Question

State whether each of these numbers is a reasonable value for a polymer's molecular weight: 100 amu, \(10,000 \mathrm{amu}\), 100,000 amu, \(1,000,000\) amu?

Short answer

The molecular weights of the given values can be classified as follows: \(100 \mathrm{amu}\) is not a reasonable value for a polymer's molecular weight as it represents a small molecule. On the other hand, \(10,000 \mathrm{amu}\), \(100,000 \mathrm{amu}\), and \(1,000,000 \mathrm{amu}\) are reasonable values for polymer molecular weights, as they represent low, typical, and high molecular weight polymers, respectively.

Step-by-step solution

Understanding molecular weight

Let's first understand what molecular weight is. Molecular weight is the mass of a single molecule of a substance, measured in atomic mass units (amu). The molecular weight of a polymer is essentially the sum of the atomic masses of all the atoms present in the polymer chain.

Compare molecular weight values for a polymer

Now we will analyze each molecular weight and determine whether it is reasonable for a polymer.

Value 1: 100 amu

100 amu is the molecular weight of a small molecule, not a polymer. Polymers usually have higher molecular weights due to larger chain length of monomers. This value is not reasonable for a polymer.

Value 2: 10,000 amu

10,000 amu is an appropriate molecular weight for a low molecular weight polymer. It means that the polymer consists of several units of monomers. This value is reasonable for a polymer.

Value 3: 100,000 amu

100,000 amu is a typical molecular weight for a larger polymer. It has a significant chain length of monomers and is indeed reasonable for a polymer.

Value 4: 1,000,000 amu

1,000,000 amu is an appropriate molecular weight for a high molecular weight polymer. Polymers with these high molecular weights are often present in nature and provide various advantageous properties. This value is reasonable for a polymer.

Conclusion

Based on our analysis, the molecular weights 100 amu is not a reasonable value for a polymer's molecular weight, while 10,000 amu, 100,000 amus, and 1,000,000 amu are reasonable values for polymer molecular weights.

Key concepts

Understanding Molecular Weight

Molecular weight plays a crucial role in chemistry, especially when discussing polymers. It refers to the mass of a single molecule of any substance. For polymers, which are large molecules made up of repeating units called monomers, the molecular weight is the sum of the masses of these building blocks. To calculate it, chemists sum up the atomic masses of every atom that makes up the polymer chain.

Higher molecular weights typically correspond to polymers with a longer chain of monomers, translating to different physical and chemical properties. For example, polymers with higher molecular weights may have greater strength, viscosity, or resistance to chemicals. It's a key factor in determining how a polymer behaves in applications like plastic manufacturing, fabric production, or biomedical devices.

Atomic Mass Unit (amu)

An atomic mass unit (amu) is a standard unit of mass that quantifies the mass of atoms or molecules. It is defined as one-twelfth the mass of a carbon-12 atom. One amu is equivalent to approximately 1.66053906660 x 10^-24 grams, making it an exceedingly small measurement of mass.

The usage of amu is critical when discussing the molecular weight of polymers, as it allows for measuring and comparing the mass of exceedingly small entities such as molecules. By utilizing amu as a standard unit, scientists are able to convey and work with molecular and atomic masses in a practical, simplified way.

Polymer Chain Length

The chain length of a polymer has a direct impact on its properties and hence its molecular weight. This chain is composed of repeated units known as monomers, which are bonded together to form a large polymer molecule. The total number of repeating units in a polymer chain can greatly vary, and with more monomeric units, the chain grows longer, increasing the molecular weight.

It's also interesting to note that different polymerization processes can lead to different molecular weights and chain lengths, resulting in polymers with diverse characteristics suitable for varied applications. This versatility is partly why polymers are ubiquitous in materials such as plastics, rubbers, and fibers.

Monomers

Monomers are the small, repeating units that link together to form polymers. They are the basic building blocks and can be simple molecules like ethylene or propylene, or more complex molecules used in the production of natural biopolymers like DNA and proteins. Each monomer has a set of reactive end groups, which allow them to chemically bond to other monomers in a process called polymerization.

The nature of the monomers not only determines the final molecular weight of the polymer but also its physical and chemical characteristics. Understanding monomers and how they chemically combine is essential for designing and synthesizing new polymers for specific purposes in industries such as pharmaceuticals, agriculture, or aerospace.