \Delta$, which matches option (A).