How To Calculate The Molar Mass Of Ammonium Sulfate (NH₄)₂SO₄

Hey guys! Ever wondered how chemists figure out the weight of tiny little molecules? It's all about something called molar mass, and it's super important for all sorts of chemistry calculations. Today, we're going to break down how to calculate the molar mass of a common chemical compound: ammonium sulfate, which has the chemical formula (NH₄)₂SO₄. We've been given the molar masses of the individual elements that make up this compound: nitrogen (N), hydrogen (H), sulfur (S), and oxygen (O). Let's dive in and figure out the molar mass of the whole compound, step by step!

First off, let's make sure we're all on the same page about what molar mass actually means. Molar mass is basically the mass of one mole of a substance. A mole is just a chemist's way of counting a really big number of things – like, 6.022 x 10²³ things (that's Avogadro's number, if you're curious!). Molar mass is usually expressed in grams per mole (g/mol), which tells us how many grams one mole of a particular substance weighs. Understanding the concept of molar mass is crucial for various calculations in chemistry, including stoichiometry, solution preparation, and determining the amount of reactants and products in a chemical reaction. In this context, we'll use the molar masses of individual elements to calculate the molar mass of the entire compound, ammonium sulfate (NH₄)₂SO₄. This process involves carefully considering the number of atoms of each element present in the chemical formula and summing their contributions to the overall molar mass. So, with the foundational understanding of molar mass in place, we're ready to tackle the specific problem of determining the molar mass of (NH₄)₂SO₄. This requires a systematic approach, breaking down the compound into its constituent elements and accounting for their respective molar masses and quantities within the molecule. It's like building with LEGOs, but instead of colorful bricks, we're using atoms with specific weights to construct the molar mass of a chemical compound. So, buckle up, because we're about to embark on a molar mass adventure!

The first thing we need to do is figure out exactly what's in this compound. The formula (NH₄)₂SO₄ might look a little complicated, but it's just a combination of different elements: nitrogen (N), hydrogen (H), sulfur (S), and oxygen (O). The subscripts and parentheses tell us how many of each atom are present. Let's break it down:

• (NH₄)₂: This part means we have two ammonium ions (NH₄⁺). Each ammonium ion contains 1 nitrogen (N) atom and 4 hydrogen (H) atoms. Since we have two of these ions, that's a total of 2 nitrogen atoms (2 x 1) and 8 hydrogen atoms (2 x 4).
• SO₄: This part is the sulfate ion, which contains 1 sulfur (S) atom and 4 oxygen (O) atoms.

So, to recap, one molecule of (NH₄)₂SO₄ contains:

• 2 nitrogen (N) atoms
• 8 hydrogen (H) atoms
• 1 sulfur (S) atom
• 4 oxygen (O) atoms

Knowing the precise composition of the molecule is the key to accurately calculating its molar mass. Without a correct understanding of the number of atoms of each element, the final molar mass calculation would be off. This initial step sets the stage for the subsequent calculations, where we'll use the given molar masses of the individual elements to determine the total molar mass of the compound. It's like reading a recipe before you start cooking – you need to know the ingredients and their quantities before you can create the final dish. In our case, the "dish" is the molar mass of ammonium sulfate, and the "ingredients" are the atoms of nitrogen, hydrogen, sulfur, and oxygen. Now that we've identified our ingredients, let's move on to the next step: calculating their contribution to the molar mass. This involves multiplying the number of atoms of each element by its molar mass and then summing up these values to get the total molar mass of the compound. So, let's get our calculators ready and dive into the calculations!

Now that we know the number of atoms of each element in (NH₄)₂SO₄, we can use the given molar masses to calculate the total molar mass of the compound. Here's how we do it:

1. Nitrogen (N): We have 2 nitrogen atoms, and each nitrogen atom has a molar mass of 14.01 g/mol. So, the total contribution from nitrogen is 2 * 14.01 g/mol = 28.02 g/mol.
2. Hydrogen (H): We have 8 hydrogen atoms, and each hydrogen atom has a molar mass of 1.01 g/mol. So, the total contribution from hydrogen is 8 * 1.01 g/mol = 8.08 g/mol.
3. Sulfur (S): We have 1 sulfur atom, and it has a molar mass of 32.07 g/mol. So, the contribution from sulfur is simply 32.07 g/mol.
4. Oxygen (O): We have 4 oxygen atoms, and each oxygen atom has a molar mass of 16.00 g/mol. So, the total contribution from oxygen is 4 * 16.00 g/mol = 64.00 g/mol.

To find the molar mass of the entire compound, we add up the contributions from each element:

Molar mass of (NH₄)₂SO₄ = 28.02 g/mol (N) + 8.08 g/mol (H) + 32.07 g/mol (S) + 64.00 g/mol (O) = 132.17 g/mol

So, the molar mass of ammonium sulfate (NH₄)₂SO₄ is 132.17 g/mol. This result is achieved by meticulously adding the individual contributions of each element, reflecting the precise stoichiometric composition of the compound. The process highlights the importance of understanding chemical formulas and how they translate into quantitative information about the compound's mass. Each step in the calculation – from identifying the number of atoms to multiplying by the respective molar masses – is critical in arriving at the correct answer. The final molar mass of 132.17 g/mol represents the mass of one mole of ammonium sulfate, a value that is essential for converting between mass and moles in chemical calculations. This conversion is fundamental in stoichiometry, where it's used to determine the amounts of reactants and products involved in a chemical reaction. Therefore, understanding and correctly calculating molar mass is not just an academic exercise; it's a practical skill with wide-ranging applications in chemistry and related fields.

Looking at the options provided, the correct answer is:

• D. 132.17 g / mol

Calculating molar mass might seem a bit tricky at first, but it's really just a matter of breaking down the formula, counting the atoms, and adding up their weights. Once you get the hang of it, you'll be calculating molar masses like a pro! This skill is crucial for understanding chemical reactions and doing all sorts of cool chemistry stuff. Keep practicing, and you'll ace it! Remember, the molar mass of a compound is a fundamental property that connects the microscopic world of atoms and molecules to the macroscopic world of grams and kilograms. Its accurate determination is essential for quantitative analysis in chemistry, enabling us to predict and control chemical reactions. By systematically breaking down the chemical formula and accounting for the atomic weights of each element, we can reliably calculate the molar mass of any compound. In the case of ammonium sulfate, our step-by-step calculation demonstrates the power of this approach. The result, 132.17 g/mol, is not just a number; it's a key piece of information that unlocks a deeper understanding of the compound's behavior and its role in chemical processes. So, whether you're a student learning the basics or a seasoned chemist working in the lab, mastering molar mass calculations is a skill that will serve you well. It's the foundation upon which many other chemical concepts are built, and it's a testament to the precision and beauty of chemistry as a science.