Step 1: Understanding the Question:
The problem asks for the specific chemical reagent that is utilized to confirm that the six carbon atoms in a glucose molecule are linked together in a continuous, unbranched straight chain.
Step 2: Key Formula or Approach:
The structural elucidation of carbohydrates involves selective functional group tests and reduction reactions. Prolonged heating with a strong reducing agent like hydroiodic acid ($\mathrm{HI}$) reduces all hydroxyl groups and carbonyls to their corresponding hydrocarbons, leaving behind the stable alkane core.
Step 3: Detailed Explanation:
When glucose ($\mathrm{C_6H_{12}O_6}$) undergoes prolonged heating in the presence of concentrated hydroiodic acid ($\mathrm{HI}$) along with red phosphorus, it experiences complete reduction.
This reaction breaks down all the carbon-oxygen bonds, converting the aldohexose into a mixture of hydrocarbons, predominantly consisting of $n$-hexane.
$$\mathrm{C_6H_{12}O_6 + 14HI \xrightarrow{\Delta} CH_3-CH_2-CH_2-CH_2-CH_2-CH_3 + 6H_2O + 7I_2}$$
The formation of $n$-hexane, which is a strictly straight-chain alkane with six carbons, serves as direct experimental proof that all six carbon atoms in the original glucose molecule are covalently arranged in a continuous, unbranched open-chain skeleton.
Step 4: Final Answer:
The reagent used to identify the straight chain structure of glucose is $\mathrm{HI}$, which corresponds to option (A).