Weight Average Molecular Mass of the Polymer

To find the weight average molecular mass of the polymer, we need to consider the molecular masses of the different types of molecules present in the sample and their respective proportions. Let's break down the problem step by step.

Step 1: Calculate the proportion of each type of molecule

Given that 30% of the molecules have a molecular mass of 20000, 40% have a molecular mass of 30000, and the remaining percentage have a molecular mass of 60000, we can calculate the proportions as follows:

- Proportion of molecules with molecular mass 20000: 30% = 0.3
- Proportion of molecules with molecular mass 30000: 40% = 0.4
- Proportion of molecules with molecular mass 60000: Remaining percentage = 1 - (0.3 + 0.4) = 0.3

Step 2: Calculate the weighted sum of the molecular masses

Next, we multiply each molecular mass by its respective proportion to obtain the weighted sum of the molecular masses:

- Weighted sum of molecular mass 20000: 20000 * 0.3 = 6000
- Weighted sum of molecular mass 30000: 30000 * 0.4 = 12000
- Weighted sum of molecular mass 60000: 60000 * 0.3 = 18000

Step 3: Calculate the total weighted sum of molecular masses

Now, we add up the weighted sums of the molecular masses calculated in the previous step:

Total weighted sum of molecular masses = 6000 + 12000 + 18000 = 36000

Step 4: Calculate the weight average molecular mass

Finally, we divide the total weighted sum of molecular masses by the total proportion of molecules in the sample:

Weight average molecular mass = Total weighted sum of molecular masses / Total proportion of molecules

Since the total proportion of molecules is 1 (or 100%), the weight average molecular mass is:

Weight average molecular mass = 36000 / 1 = 36000

Explanation:

The weight average molecular mass of the polymer is 36000. This means that, on average, the polymer molecules in the given sample have a molecular mass of 36000. The weight average takes into account both the molecular masses and the proportions of the different types of molecules present in the sample.

By calculating the weighted sum of the molecular masses and dividing it by the total proportion of molecules, we obtain the weight average molecular mass. This calculation accounts for the relative abundance of each type of molecule in the sample, giving more weight to the molecules with higher proportions.

This approach provides a more accurate representation of the overall molecular mass of the polymer sample compared to other types of average, such as the number average or the Z-average.