What is the polydispersity index of polymer if the mass average molecular mass & number average molecular mass of a polymer are respectively 40,000 and 30,000 ?

Options

A. `lt 1`
B. `gt1`
C. 1
D. 0

Answer

To find the polydispersity index (PDI) of a polymer, we can follow these steps:

### Step 1: Understand the Definitions
- **Mass Average Molecular Mass (Mw)**: This is the average molecular mass of the polymer calculated based on the mass of the polymer chains.
- **Number Average Molecular Mass (Mn)**: This is the average molecular mass of the polymer calculated based on the number of polymer chains.

### Step 2: Identify the Given Values
From the question, we have:
- Mass Average Molecular Mass (Mw) = 40,000
- Number Average Molecular Mass (Mn) = 30,000

### Step 3: Use the Formula for Polydispersity Index
The formula for calculating the Polydispersity Index (PDI) is:
\[ \text{PDI} = \frac{M_w}{M_n} \]

### Step 4: Substitute the Values into the Formula
Now, substituting the given values into the formula:
\[ \text{PDI} = \frac{40,000}{30,000} \]

### Step 5: Perform the Calculation
Calculating the above expression:
\[ \text{PDI} = \frac{40,000}{30,000} = \frac{4}{3} \approx 1.33 \]

### Step 6: Conclusion
Thus, the polydispersity index of the polymer is approximately 1.33.