To address your request, I'll follow a systematic, quantitative approach using **boiling point, molecular weight, and electronegativity of the halogen substituent** as the primary _Specified_physicochemical_Properties_. 

These are common, database-quantifiable properties that directly reflect differences from the identity of the halogen, and are highly relevant to reactivity, volatility, and polarity.

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## **Summary Table of Quantitative Properties**

| Substance           | Boiling Point (°C) | Molecular Weight (g/mol) | Halogen Electronegativity (Pauling) |
|---------------------|--------------------|--------------------------|--------------------------------------|
| 2-bromopyridine     |    ~204            |         158.01           | Br: 2.96                             |
| 2-chloropyridine    |    ~192            |         128.55           | Cl: 3.16                             |
| 2-iodopyridine      |    ~235            |         204.01           | I: 2.66                              |

(All data sourced from standard chemical databases such as PubChem, Reaxys, or the CRC Handbook.)

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## **Classification Approach**

We'll consider the following quantitative cutoffs:

1. **Boiling Point (Volatility) Groups:**
    - **Low:** <150°C
    - **Medium:** 150–210°C
    - **High:** >210°C

2. **Molecular Weight Groups:**
    - **Light:** <130 g/mol
    - **Moderate:** 130–170 g/mol
    - **Heavy:** >170 g/mol

3. **Halogen Electronegativity Groups:**  
   (Affects electron distribution/reactivity, threshold at 3.0)
    - **High:** ≥3.0
    - **Moderate:** 2.8–2.99
    - **Low:** <2.8

---

## **Assignment**

#### **By Boiling Point (Volatility):**
- **Medium:** 2-chloropyridine (192°C), 2-bromopyridine (204°C)
- **High:** 2-iodopyridine (235°C)

#### **By Molecular Weight:**
- **Light:** 2-chloropyridine (128.55 g/mol)
- **Moderate:** 2-bromopyridine (158.01 g/mol)
- **Heavy:** 2-iodopyridine (204.01 g/mol)

#### **By Halogen Electronegativity:**
- **High:** 2-chloropyridine (3.16)
- **Moderate:** 2-bromopyridine (2.96)
- **Low:** 2-iodopyridine (2.66)

---

## **Best Classification Scheme**

**Using the above, classification by _halogen electronegativity_ gives the clearest, completely non-overlapping groups** with direct relevance to physicochemical properties and reactivity:

1. **High Electronegativity:**  
   - 2-chloropyridine

2. **Moderate Electronegativity:**  
   - 2-bromopyridine

3. **Low Electronegativity:**  
   - 2-iodopyridine

Other properties either distribute the compounds unequally (e.g., two in "medium" boiling point) or do not provide as clean a division.

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## **Final Classification (NO MORE THAN THREE CLASSES, Quantitative Justification)**

| Electronegativity Group  | Compounds            | Quantitative Value (Pauling) |
|--------------------------|----------------------|------------------------------|
| **High (≥3.0)**          | 2-chloropyridine     | 3.16                         |
| **Moderate (2.8–2.99)**  | 2-bromopyridine      | 2.96                         |
| **Low (<2.8)**           | 2-iodopyridine       | 2.66                         |

### **Justification:**
- All groupings are based on measured, widely accepted quantitative data.
- This approach uses a direct, numerically-defined criterion for each class.  
- Other properties (boiling point, molecular weight) do not yield precise three-group separations for these compounds and/or do not map as directly onto a single, well-defined class per molecule.

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**If a single group were needed, one could argue that all are "halogen-substituted pyridines," but clear quantitative differences per the data above justify three separate classes by halogen electronegativity.**