Identify the reaction order from each of the following rate constants
`(i) k= 3 xx 10^(-5) s^(-)`
`(ii) k=9 xx 10^(-4) mol ^(-) "litre "s^(-)`
`(iii) k= 6 xx 10^(-2) ` litre `mol ^(-) s^(-)`
`(iv) k= 2.3 xx 10^(-5) L mol ^(-1) s^(-1)`
`(v) k= 3 xx 10^(-3) mol L^(-1) s^(-1)`

Explanation

To determine the order of the reaction from the given rate constants, we can analyze the units of each rate constant. The general formula for the units of the rate constant (k) is given by:

\[ \text{Unit of } k = \text{(mole/L)}^{1-n} \cdot \text{s}^{-1} \]

Where \( n \) is the order of the reaction. We will analyze each rate constant step by step.

### Step-by-Step Solution:

**(i) \( k = 3 \times 10^{-5} \, \text{s}^{-1} \)**

1. The unit of \( k \) is \( \text{s}^{-1} \).
2. From the formula, we have:
\[ 1 - n = 0 \]
3. Solving for \( n \):
\[ n = 1 \]
4. **Order of reaction**: 1 (First order)

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**(ii) \( k = 9 \times 10^{-4} \, \text{mol}^{-1} \, \text{L} \, \text{s}^{-1} \)**

1. The unit of \( k \) is \( \text{mol}^{-1} \, \text{L} \, \text{s}^{-1} \).
2. This can be rewritten as:
\[ \text{(mol/L)}^{-1} \cdot \text{s}^{-1} \]
3. From the formula, we have:
\[ 1 - n = -1 \]
4. Solving for \( n \):
\[ n = 2 \]
5. **Order of reaction**: 2 (Second order)

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**(iii) \( k = 6 \times 10^{-2} \, \text{L} \, \text{mol}^{-1} \, \text{s}^{-1} \)**

1. The unit of \( k \) is \( \text{L} \, \text{mol}^{-1} \, \text{s}^{-1} \).
2. This can be rewritten as:
\[ \text{(mol/L)}^{-1} \cdot \text{s}^{-1} \]
3. From the formula, we have:
\[ 1 - n = -1 \]
4. Solving for \( n \):
\[ n = 2 \]
5. **Order of reaction**: 2 (Second order)

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**(iv) \( k = 2.3 \times 10^{-5} \, \text{L} \, \text{mol}^{-1} \, \text{s}^{-1} \)**

1. The unit of \( k \) is \( \text{L} \, \text{mol}^{-1} \, \text{s}^{-1} \).
2. This can be rewritten as:
\[ \text{(mol/L)}^{-1} \cdot \text{s}^{-1} \]
3. From the formula, we have:
\[ 1 - n = -1 \]
4. Solving for \( n \):
\[ n = 2 \]
5. **Order of reaction**: 2 (Second order)

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**(v) \( k = 3 \times 10^{-3} \, \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \)**

1. The unit of \( k \) is \( \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \).
2. This can be rewritten as:
\[ \text{(mol/L)}^{1} \cdot \text{s}^{-1} \]
3. From the formula, we have:
\[ 1 - n = 1 \]
4. Solving for \( n \):
\[ n = 0 \]
5. **Order of reaction**: 0 (Zero order)

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### Summary of Reaction Orders:
- (i) First order
- (ii) Second order
- (iii) Second order
- (iv) Second order
- (v) Zero order