The final product of which of the following reactions furnishes
evidence that glucose has unbranched carbon chain :

Options

A. `Glucose underset(2 "Red P+H")overset(1. Br, H_2 O)to`
B. `Glucose underset(2 "Red P+HI")overset(1.NaBH_4)to`
C. `Glucose underset(3 "Red P+HI")underset(2. H_3^(o+)O)overset(1.HCN)to`
D. `Glucose overset(CH_3OH,H^(o+))to`

Explanation

To determine which reaction provides evidence that glucose has an unbranched carbon chain, we need to analyze the reactions involving glucose and their products. Here’s a step-by-step breakdown of the reactions mentioned:

### Step 1: Analyze the First Reaction
- **Reaction**: Glucose + Bromine Water
- **Product**: Gluconic Acid
- **Next Step**: Gluconic Acid + Red Phosphorus + HI
- **Final Product**: n-Hexane

**Conclusion**: The formation of n-hexane indicates that the glucose has an unbranched carbon chain.

### Step 2: Analyze the Second Reaction
- **Reaction**: Glucose + NaBH4
- **Product**: Hexane-1,2,3,4,5,6-hexol
- **Next Step**: Hexol + Red Phosphorus + HI
- **Final Product**: n-Hexane

**Conclusion**: Similar to the first reaction, the formation of n-hexane from hexol also indicates an unbranched carbon chain.

### Step 3: Analyze the Third Reaction
- **Reaction**: Glucose + HCN
- **Intermediate Product**: A compound with a carbon chain that includes a triple bond and hydroxyl groups.
- **Next Step**: H3O+ (Hydronium ion)
- **Final Step**: Red Phosphorus + HI
- **Final Product**: n-Heptane

**Conclusion**: The increase in carbon count leading to n-heptane also supports the presence of an unbranched carbon chain.

### Step 4: Analyze the Fourth Reaction
- **Reaction**: Glucose + CH3OH
- **Product**: Methylated Glucose

**Conclusion**: Since methylated glucose does not provide clear evidence of the carbon chain structure (it could be branched or unbranched), this reaction does not support the claim.

### Final Answer
The reactions that furnish evidence that glucose has an unbranched carbon chain are:
1. Glucose + Bromine Water → n-Hexane
2. Glucose + NaBH4 → n-Hexane
3. Glucose + HCN → n-Heptane

Thus, the correct options are 1, 2, and 3.

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