Assertion : The reaction
`underset("Cane sugar")(C_(12)H_(22)O_(11)) + H_(2) O overset(H^(+))(t0) underset("Glucose")(C_(6)h_(12)O_(6)) + underset("Fructose")(C_(6)H_(12)O_(6))` is a first order reaction.
Reason : Change in concentration of `H_(2)O` is negligible.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction given is the hydrolysis of cane sugar (sucrose) in the presence of water:
\[ C_{12}H_{22}O_{11} + H_2O \overset{H^+}{\rightarrow} C_6H_{12}O_6 + C_6H_{12}O_6 \]
This reaction produces glucose and fructose.

2. **Determining the Order of the Reaction**:
- The general rate law for a reaction can be expressed as:
\[ \text{Rate} = k [\text{Cane Sugar}]^m [\text{H}_2O]^n \]
- In this case, since water is in excess, its concentration remains relatively constant throughout the reaction. This allows us to treat it as a constant factor.

3. **Pseudo First Order Reaction**:
- When a reactant is in excess (like water here), the reaction can be simplified to a first-order reaction with respect to the limiting reactant (cane sugar).
- Therefore, we can express the rate as:
\[ \text{Rate} = k' [\text{Cane Sugar}] \]
where \( k' = k [H_2O]^n \) (with \( n \) being effectively 0 due to the excess of water).

4. **Conclusion on the Assertion**:
- The assertion states that the reaction is a first-order reaction. This is true because, under the conditions given (excess water), the reaction behaves as a first-order reaction with respect to cane sugar.

5. **Analyzing the Reason**:
- The reason states that the change in concentration of \( H_2O \) is negligible. This is also true because the concentration of water does not significantly change during the reaction due to its excess.

6. **Final Evaluation**:
- Both the assertion and the reason are true, and the reason correctly explains the assertion. Therefore, we conclude that both the assertion and reason are true, and the reason is the correct explanation of the assertion.

### Final Answer:
Both assertion and reason are true, and the reason is the correct explanation of the assertion.

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