The method of choice for determining the molecular weight of polymer is:

Options

A. Osmotic pressre
B. Gas density
C. Lowering of freezing point
D. Direct weighing of a single molecule

Explanation

To determine the molecular weight of a polymer, we can analyze the options provided and arrive at the correct method step by step.

### Step-by-Step Solution:

1. **Understanding Molecular Weight Determination**:
- Molecular weight is a critical parameter in characterizing polymers. Various methods exist to determine it, and we need to identify the most suitable one.

2. **Evaluating the Options**:
- The options provided are:
- A) Osmotic Pressure
- B) Gas Density
- C) Lowering of Freezing Point
- D) Direct Weighting of a Single Molecule

3. **Analyzing Osmotic Pressure**:
- Osmotic pressure is a colligative property, which means it depends on the number of solute particles in a solution rather than their identity.
- It can be measured even at very small values, making it a reliable method for polymers.

4. **Comparing Other Methods**:
- **Gas Density**: This method can alter the properties of the polymer, making it unsuitable for accurate molecular weight determination.
- **Lowering of Freezing Point**: Similar to gas density, this method can also change the properties of the polymer and is not reliable.
- **Direct Weighting of a Single Molecule**: This method is impractical for polymers due to their large size and complexity.

5. **Conclusion**:
- Among the options provided, the osmotic pressure method is the best choice for determining the molecular weight of a polymer because it does not require heating (which could alter the polymer properties) and provides measurable results.

### Final Answer:
The method of choice for determining the molecular weight of a polymer is **A) Osmotic Pressure**.

---