Question

How many ethylene units are in a polyethylene molecule that has a molecular weight of approximately \(42,000 ?\)

Short answer

There are 1,500 ethylene units in the polyethylene molecule.

Step-by-step solution

Understand the Problem

Polyethylene is a polymer made from repeating units of ethylene. Each ethylene unit contributes to the overall molecular weight of the polyethylene chain. We need to find how many of these units are present in a polyethylene molecule with a molecular weight of approximately 42,000.

Identify the Molecular Weight of Ethylene

Ethylene, \(C_2H_4\), has a molecular weight of approximately \(28\) g/mol. This is calculated by adding the atomic weights of its constituent atoms: 2 carbons (\(12\) g/mol each) and 4 hydrogens (\(1\) g/mol each).

Calculate the Number of Ethylene Units

Divide the total molecular weight of the polyethylene by the molecular weight of a single ethylene unit. This gives us the number of repeating units in the polymer:\[\text{Number of Ethylene Units} = \frac{42,000}{28}\]

Perform the Division

Calculate \( \frac{42,000}{28} \):\[\frac{42,000}{28} = 1,500\]This calculation shows that there are 1,500 ethylene units in the polyethylene molecule.

Key concepts

Exploring Polymer Chemistry

Polymer chemistry is a fascinating field that focuses on the science of polymers. Polymers are large molecules made up of repeating subunits called monomers. These repeating units are covalently bonded in a chain, creating substances that have unique physical and chemical properties. In the case of polyethylene, which is one of the simplest yet most widely produced industrial polymers, the repeating unit is ethylene. Understanding polymer chemistry is crucial because polymers are used in countless products, from plastic bags to medical devices. By grasping the basics of how these long-chain molecules form and function, one can better appreciate the material's versatility and significance in everyday applications.

Identifying the Ethylene Unit

The ethylene unit, also known as ethenyl, is the building block of polyethylene. It consists of two carbon atoms double-bonded to each other, with each carbon atom also bonded to two hydrogen atoms, giving the molecular formula $C_2H_4$. This simple structure makes ethylene highly reactive, allowing it to undergo polymerization to form polyethylene.

• The double bond between the carbon atoms in ethylene is key to its ability to form polymers.
• During polymerization, these double bonds open up and connect with other ethylene molecules.
• The result is a long chain of $C_2H_4$ units, making up polyethylene.

Understanding the role and structure of the ethylene unit is essential in comprehending how polyethylene is created and its characteristics as a polymer.

Molecular Weight Calculation

Calculating the molecular weight of a polymer like polyethylene involves understanding the weight of its monomer units.The molecular weight of ethylene is approximately 28 g/mol, calculated by adding up the atomic masses of its two carbon atoms (12 g/mol each) and four hydrogen atoms (1 g/mol each). When dealing with polyethylene molecules of substantial length, such as one with a molecular weight of 42,000 g/mol, we utilize this value to determine the number of ethylene units.To find out how many ethylene units are there in such a molecule, you divide the total molecular weight of the polymer by the molecular weight of a single ethylene unit:\[\text{Number of Ethylene Units} = \frac{42,000}{28} = 1,500\]This calculation reveals that a polyethylene molecule of this size contains 1,500 ethylene units, helping us understand the polymer's structure and mass.