The unit of first order rate constant is ………….. .

Answer

To determine the unit of the first-order rate constant (k), we can follow these steps:

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

### Step 2: Define the Rate
The rate of a reaction is defined as the change in concentration over time. Therefore, the unit of rate can be expressed as:
\[ \text{Rate} = \frac{\text{change in concentration}}{\text{time}} \]
The concentration is typically measured in moles per liter (mol/L).

### Step 3: Write the Units for Rate
Thus, the unit of rate can be expressed as:
\[ \text{Unit of Rate} = \frac{\text{mol/L}}{\text{s}} = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 4: Substitute Units into the Rate Law
Now, substituting the unit of rate into the rate law:
\[ \text{mol L}^{-1} \text{s}^{-1} = k \cdot \text{mol L}^{-1} \]

### Step 5: Solve for the Unit of k
To isolate \( k \), we rearrange the equation:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol L}^{-1}} \]
The units of concentration (mol L\(^{-1}\)) cancel out, leaving us with:
\[ k = \text{s}^{-1} \]

### Conclusion
Thus, the unit of the first-order rate constant \( k \) is:
\[ \text{Unit of } k = \text{s}^{-1} \]