The weight average molar mass (Mw) is calculated by summing the product of the weight fraction of each molecule (wi) and its molar mass (Mi).
Here's a breakdown of how to calculate it:
Understanding Weight Average Molar Mass (Mw)
The weight average molar mass gives more weight to larger molecules when determining the average molar mass of a polymer sample. This is because larger molecules contribute more to the overall weight of the sample. It is a more sensitive measure of high molecular weight polymers than the number average molecular weight.
Formula for Calculation
The weight average molar mass (Mw) is calculated using the following formula:
Mw = Σ (wi * Mi)
Where:
- Mw = Weight average molar mass
- wi = Weight fraction of molecules with molar mass Mi
- Mi = Molar mass of molecules with a specific chain length/size
- Σ = Summation over all molecule sizes/molar masses present in the sample
Steps to Calculate Mw
-
Determine the Weight Fraction (wi) for each molar mass (Mi):
- The weight fraction represents the proportion by weight of molecules having a particular molar mass within the entire sample.
- wi = Weight of molecules with molar mass Mi / Total weight of the sample
-
Multiply the Weight Fraction (wi) by the Molar Mass (Mi) for each fraction:
- For each fraction of molecules with a specific molar mass, multiply its weight fraction by its molar mass.
-
Sum the Products:
- Add up all the products calculated in the previous step. This sum is the weight average molar mass (Mw).
Example Calculation
Let's say you have a polymer sample with the following characteristics:
| Molar Mass (Mi) (g/mol) | Weight Fraction (wi) |
|---|---|
| 10,000 | 0.2 |
| 20,000 | 0.5 |
| 30,000 | 0.3 |
Then, the weight average molar mass (Mw) would be calculated as follows:
Mw = (0.2 10,000) + (0.5 20,000) + (0.3 * 30,000)
Mw = 2,000 + 10,000 + 9,000
Mw = 21,000 g/mol
Therefore, the weight average molar mass of this polymer sample is 21,000 g/mol.
Importance of Weight Average Molar Mass
The weight average molar mass is an important parameter for characterizing polymers and is used in determining their physical and mechanical properties. It has a greater influence on the polymer's properties (like viscosity, tensile strength) than the number average molar mass.
