For the following elementary homogeneous reaction, the unit of rate constant is : `A+B overset(k) rarr C`

Options

A. `"mol"^(-1) L s^(-1)`
B. `s^(-1)`
C. s
D. `"mol L"^(-1) s^(-1)`

Explanation

To determine the unit of the rate constant (k) for the elementary homogeneous reaction \( A + B \overset{k}{\rightarrow} C \), we can follow these steps:

### Step 1: Identify the Reaction Order
For the given elementary reaction, the stoichiometric coefficients of the reactants \( A \) and \( B \) are both 1. Therefore, the overall order of the reaction is the sum of the stoichiometric coefficients:
\[ \text{Order} = 1 + 1 = 2 \]

### Step 2: Write the Rate Law
For an elementary reaction, the rate law can be expressed as:
\[ \text{Rate} = k[A]^1[B]^1 = k[A][B] \]

### Step 3: Determine the Units of Rate
The rate of a reaction is typically expressed in terms of concentration change over time. The unit of rate is:
\[ \text{Unit of Rate} = \text{mole L}^{-1} \text{s}^{-1} \]

### Step 4: Relate the Units of Rate Constant to the Reaction Order
The unit of the rate constant \( k \) can be derived from the rate law. Rearranging the rate equation gives:
\[ k = \frac{\text{Rate}}{[A][B]} \]

### Step 5: Substitute the Units
Substituting the units into the equation:
\[ \text{Unit of } k = \frac{\text{mole L}^{-1} \text{s}^{-1}}{(\text{mole L}^{-1})(\text{mole L}^{-1})} \]
This simplifies to:
\[ \text{Unit of } k = \frac{\text{mole L}^{-1} \text{s}^{-1}}{\text{mole}^2 \text{L}^{-2}} = \text{mole}^{-1} \text{L} \text{s}^{-1} \]

### Conclusion
Thus, the unit of the rate constant \( k \) for the reaction \( A + B \rightarrow C \) is:
\[ \text{Unit of } k = \text{mole}^{-1} \text{L} \text{s}^{-1} \]

### Final Answer
The correct option is \( \text{mole}^{-1} \text{L} \text{s}^{-1} \).

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