The unit of rate constant of a reaction having order `1.5` would be

Options

A. `("mol L"^(-1))^(1//2)s^(-1)`
B. `("mol L"^(-1))^(-3//2)s^(-1)`
C. `("conc.")^(-0.5) time^(-1)`
D. `("conc.")^(-0.75) time^(-1)`

Explanation

To find the unit of the rate constant (k) for a reaction of order 1.5, we can follow these steps:

### Step 1: Write the rate law expression
For a reaction of order \( n \), the rate law can be expressed as:
\[ \text{Rate} = k [A]^n \]
where \( [A] \) is the concentration of the reactant.

### Step 2: Substitute the order of the reaction
In this case, the order \( n \) is given as 1.5. Therefore, we can write:
\[ \text{Rate} = k [A]^{1.5} \]

### Step 3: Identify the units of rate and concentration
The unit of rate (R) is typically expressed in moles per liter per second (mol/L·s). The unit of concentration ([A]) is in moles per liter (mol/L).

### Step 4: Substitute the units into the rate law
Now, substituting the units into the rate law:
\[ \text{Rate} = k [A]^{1.5} \]
This can be rewritten in terms of units:
\[ \text{(mol/L·s)} = k \cdot \left(\text{(mol/L)}\right)^{1.5} \]

### Step 5: Simplify the expression
The right side becomes:
\[ k \cdot \left(\text{(mol/L)}^{1.5}\right) = k \cdot \left(\text{mol}^{1.5} \cdot \text{L}^{-1.5}\right) \]
Thus, we have:
\[ \text{(mol/L·s)} = k \cdot \left(\text{mol}^{1.5} \cdot \text{L}^{-1.5}\right) \]

### Step 6: Solve for the unit of k
Rearranging the equation to isolate k gives:
\[ k = \frac{\text{(mol/L·s)}}{\text{(mol}^{1.5} \cdot \text{L}^{-1.5})} \]

### Step 7: Simplify the units
This simplifies to:
\[ k = \frac{\text{mol}}{\text{L} \cdot \text{s}} \cdot \frac{\text{L}^{1.5}}{\text{mol}^{1.5}} = \frac{\text{L}^{0.5}}{\text{mol}^{0.5} \cdot \text{s}} \]

### Final Result
Thus, the unit of the rate constant \( k \) for a reaction of order 1.5 is:
\[ \text{L}^{0.5} \cdot \text{mol}^{-0.5} \cdot \text{s}^{-1} \]