The inversion of cane sugar is represented by
`C_(12)H_(22)O_(11) + H_(2)O rarr C_(6)H_(12)O_(6) + C_(6)H_(12)O_(6)`
It is a reaction of

Options

A. (a) Unimolecular
B. (b) Second order
C. (c) Zero order
D. (d) First order

Answer

To determine the order of the reaction represented by the inversion of cane sugar, we can follow these steps:

### Step 1: Write the Reaction
The reaction for the inversion of cane sugar is given as:
\[ C_{12}H_{22}O_{11} + H_{2}O \rightarrow C_{6}H_{12}O_{6} + C_{6}H_{12}O_{6} \]

### Step 2: Identify the Reactants
In this reaction, the reactants are:
- Cane sugar (sucrose) \( C_{12}H_{22}O_{11} \)
- Water \( H_{2}O \)

### Step 3: Analyze the Concentration of Water
In this reaction, water is typically present in excess. This means that its concentration does not change significantly during the reaction and can be considered constant.

### Step 4: Write the Rate Law
The rate of the reaction can be expressed using the rate law:
\[ \text{Rate} = k [C_{12}H_{22}O_{11}]^m [H_{2}O]^n \]
Where:
- \( k \) is the rate constant,
- \( m \) is the order with respect to sucrose,
- \( n \) is the order with respect to water.

Since water is in excess, we can treat its concentration as a constant. Therefore, the rate law simplifies to:
\[ \text{Rate} = k' [C_{12}H_{22}O_{11}]^m \]
Where \( k' = k [H_{2}O]^n \) is a new constant.

### Step 5: Determine the Order of the Reaction
The order of the reaction is determined by the exponent \( m \) in the rate law. Since the stoichiometric coefficient of sucrose \( C_{12}H_{22}O_{11} \) is 1, we have:
\[ m = 1 \]
Thus, the reaction is first order with respect to sucrose.

### Step 6: Determine the Molecularity
Molecularity refers to the number of reactant species involved in the rate-determining step of the reaction. In this case, there are two reactants (sucrose and water), so the molecularity of the reaction is 2.

### Conclusion
The inversion of cane sugar is a first-order reaction with respect to sucrose, and the overall molecularity of the reaction is 2.

### Summary
- **Order of the Reaction**: First order (with respect to sucrose)
- **Molecularity of the Reaction**: 2

---