Calculate Sucrose Mass: A Chemistry Guide

by Chloe Fitzgerald 42 views

Hey guys! Let's dive into a fun chemistry problem today. We're going to figure out the mass of a sucrose sample using its molar mass and the number of moles. This is a classic chemistry calculation, and I'm here to break it down for you in a super easy-to-understand way. So, grab your calculators, and let's get started!

Understanding Molar Mass and Moles

Before we jump into the problem, let's quickly review what molar mass and moles are. These are fundamental concepts in chemistry, and grasping them is crucial for solving stoichiometry problems like this one.

What is Molar Mass?

Molar mass is essentially the mass of one mole of a substance. A mole is a unit of measurement used in chemistry to express amounts of a chemical substance. Think of it like a chemist's dozen. Just like a dozen means 12 items, a mole represents a specific number of particles – specifically, 6.022 x 10^23 particles. This number is known as Avogadro's number. Molar mass is usually expressed in grams per mole (g/mol).

For example, the molar mass of sucrose ($ ext{C}{12} ext{H}{22} ext{O}_{11}$) is given as 342.3 g/mol. This means that one mole of sucrose weighs 342.3 grams. This value is derived from the atomic masses of each element in the sucrose molecule (Carbon, Hydrogen, and Oxygen) which are found on the periodic table. You sum the atomic masses of all the atoms in the molecule to get the molar mass.

Understanding molar mass is crucial because it provides a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams that we can measure in the lab. It's a key conversion factor in many chemical calculations.

What is a Mole?

Now, let's talk about the mole itself. As mentioned earlier, a mole is a unit of amount in chemistry. It's the amount of a substance that contains the same number of particles (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. That magical number is Avogadro's number: 6.022 x 10^23.

The mole concept allows us to relate the number of particles to the mass of a substance. This is super handy because we can't directly count individual atoms or molecules in a sample, but we can measure mass. Using the mole, we can figure out how many particles are present in a given mass of a substance. This is essential for balancing chemical equations and predicting the amounts of reactants and products in a chemical reaction.

For example, if we have 0.500 moles of sucrose, it means we have 0.500 times Avogadro's number of sucrose molecules. The mole is the central unit in stoichiometry, the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. So, understanding moles is a cornerstone of your chemistry knowledge.

The Problem: Finding the Mass of Sucrose

Okay, with those concepts fresh in our minds, let's tackle the problem. We're given the molar mass of sucrose ($ ext{C}{12} ext{H}{22} ext{O}_{11}$) as 342.3 g/mol, and we have a 0.500-mol sample of sucrose. Our mission is to find the mass of this sample in grams.

This is a classic example of a mole-to-mass conversion. We're starting with the number of moles and want to find the mass. The molar mass acts as our conversion factor, linking moles and grams. Think of it as the bridge that allows us to cross from the world of moles to the world of grams, and vice versa.

The relationship we'll use is pretty straightforward:

Mass (grams) = Number of moles × Molar mass (g/mol)

This formula is the key to solving a wide variety of chemistry problems. It allows us to easily convert between the amount of a substance in moles and its mass in grams. It is one of the most fundamental equations you will use in your chemistry journey!

Step-by-Step Solution

Let's plug in the values we have and solve for the mass. This is where the math magic happens, but don't worry, it's super simple.

  1. Identify the given information:

    • Number of moles of sucrose = 0.500 mol
    • Molar mass of sucrose = 342.3 g/mol

  2. Apply the formula:

    • Mass (grams) = Number of moles × Molar mass
    • Mass = 0.500 mol × 342.3 g/mol

  3. Calculate the mass:

    • Mass = 171.15 g

So, the mass of the 0.500-mol sample of sucrose is 171.15 grams. But let's consider significant figures here!

Significant Figures: The Chemist's Precision Tool

In chemistry, we always pay attention to significant figures. They tell us about the precision of our measurements and calculations. In this problem, both the number of moles (0.500 mol) and the molar mass (342.3 g/mol) have three significant figures.

When we multiply or divide, the result should have the same number of significant figures as the measurement with the fewest significant figures. In our case, both numbers have three significant figures, so our answer should also have three significant figures.

Therefore, we round 171.15 g to 171 g. So, our final answer, considering significant figures, is:

Mass = 171 grams

Significant figures ensure that we're not overstating the accuracy of our results. It's a crucial practice in scientific calculations to reflect the precision of the measurements we're working with.

The Answer and Why It Makes Sense

So, the mass of the 0.500-mol sample of sucrose is 171 grams. That's option A in our choices. Yay, we got it!

Now, let's think about why this answer makes sense. We have half a mole of sucrose (0.500 mol), and we know that one mole of sucrose weighs 342.3 grams. So, it's logical that half a mole would weigh approximately half of 342.3 grams. And indeed, 171 grams is very close to half of 342.3 grams. Thinking about the reasonableness of our answers is always a good practice to make sure we haven't made any calculation errors!

Common Mistakes to Avoid

When solving problems like this, there are a few common mistakes that students often make. Let's quickly go over them so you can avoid falling into these traps:

  1. Forgetting the Units: Always, always, always include units in your calculations and final answer. Units not only tell you what the number represents but also help you catch mistakes. If your units don't cancel out correctly, you know you've probably done something wrong.

  2. Using the Wrong Formula: Make sure you're using the correct formula for the conversion. In this case, we used Mass = Number of moles × Molar mass. Confusing this with other formulas can lead to incorrect results.

  3. Ignoring Significant Figures: As we discussed earlier, significant figures are crucial. Make sure to apply the rules of significant figures correctly in your calculations and final answer. Rounding errors can significantly affect your answer's accuracy.

  4. Misunderstanding Molar Mass: Ensure you have a clear understanding of what molar mass represents. It's the mass of one mole of a substance, not the mass of a single molecule. This distinction is key to using molar mass correctly in calculations.

By being mindful of these common pitfalls, you'll be well-equipped to tackle mole-mass conversions with confidence!

Practice Problems: Sharpening Your Skills

Okay, guys, now that we've walked through the solution, it's time to flex those chemistry muscles! Practice makes perfect, so let's try a couple of similar problems.

  1. Problem 1: What is the mass of a 2.00-mol sample of water (H2O), given that the molar mass of water is 18.015 g/mol?

  2. Problem 2: A chemist has a 0.250-mol sample of sodium chloride (NaCl). The molar mass of NaCl is 58.44 g/mol. Calculate the mass of the sample.

Work through these problems step-by-step, using the same approach we used for the sucrose problem. Remember to pay attention to units and significant figures. The more you practice, the more comfortable you'll become with these types of calculations.

Real-World Applications: Why This Matters

You might be wondering,