For a reaction `r=K(A)^(3//2)` then unit of rate of reaction and rate constant respectively :-

Options

A. `molL^(-1)s^(-1),mol^(-1//2)L^(1//2)s^(-1)`
B. `mol^(-1)L^(-1)s^(-1),mol^(-1//2)L^(1//2)s^(-1)`
C. `molL^(-1)s^(-1),mol^(+1//2)L^(1//2)s^(-1)`
D. `mol,mol^(+1//2)L^(1//2)s`

Explanation

To solve the question regarding the units of the rate of reaction and the rate constant for the reaction given by the equation \( r = K(A)^{3/2} \), we can follow these steps:

### Step 1: Understand the rate of reaction
The rate of reaction \( r \) is defined as the change in concentration of a reactant or product per unit time. The unit of concentration is typically expressed in moles per liter (mol/L), and the unit of time is seconds (s). Therefore, the unit of the rate of reaction can be expressed as:

\[ \text{Unit of Rate of Reaction} = \frac{\text{moles}}{\text{liters} \cdot \text{seconds}} = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 2: Identify the rate constant \( K \)
From the rate equation \( r = K(A)^{3/2} \), we can rearrange it to express \( K \):

\[ K = \frac{r}{(A)^{3/2}} \]

### Step 3: Determine the units of \( K \)
We already established that the unit of the rate of reaction \( r \) is \( \text{mol L}^{-1} \text{s}^{-1} \). The concentration \( A \) has the unit of \( \text{mol L}^{-1} \). Therefore, we can substitute these units into the equation for \( K \):

\[ \text{Unit of } K = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^{3/2}} \]

### Step 4: Simplify the units of \( K \)
Calculating the denominator:

\[ (\text{mol L}^{-1})^{3/2} = \text{mol}^{3/2} \cdot \text{L}^{-3/2} \]

Now substituting back into the equation for \( K \):

\[ \text{Unit of } K = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^{3/2} \cdot \text{L}^{-3/2}} = \text{mol}^{1 - 3/2} \cdot \text{L}^{1 + 3/2} \cdot \text{s}^{-1} = \text{mol}^{-1/2} \cdot \text{L}^{5/2} \cdot \text{s}^{-1} \]

### Conclusion
Thus, the units of the rate of reaction and the rate constant \( K \) are:

- **Unit of Rate of Reaction**: \( \text{mol L}^{-1} \text{s}^{-1} \)
- **Unit of Rate Constant \( K \)**: \( \text{mol}^{-1/2} \cdot \text{L}^{5/2} \cdot \text{s}^{-1} \)