Mass-average molecular mass of a polymer is determined by:

Options

A. Light scattering and ultracentrifuge method
B. Osmotic pressure
C. Depression of frezing point
D. Elevation in boiling point

Answer

To determine the mass-average molecular mass of a polymer, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Mass-Average Molecular Mass**:
- The mass-average molecular mass (M_w) of a polymer is a measure of the average mass of the polymer molecules in a sample. It is calculated using the formula:
\[ M_w = \frac{\sum (n_i \cdot m_i^2)}{\sum (n_i \cdot m_i)} \]
- Here, \(n_i\) is the number of molecules of type \(i\) and \(m_i\) is the molecular mass of type \(i\).

2. **Identifying Methods for Determination**:
- The question asks which methods are used to determine the mass-average molecular mass of polymers.
- Common methods include light scattering and ultracentrifugation.

3. **Differentiating Between Average Molecular Mass Types**:
- It's important to differentiate between mass-average molecular mass (M_w) and number-average molecular mass (M_n).
- The number-average molecular mass is calculated using:
\[ M_n = \frac{\sum (n_i \cdot m_i)}{\sum n_i} \]
- The methods typically used for determining number-average molecular mass include colligative properties.

4. **Final Conclusion**:
- The methods specifically used for determining mass-average molecular mass are light scattering and ultracentrifugation.
- Therefore, the correct answer to the question is that mass-average molecular mass of a polymer is determined by **light scattering and ultracentrifuge methods**.

### Answer:
The mass-average molecular mass of a polymer is determined by **light scattering and ultracentrifuge methods**.

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