Polystyrene Molar Mass: Step-by-Step Calculation

Hey everyone! Today, let's dive into a fascinating chemistry question about polystyrene. We're going to figure out the average molar mass of this common plastic, given its molecular weight and the structure of its repeating units. It's like a puzzle, and we're going to crack it together!

The Polystyrene Puzzle: Question Breakdown

So, here's the core of our problem: What is the number-average molar mass of polystyrene with a molecular weight of 25,000 g/mol, considering the structure of polystyrene is formed by repeating units of styrene? We've got some answer choices to consider:

• a) 104 g/mol
• b) 250 g/mol
• c) 1,000 g/mol
• d) 25,000 g/mol

To solve this, we need to understand a few key concepts about polymers and molar mass. Let's break it down step by step.

Understanding Polystyrene: The Building Blocks

Let's start with the basics. Polystyrene is a polymer, which means it's a large molecule made up of many repeating smaller units called monomers. Think of it like a long chain where each link is the same smaller piece. In the case of polystyrene, the monomer is styrene. This is our fundamental building block. To really understand the problem, we need to know what styrene looks like and how much it weighs.

Styrene is a chemical compound with the formula C₈H₈. It's an aromatic hydrocarbon, which means it contains a benzene ring (a six-carbon ring with alternating single and double bonds) attached to an ethene group (two carbon atoms connected by a double bond). This structure is crucial because it dictates how styrene monomers link together to form the polystyrene chain. Now, let's get down to the mass!

To calculate the molar mass of styrene, we need to add up the atomic masses of all the atoms in the molecule. Carbon (C) has an atomic mass of approximately 12 g/mol, and hydrogen (H) has an atomic mass of approximately 1 g/mol. So, for styrene (C₈H₈), we have:

• 8 carbon atoms × 12 g/mol = 96 g/mol
• 8 hydrogen atoms × 1 g/mol = 8 g/mol

Adding these together, we get the molar mass of styrene: 96 g/mol + 8 g/mol = 104 g/mol. This is a key number that we will use to solve the problem. This represents the weight of a single 'link' in our polystyrene chain.

Molecular Weight vs. Molar Mass: Clearing Up the Confusion

Okay, let's make sure we are all on the same page with some terminology. It is super easy to get molecular weight and molar mass confused, but they are slightly different. Molecular weight is a dimensionless quantity that represents the mass of a single molecule relative to the atomic mass unit (amu). It's basically how much a single molecule 'weighs' compared to a standard. On the other hand, molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). A mole is just a specific number of molecules (6.022 x 10²³ to be exact – Avogadro's number!).

In practice, the numerical values of molecular weight and molar mass are often the same, but their units are different. For our problem, we are given a molecular weight of 25,000 g/mol, which we can treat as the molar mass of the entire polystyrene molecule. This means that one mole of this particular polystyrene sample weighs 25,000 grams. It is a hefty molecule!

Now, here’s where it gets interesting. This 25,000 g/mol is the total weight of the polymer chain, but it is made up of many, many styrene units linked together. Our goal is to find the number-average molar mass, which essentially tells us the average weight of a single repeating unit within the polymer chain, considering the total weight and the number of units.

Calculating the Number-Average Molar Mass: Putting It All Together

Alright, let's put on our problem-solving hats! We know the molar mass of the entire polystyrene molecule (25,000 g/mol) and the molar mass of a single styrene unit (104 g/mol). To find the number-average molar mass, we need to figure out how many styrene units are linked together to make up the polystyrene molecule. It is like figuring out how many links are in a chain, given the total weight of the chain and the weight of each link.

The formula to calculate the number of repeating units is pretty straightforward:

Number of repeating units = (Molar mass of the polymer) / (Molar mass of the monomer)

In our case, this translates to:

Number of styrene units = (25,000 g/mol) / (104 g/mol) ≈ 240.38

So, there are approximately 240 styrene units in our polystyrene molecule. However, the question is asking for the number-average molar mass, not the number of units. Thinking about this, the number-average molar mass should be the same as the molar mass of a single styrene unit, because that is the fundamental repeating unit that makes up the polymer. The total molar mass of the polymer is just the molar mass of the monomer multiplied by the number of monomers.

Therefore, the number-average molar mass of polystyrene is simply the molar mass of styrene, which we calculated earlier to be 104 g/mol. This makes sense because we are essentially asking for the average weight of each “link” in the polystyrene chain. Since each link is a styrene molecule, the average weight is just the weight of one styrene molecule.

The Answer: Cracking the Code

So, after all that calculation and thinking, we've arrived at our answer. Looking back at our multiple-choice options:

• a) 104 g/mol
• b) 250 g/mol
• c) 1,000 g/mol
• d) 25,000 g/mol

The correct answer is a) 104 g/mol. This is because the number-average molar mass represents the average mass of the repeating unit, which is styrene, and we calculated the molar mass of styrene to be 104 g/mol. The total molecular weight of the polystyrene (25,000 g/mol) tells us about the size of the entire polymer chain, but the number-average molar mass focuses on the individual building blocks.

Why the Other Answers Are Wrong: Avoiding Common Pitfalls

It's always good to understand why the other options are incorrect. This helps solidify our understanding and avoid similar mistakes in the future. Let's take a quick look:

• b) 250 g/mol: This value doesn't directly relate to either the molar mass of styrene or the total molar mass of polystyrene. It might be a distractor number designed to confuse those who aren't sure of the process.
• c) 1,000 g/mol: Similar to option b, this number doesn't have a clear connection to the given information or the calculation we performed.
• d) 25,000 g/mol: This is the total molecular weight of the polystyrene molecule. While it's a crucial piece of information, it's not the number-average molar mass, which focuses on the repeating unit.

Understanding these distinctions is key to mastering polymer chemistry problems!

Polystyrene in the Real World: More Than Just a Plastic

Polystyrene isn't just some abstract chemical we calculate molar masses for. It's a ubiquitous material that we encounter every day! It's used in a wide range of applications, from packaging and insulation to disposable cups and cutlery. Knowing its properties, including its molar mass and structure, is crucial for understanding its behavior and how it can be used.

For example, the molar mass of a polymer affects its physical properties like strength, flexibility, and melting point. Polystyrene with a higher molar mass tends to be stronger and more resistant to heat. This is why understanding these concepts is so important for material scientists and engineers who design and develop new products.

Key Takeaways: Mastering Molar Mass and Polymers

Let's wrap up with some key takeaways from our polystyrene adventure:

• Polymers are large molecules made up of repeating units called monomers.
• The molar mass of a substance is the mass of one mole of that substance (usually in g/mol).
• The number-average molar mass of a polymer represents the average mass of the repeating unit.
• To calculate the number-average molar mass, you often need to know the molar mass of the monomer and the molar mass of the polymer.
• Understanding the structure of the monomer is crucial for calculating its molar mass.

By grasping these concepts, you'll be well-equipped to tackle similar chemistry problems and gain a deeper understanding of the world of polymers!

Practice Makes Perfect: Keep Exploring

Chemistry is a subject that builds upon itself, so the more you practice, the better you'll become. Try working through similar problems with different polymers and monomers. You can also explore online resources and textbooks for more examples and explanations.

And remember, chemistry isn't just about formulas and equations. It's about understanding the world around us at a molecular level. So, keep exploring, keep questioning, and keep learning!