The `PDI`(polydispersity index) is the ratio of weight to number-average molecular masses`(Mbar(w))//(M(bar(n))` .In natural polymers,which are generally monodispersed,`PDI`is………and in synthetic polymers which are always polydispersed, `PDI` is …….. because `Mbar(w)` is always .......than `Mbar(n)` .

Answer

To solve the question regarding the Polydispersity Index (PDI) in natural and synthetic polymers, we will break down the information step by step.

### Step 1: Understanding PDI
The Polydispersity Index (PDI) is defined as the ratio of weight-average molecular mass (M̅w) to number-average molecular mass (M̅n). Mathematically, it is expressed as:
\[ \text{PDI} = \frac{M̅w}{M̅n} \]

### Step 2: PDI in Natural Polymers
Natural polymers are generally monodispersed, meaning they have a uniform molecular weight. In this case, the weight-average molecular mass and the number-average molecular mass are equal. Therefore, the PDI for natural polymers is:
\[ \text{PDI} = \frac{M̅w}{M̅n} = \frac{M̅n}{M̅n} = 1 \]

### Step 3: PDI in Synthetic Polymers
Synthetic polymers, on the other hand, are typically polydispersed, meaning they have a distribution of molecular weights. In this case, the weight-average molecular mass (M̅w) is always greater than the number-average molecular mass (M̅n). Thus, the PDI for synthetic polymers is:
\[ \text{PDI} > 1 \]

### Step 4: Relationship Between M̅w and M̅n
Since synthetic polymers have a distribution of molecular weights, it follows that:
\[ M̅w > M̅n \]
This inequality leads to the conclusion that the PDI will always be greater than 1.

### Final Answers
1. In natural polymers, the PDI is **1**.
2. In synthetic polymers, the PDI is **greater than 1**.
3. This is because **M̅w is always higher than M̅n**.

### Summary of Answers
- For natural polymers: PDI = 1
- For synthetic polymers: PDI > 1
- Reason: M̅w is always higher than M̅n.