Step 1: Understanding the Question:
The question asks to identify the correct statement(s) among the given options regarding the chemical properties and definitions related to sugars. This question might have multiple correct answers.
Step 2: Key Formula or Approach:
Analyze each statement based on knowledge of carbohydrate chemistry, oxidation reactions, and physical properties (specific rotation).
Step 3: Detailed Explanation:
Let's evaluate each statement:
(A) On treatment with HNO$_3$, gluconic acid is oxidized to saccharic acid, whereas glucose is not oxidized to saccharic acid.
- Glucose oxidation: Glucose ($\text{CHO-(CHOH)}_4\text{-CH}_2\text{OH}$) is an aldohexose. On treatment with strong oxidizing agents like HNO$_3$, both the aldehyde group (at C1) and the primary alcohol group (at C6) are oxidized to carboxylic acid groups. This yields saccharic acid (glucaric acid, $\text{COOH-(CHOH)}_4\text{-COOH}$). So, "glucose is not oxidized to saccharic acid" is Incorrect.
- Gluconic acid oxidation: Gluconic acid ($\text{COOH-(CHOH)}_4\text{-CH}_2\text{OH}$) has a carboxylic acid group at C1 and a primary alcohol group at C6. HNO$_3$ can oxidize the primary alcohol group at C6 to a carboxylic acid group, forming saccharic acid. So, "gluconic acid is oxidized to saccharic acid" is Correct.
- Since the latter part of the statement about glucose is incorrect, the entire statement (A) is Incorrect.
(B) Fructose gives a positive Fehling's test because it isomerises to glucose and another aldohexose in the presence of Fehling's reagent.
- Fehling's test: This test detects reducing sugars (aldehydes). Fructose is a ketohexose (ketone), so it doesn't have an aldehyde group.
- However, fructose is an \(\alpha\)-hydroxyketone. In the presence of a base (like the alkaline Fehling's reagent), fructose can isomerize to an aldose (like glucose and mannose) through an enediol intermediate (Loebry de Bruyn-van Ekenstein transformation). These aldoses then have a free aldehyde group and can reduce Fehling's reagent.
- So, "Fructose gives a positive Fehling's test because it isomerises to glucose and another aldohexose in the presence of Fehling's reagent" is Correct.
(C) Invert sugar is an equimolar mixture of D-glucose and D-fructose formed after hydrolysis of the corresponding disaccharide.
- Sucrose hydrolysis: Sucrose is a disaccharide composed of one unit of D-glucose and one unit of D-fructose. Hydrolysis of sucrose (e.g., by acid or the enzyme invertase) yields an equimolar mixture of D-glucose and D-fructose.
- Invert sugar: This equimolar mixture is called invert sugar because the specific rotation changes from positive (for sucrose, $+66.5^{\circ}$) to negative (for the mixture). D-glucose is dextrorotatory ($+52.5^{\circ}$), and D-fructose is levorotatory ($-92.5^{\circ}$). The mixture has a net negative specific rotation.
- This statement is Correct.
(D) Specific rotation of invert sugar is $-40^{\circ$.}
- The specific rotation of D-glucose is $+52.5^{\circ}$.
- The specific rotation of D-fructose is $-92.5^{\circ}$.
- For an equimolar mixture (invert sugar), the specific rotation is the average:
\[ [\alpha]_{\text{invert sugar}} = \frac{[\alpha]_{\text{D-glucose}} + [\alpha]_{\text{D-fructose}}}{2} \]
\[ = \frac{+52.5^{\circ} + (-92.5^{\circ})}{2} = \frac{-40^{\circ}}{2} = -20^{\circ} \]
- The statement says specific rotation is $-40^{\circ}$. This is Incorrect.
Based on this analysis, statements (B) and (C) are correct.
Step 4: Final Answer:
Statements (B) and (C) are correct.