Mass Of 4.54 Moles Of Na₂SO₄: Step-by-Step Calculation

Aug 5, 2025 by ADMIN 55 views

Calculating the Mass of 4.54 Moles of Na₂SO₄: A Chemistry Deep Dive

Hey everyone! Today, we're diving into a classic chemistry problem: calculating the mass of a given number of moles of a compound. Specifically, we'll be figuring out the mass of 4.54 moles of sodium sulfate ($Na_2SO_4$). This is a fundamental concept in chemistry, and mastering it will help you tackle all sorts of stoichiometry problems. So, let's break it down step by step.

Understanding Moles, Molar Mass, and the Connection

Before we jump into the calculation, let's make sure we're all on the same page with the key concepts. The mole is the SI unit for the amount of substance. Think of it like a chemist's counting unit. Just like a dozen means 12, a mole represents a specific number of particles: 6.022 x 10²³. This incredibly large number is known as Avogadro's number. Why such a big number? Because atoms and molecules are incredibly tiny! A mole of anything contains Avogadro's number of those things, whether it's atoms, molecules, ions, or even elephants (though a mole of elephants would be a bit… much).

Now, what about molar mass? The molar mass of a substance is the mass of one mole of that substance, usually expressed in grams per mole (g/mol). It's a crucial link between the number of moles and the mass of a substance. You can find the molar mass of a compound by adding up the atomic masses of all the atoms in its chemical formula. These atomic masses are readily available on the periodic table. For example, the molar mass of water ($H_2O$) is approximately 18.015 g/mol (2 times the atomic mass of hydrogen plus the atomic mass of oxygen).

The connection between moles, molar mass, and mass is beautifully simple: mass (g) = moles (mol) x molar mass (g/mol). This equation is the cornerstone of many stoichiometric calculations. It allows us to convert between the amount of a substance in moles and its mass in grams, and vice versa. Understanding this relationship is key to solving our problem today and many other chemistry challenges.

To really solidify this concept, let's think about an analogy. Imagine you're buying apples. You could buy them individually, but if you need a lot, it's easier to buy them by the bag. Let's say each bag contains a "mole" of apples (okay, not literally Avogadro's number, but go with it!). The "molar mass" would be the weight of one bag of apples. If you know how many bags (moles) you want, and you know the weight of one bag (molar mass), you can easily calculate the total weight of apples you'll be buying. This is exactly what we're doing with chemical substances!

Now that we've got a solid grasp of moles and molar mass, we're ready to tackle the specific problem at hand: calculating the mass of 4.54 moles of $Na_2SO_4$. We'll break down the calculation step-by-step, making sure we understand each part of the process. So, let's get calculating!

Calculating the Molar Mass of $Na_2SO_4$

The first step in finding the mass of 4.54 moles of $Na_2SO_4$ is to determine the molar mass of the compound. Remember, the molar mass is the mass of one mole of a substance, and we can calculate it by adding up the atomic masses of all the atoms in the chemical formula. For $Na_2SO_4$ (sodium sulfate), the formula tells us we have:

2 sodium (Na) atoms
1 sulfur (S) atom
4 oxygen (O) atoms

To find the atomic masses, we'll consult the periodic table. Here's what we find:

Sodium (Na): 22.99 g/mol
Sulfur (S): 32.07 g/mol
Oxygen (O): 16.00 g/mol

Now, we multiply the atomic mass of each element by the number of atoms of that element in the formula, and then add them all together:

(2 atoms Na * 22.99 g/mol) + (1 atom S * 32.07 g/mol) + (4 atoms O * 16.00 g/mol) = Molar mass of $Na_2SO_4$

Let's do the math:

(2 * 22.99) + (1 * 32.07) + (4 * 16.00) = 45.98 + 32.07 + 64.00 = 142.05 g/mol

So, the molar mass of $Na_2SO_4$ is 142.05 g/mol. You might notice this is slightly different from the value provided in the problem (142.04 g/mol). This is likely due to rounding differences in the atomic masses used. For the sake of consistency and to demonstrate the calculation process, we'll use the value we just calculated (142.05 g/mol) in the next step. However, in a real-world scenario, it's always best to use the molar mass provided in the problem or the most accurate values available to you.

Understanding how to calculate molar mass is a fundamental skill in chemistry. It's not just about plugging numbers into a formula; it's about understanding the relationship between the chemical formula and the mass of a substance. This skill will be crucial for solving a wide range of problems, from simple stoichiometry calculations to more complex chemical reactions. So, make sure you practice calculating molar mass for different compounds until it becomes second nature.

With the molar mass of $Na_2SO_4$ in hand, we're now ready for the final step: calculating the mass of 4.54 moles. We'll use the key equation we discussed earlier, and it will all come together beautifully. So, let's move on to the grand finale of our calculation!

Calculating the Mass Using the Mole-Mass Conversion

Alright, guys, we've reached the final step! We know the number of moles of $Na_2SO_4$ (4.54 moles), and we've calculated the molar mass (142.05 g/mol). Now, we can use the mole-mass conversion formula to find the mass in grams:

Mass (g) = Moles (mol) x Molar Mass (g/mol)

Let's plug in the values:

Mass (g) = 4.54 mol * 142.05 g/mol

Now, we just need to do the multiplication:

Mass (g) = 644.817 g

Since we're dealing with experimental measurements, it's important to consider significant figures. The number of moles (4.54) has three significant figures, and the molar mass (142.05) has five significant figures. When multiplying, we round our final answer to the same number of significant figures as the value with the fewest significant figures. In this case, that's three significant figures.

So, rounding 644.817 g to three significant figures gives us 645 g.

Therefore, the mass of 4.54 moles of $Na_2SO_4$ is approximately 645 grams.

Congratulations! We've successfully calculated the mass of a given number of moles of a compound. This is a fundamental skill in chemistry, and you've now mastered it. Remember the key equation (Mass = Moles x Molar Mass) and practice using it with different compounds and different numbers of moles. The more you practice, the more confident you'll become in your ability to solve stoichiometry problems.

This calculation highlights the power of the mole concept in chemistry. It allows us to bridge the gap between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms that we can measure in the lab. By understanding the relationship between moles, molar mass, and mass, we can accurately quantify chemical substances and predict the outcomes of chemical reactions.

Key Takeaways and Further Practice

Let's recap the key takeaways from this exercise:

The mole is a unit for the amount of substance. It represents Avogadro's number (6.022 x 10²³) of particles.
Molar mass is the mass of one mole of a substance. It's calculated by summing the atomic masses of all atoms in the chemical formula.
The key equation for mole-mass conversion is: Mass (g) = Moles (mol) x Molar Mass (g/mol).
Significant figures are important! Always round your final answer to the correct number of significant figures.

To further solidify your understanding, try working through similar problems with different compounds. For example, you could calculate the mass of 2.75 moles of glucose ($C_6H_{12}O_6$) or the number of moles in 100 grams of sodium chloride (NaCl). You can also explore the reverse problem: calculating the number of moles in a given mass of a substance.

Chemistry is a fascinating and challenging subject, but with practice and a solid understanding of the fundamentals, you can master it. Keep exploring, keep questioning, and keep calculating! You've got this!