Units of rate constant of first and zero order reactions in terms of molarity `M` are respectively:

Options

A. `S^(-1), ML^(-1) S^(-1)`
B. `S^(-1),M`
C. `M S^(-1), S^(-1)`
D. `M, S^(-1)`

Explanation

To determine the units of the rate constant for first and zero order reactions in terms of molarity (M), we can follow these steps:

### Step 1: Understand the General Formula for Rate Constant
The unit of the rate constant \( k \) for a reaction of order \( n \) is given by the formula:
\[ k = \text{(concentration)}^{(1-n)} \cdot \text{(time)}^{-1} \]
Where concentration is expressed in molarity (M), which is moles per liter (mol/L).

### Step 2: Calculate the Unit for Zero Order Reaction
For a zero order reaction, the order \( n = 0 \).
Substituting \( n = 0 \) into the formula:
\[ k = M^{(1-0)} \cdot \text{s}^{-1} = M^{1} \cdot \text{s}^{-1} = M \cdot \text{s}^{-1} \]
Thus, the unit of the rate constant for a zero order reaction is:
\[ \text{Unit of } k \text{ for zero order} = \text{M/s} \]

### Step 3: Calculate the Unit for First Order Reaction
For a first order reaction, the order \( n = 1 \).
Substituting \( n = 1 \) into the formula:
\[ k = M^{(1-1)} \cdot \text{s}^{-1} = M^{0} \cdot \text{s}^{-1} = \text{s}^{-1} \]
Thus, the unit of the rate constant for a first order reaction is:
\[ \text{Unit of } k \text{ for first order} = \text{s}^{-1} \]

### Step 4: Summary of Units
- For zero order reactions: \( k \) has units of \( \text{M/s} \)
- For first order reactions: \( k \) has units of \( \text{s}^{-1} \)

### Final Answer
The units of the rate constant of first and zero order reactions in terms of molarity \( M \) are respectively:
- First order: \( \text{s}^{-1} \)
- Zero order: \( \text{M/s} \)

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