The unit of rate constant of zero order and first order chemical reactions are respectively :

Options

A. `mol L^(-1) s^(-1), mol L^(-1)s^(-1)`
B. ` s^(-1), mol L^(-1)s^(-1)`
C. ` mol L^(-1)s^(-1), s^(-1)`
D. None of these

Answer

To determine the units of the rate constant for zero-order and first-order chemical reactions, we can follow these steps:

### Step 1: Understand the Rate Law Expression
The rate law expression for a reaction can be written as:
\[ R = k [A]^n \]
where:
- \( R \) is the rate of the reaction,
- \( k \) is the rate constant,
- \( [A] \) is the concentration of the reactant,
- \( n \) is the order of the reaction.

### Step 2: Determine the Units for Zero-Order Reactions
For a zero-order reaction, the rate does not depend on the concentration of the reactant. Therefore, the rate expression simplifies to:
\[ R = k \]
This means that the rate \( R \) is equal to the rate constant \( k \).

#### Units of Rate:
The rate of a reaction is defined as the change in concentration over time:
\[ R = \frac{\Delta [A]}{\Delta t} \]
The units of concentration are typically moles per liter (mol/L), and the unit of time is seconds (s). Thus, the units of rate become:
\[ \text{Units of } R = \frac{\text{mol/L}}{\text{s}} = \text{mol L}^{-1} \text{s}^{-1} \]

Since \( R = k \) for a zero-order reaction, the units of the rate constant \( k \) are also:
\[ \text{Units of } k = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 3: Determine the Units for First-Order Reactions
For a first-order reaction, the rate expression is:
\[ R = k [A] \]
Here, the rate \( R \) is equal to the rate constant \( k \) multiplied by the concentration \( [A] \).

#### Rearranging for \( k \):
To find the units of \( k \), we rearrange the equation:
\[ k = \frac{R}{[A]} \]

#### Units of Rate and Concentration:
We already established that:
- Units of \( R = \text{mol L}^{-1} \text{s}^{-1} \)
- Units of \( [A] = \text{mol L}^{-1} \)

Now substituting these units into the equation for \( k \):
\[ \text{Units of } k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol L}^{-1}} \]

The moles per liter (mol/L) cancel out:
\[ \text{Units of } k = \text{s}^{-1} \]

### Conclusion
Thus, the units of the rate constant for zero-order and first-order reactions are:
- **Zero-order reaction:** \( \text{mol L}^{-1} \text{s}^{-1} \)
- **First-order reaction:** \( \text{s}^{-1} \)

### Final Answer
The units of the rate constant of zero-order and first-order chemical reactions are respectively:
- Zero-order: \( \text{mol L}^{-1} \text{s}^{-1} \)
- First-order: \( \text{s}^{-1} \)

---