For a second-order reaction, what is the unit of the rate of the reaction

Options

A. `s^(-1)`
B. ` mol L^(-1)s^(-1)`
C. ` mol ^(-1)Ls^(-1)`
D. ` mol ^(-2)L^(2)s^(-1)`

Answer

To determine the unit of the rate of a second-order reaction, we can follow these steps:

### Step 1: Understand the general formula for the unit of the rate of reaction.
The unit of the rate of reaction can be expressed as:
\[ \text{Rate} = \text{concentration} \times \text{time}^{-1} \]
For a reaction, the concentration is typically measured in moles per liter (mol/L).

### Step 2: Identify the order of the reaction.
In this case, we are given that the reaction is a second-order reaction. The order of the reaction (n) is 2.

### Step 3: Apply the formula for the unit of the rate of reaction.
The general formula for the unit of the rate of reaction in terms of the order (n) is:
\[ \text{Unit of Rate} = \text{mol L}^{-1} \cdot \text{s}^{-1} \cdot \text{(L mol}^{-1})^{(n-1)} \]
For a second-order reaction (n = 2):
\[ \text{Unit of Rate} = \text{mol L}^{-1} \cdot \text{s}^{-1} \cdot \text{(L mol}^{-1})^{(2-1)} \]

### Step 4: Simplify the expression.
Substituting n = 2 into the formula:
\[ \text{Unit of Rate} = \text{mol L}^{-1} \cdot \text{s}^{-1} \cdot \text{(L mol}^{-1})^{1} \]
This simplifies to:
\[ \text{Unit of Rate} = \text{mol L}^{-1} \cdot \text{s}^{-1} \cdot \text{L mol}^{-1} \]

### Step 5: Further simplification.
The units of L and mol cancel out:
\[ \text{Unit of Rate} = \text{mol}^{-1} \cdot \text{L} \cdot \text{s}^{-1} \]
This can be rearranged to:
\[ \text{Unit of Rate} = \text{mol}^{-1} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]

### Conclusion:
Thus, the unit of the rate of a second-order reaction is:
\[ \text{mol}^{-1} \cdot \text{L} \cdot \text{s}^{-1} \]
or equivalently:
\[ \text{mol}^{-1} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]