The rate law for the reaction Sucrose + Water `overset([H^(+)])to` Glucose + Fructose is given by :

Options

A. Rate = K [sucrose] [water]
B. Rate = K [sucrose] `["water"]^0`
C. Rate = K `["sucrose"]^0` [water]
D. Rate = K `["sucrose"]^(1//2) ["water"]^(1//2)`

Answer

To derive the rate law for the hydrolysis of sucrose in the presence of water and H+, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Reaction**: The reaction is given as:
\[ \text{Sucrose} + \text{Water} \overset{[H^+]}{\rightarrow} \text{Glucose} + \text{Fructose} \]
Here, sucrose (C12H22O11) reacts with water (H2O) in an acidic medium (H+) to produce glucose (C6H12O6) and fructose (C6H12O6).

**Hint**: Identify the reactants and products in the chemical equation.

2. **Determine the Order of Reaction**: The reaction involves two reactants: sucrose and water. Initially, it may seem like a second-order reaction since there are two reactants.

**Hint**: Consider the number of reactants when determining the order of the reaction.

3. **Consider the Role of Water**: In hydrolysis reactions, water is typically present in excess. This means that its concentration does not change significantly during the reaction.

**Hint**: Think about how the concentration of water affects the rate of the reaction.

4. **Express the Rate Law**: The general form of the rate law can be written as:
\[ R = k[\text{sucrose}][\text{water}] \]
However, since water is in excess, we can treat its concentration as a constant. Thus, we can define a new rate constant \( k' = k[\text{water}] \).

**Hint**: Remember that when a reactant is in excess, its concentration can be treated as a constant.

5. **Final Rate Law**: The rate law can now be simplified to:
\[ R = k'[\text{sucrose}] \]
This indicates that the reaction is pseudo-first-order with respect to sucrose.

**Hint**: Simplify the rate law by substituting constants for concentrations that do not change.

6. **Conclusion**: The rate law for the hydrolysis of sucrose is dependent only on the concentration of sucrose and not on water, confirming that it is a pseudo-first-order reaction.

**Hint**: Conclude by summarizing how the reaction behaves based on the concentrations of the reactants.

### Summary:
The rate law for the reaction of sucrose hydrolysis in the presence of water and H+ is:
\[ R = k'[\text{sucrose}] \]
where \( k' \) is a modified rate constant that includes the concentration of water, treated as constant due to its excess.