The rate constant for a reaction is `2.05xx10^(-5)` mole `"lit"^(-1)."sec"^(-1)`. The rection obeys ……order

Options

A. First
B. Second
C. Zero
D. Half

Answer

To determine the order of the reaction based on the given rate constant, we need to analyze the units of the rate constant and compare them with the expected units for different reaction orders.

### Step-by-Step Solution:

1. **Identify the given rate constant**:
The rate constant \( k \) is given as \( 2.05 \times 10^{-5} \, \text{mole} \, \text{lit}^{-1} \, \text{sec}^{-1} \).

2. **Understand the units of the rate constant**:
The units of the rate constant depend on the order of the reaction. The general formula for the units of the rate constant \( k \) is:
\[ k = \text{mole}^{1-n} \cdot \text{lit}^{n-1} \cdot \text{time}^{-1} \]
where \( n \) is the order of the reaction.

3. **Check the units for different orders**:
- **For first-order reaction (n = 1)**:
\[ k = \text{mole}^{1-1} \cdot \text{lit}^{1-1} \cdot \text{sec}^{-1} = \text{sec}^{-1} \]
- **For second-order reaction (n = 2)**:
\[ k = \text{mole}^{1-2} \cdot \text{lit}^{2-1} \cdot \text{sec}^{-1} = \text{lit} \cdot \text{mole}^{-1} \cdot \text{sec}^{-1} \]
- **For zero-order reaction (n = 0)**:
\[ k = \text{mole}^{1-0} \cdot \text{lit}^{0-1} \cdot \text{sec}^{-1} = \text{mole} \cdot \text{lit}^{-1} \cdot \text{sec}^{-1} \]
- **For half-order reaction (n = 0.5)**:
\[ k = \text{mole}^{1-0.5} \cdot \text{lit}^{0.5-1} \cdot \text{sec}^{-1} = \text{mole}^{0.5} \cdot \text{lit}^{-0.5} \cdot \text{sec}^{-1} \]

4. **Compare the given units with the calculated units**:
The given units of the rate constant are \( \text{mole} \, \text{lit}^{-1} \, \text{sec}^{-1} \). This matches the units derived for a zero-order reaction.

5. **Conclusion**:
Since the units of the given rate constant correspond to a zero-order reaction, we conclude that the reaction obeys zero order.

### Final Answer:
The reaction obeys **zero order**.

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