Question

A sample of a polymer has 200 molecules of molarmass 1000 each, 300 molecules of molarmass 10,000 each and 500 molecules of molarmass 1,00000 . The weight average molecular mass of this polymer is? (a) 55394 (b) 49553 (c) 94553 (d) 35594

Short answer

The weight average molecular mass of the polymer is 53300.

Step-by-step solution

Understand the Given Data

We have three types of molecules in the polymer sample. For each type, we know how many molecules there are and their molar mass. Specifically: - 200 molecules with a molar mass of 1000. - 300 molecules with a molar mass of 10000. - 500 molecules with a molar mass of 100000.

Calculate the Total Mass for Each Molar Mass

To find the total mass for each type of molecule, multiply the number of molecules by their respective molar mass:- Total mass for 1000 molar mass: \( 200 \times 1000 = 200000 \)- Total mass for 10000 molar mass: \( 300 \times 10000 = 3000000 \)- Total mass for 100000 molar mass: \( 500 \times 100000 = 50000000 \)

Determine the Total Mass of the Polymer

Add the total masses calculated in Step 2 to get the overall mass of the polymer sample:\[ 200000 + 3000000 + 50000000 = 53300000 \]

Calculate the Total Number of Molecules

Add the number of molecules from each group to get the total number of molecules:\[ 200 + 300 + 500 = 1000 \]

Calculate the Weight Average Molecular Mass

The weight average molecular mass is calculated using the formula:\[ \text{Weight Average Molecular Mass} = \frac{\text{Total Mass of Polymer}}{\text{Total Number of Molecules}} \]Substitute the values:\[ \frac{53300000}{1000} = 53300 \]

Key concepts

Polymer Chemistry

Polymer chemistry focuses on the study of polymers, which are large molecules made up of repeating subunits called monomers. These polymers can have diverse structures and properties depending on their chemical composition and arrangement. Understanding polymers involves considering a few key factors:

• Molecular Structure: Polymers can be linear, branched, or cross-linked, affecting their properties.


• Molar Mass Distribution: Unlike simple molecules with a definite molar mass, polymers have a range of masses due to differing lengths of polymer chains.


• Properties: The properties of a polymer, such as flexibility, strength, and melting point, depend on both its molecular structure and its molar mass.

In the provided exercise, we looked at calculating the weight average molecular mass of a polymer, which helps chemists understand the material's properties at a molecular level.

Molecular Mass Calculation

Molecular mass calculation in polymer chemistry involves determining the average mass of polymers based on the mass distribution of their repeating units. This calculation is crucial in understanding how a polymer might behave in various chemical and physical contexts.

• Types of Averages: There are different types of averages used in polymer chemistry, like number average and weight average molecular masses. The weight average molecular mass takes into account how much each molecule contributes based on its mass, providing more weight to heavier molecules.


• Calculation Process: Start by multiplying the molar mass of each type of molecule by its number, then sum these to get the total mass. This gives a comprehensive picture of the molar masses in the polymer sample.


• Total Mass and Number: The total mass of all molecules divided by the total number of molecules gives the weight average molecular mass, a crucial metric for characterizing polymers.

In our exercise, calculating the weight average molecular mass was vital to identify the properties of the sample polymer.

Chemistry Problem Solving

Solving chemistry problems often involves a structured and systematic approach. This ensures accuracy and helps students understand complex concepts more clearly.

• Identify Given Data: Carefully note down the specifics, such as the number of molecules and their molar masses. Clear understanding of given data lays the foundation for problem-solving.


• Breakdown Steps: Divide the problem into manageable steps, such as determining individual masses and total mass, simplifying the larger problem into smaller, solvable parts.


• Apply Formulas: Use appropriate formulas, like the weight average molecular mass formula in this exercise, to connect the calculated values to the desired outcome.


• Verification: Once you get a solution, verify it against possible answers or re-check your calculations to ensure accuracy.

In the exercise, we utilized these steps to correctly find the weight average molecular mass of a polymer, showcasing a methodical problem-solving approach common in chemistry.