N₂O Gas Mass Calculation Based On SO₂ Sulfur Content

Oct 13, 2025 by ADMIN 53 views

Hey guys! Let's dive into a fascinating chemistry problem where we'll calculate the mass of N₂O gas based on the sulfur content in a given amount of SO₂ gas. This type of problem often pops up in stoichiometry, and understanding the steps involved is crucial for mastering chemical calculations. So, grab your calculators, and let's get started!

Understanding the Problem

The core of this problem lies in understanding the relationships between the masses of elements within different compounds. We're given 3.2 grams of sulfur dioxide (SO₂) gas and asked to find out how many grams of nitrous oxide (N₂O) gas contain the same mass of oxygen as the mass of sulfur in the SO₂. Sounds a bit complex, right? Don't worry; we'll break it down step by step.

Key Information and Concepts

Before we jump into the calculations, let's highlight the essential information and concepts:

Molar masses: We're given the molar masses of nitrogen (N = 14 g/mol), oxygen (O = 16 g/mol), and sulfur (S = 32 g/mol). These are our conversion factors between grams and moles.
SO₂ gas: We have 3.2 grams of SO₂. We need to figure out the mass of sulfur in this compound.
N₂O gas: We need to find the mass of N₂O that contains the same mass of oxygen as the sulfur we calculated from the SO₂.
Stoichiometry: This is the heart of the problem – the quantitative relationship between reactants and products in chemical reactions and compounds. In this case, it's the relationship between the elements within the compounds.

Breaking Down the Question

To make it clearer, let's rephrase the question:

How much sulfur is present in 3.2 grams of SO₂?
How much oxygen has the same mass as the sulfur calculated in step 1?
How many grams of N₂O contain the mass of oxygen calculated in step 2?

Now, with this roadmap, let's start crunching the numbers!

Step-by-Step Solution

Let's tackle this problem step by step to make sure we've got it all covered. We'll start by figuring out how much sulfur is in the SO₂.

Step 1: Calculate Moles of SO₂

The first thing we need to do is convert the mass of SO₂ to moles. To do this, we'll use the molar mass of SO₂. The molar mass of SO₂ is calculated by adding the molar masses of its constituent elements: sulfur (S) and oxygen (O).

Molar mass of S = 32 g/mol
Molar mass of O = 16 g/mol
Molar mass of SO₂ = 32 (for S) + 2 * 16 (for O₂) = 32 + 32 = 64 g/mol

Now we can convert grams of SO₂ to moles using the formula:

Moles = Mass / Molar mass

Moles of SO₂ = 3.2 g / 64 g/mol = 0.05 moles

So, we have 0.05 moles of SO₂.

Step 2: Determine Moles and Mass of Sulfur in SO₂

In each molecule of SO₂, there is one atom of sulfur. This means that the number of moles of sulfur is the same as the number of moles of SO₂.

Moles of S = 0.05 moles (since there's one sulfur atom per SO₂ molecule)

Now, let's convert moles of sulfur back to grams using the molar mass of sulfur:

Mass of S = Moles * Molar mass

Mass of S = 0.05 moles * 32 g/mol = 1.6 grams

So, in 3.2 grams of SO₂, there are 1.6 grams of sulfur. That wasn't so hard, was it?

Step 3: Determine the Mass of Oxygen to Match Sulfur

The question asks us to find the amount of N₂O that contains the same mass of oxygen as the mass of sulfur we just calculated. So, we need to find the amount of N₂O that contains 1.6 grams of oxygen.

Step 4: Calculate Moles of Oxygen

To work with oxygen in N₂O, we first need to find out how many moles of oxygen are equivalent to 1.6 grams. We use the molar mass of oxygen (O = 16 g/mol):

Moles of O = Mass / Molar mass

Moles of O = 1.6 g / 16 g/mol = 0.1 moles

So, we need 0.1 moles of oxygen.

Step 5: Determine Moles of N₂O

Now, let's look at the formula for nitrous oxide, N₂O. In each molecule of N₂O, there is one oxygen atom. This means that the number of moles of N₂O will be the same as the number of moles of oxygen.

Moles of N₂O = Moles of O = 0.1 moles

Step 6: Calculate the Mass of N₂O

Finally, we can calculate the mass of N₂O using its molar mass. The molar mass of N₂O is calculated as follows:

Molar mass of N = 14 g/mol
Molar mass of O = 16 g/mol
Molar mass of N₂O = (2 * 14) + 16 = 28 + 16 = 44 g/mol

Now, we use the formula:

Mass = Moles * Molar mass

Mass of N₂O = 0.1 moles * 44 g/mol = 4.4 grams

Therefore, 4.4 grams of N₂O gas contain the same mass of oxygen as the mass of sulfur in 3.2 grams of SO₂ gas.

Final Answer

So, the final answer is 4.4 grams (Option B). We made it through the problem step by step, and now we have a clear understanding of how to solve it!

Key Takeaways

Let's recap the key steps we took to solve this problem:

Convert grams to moles: We started by converting the mass of SO₂ to moles using its molar mass.
Determine moles of the element: We identified the moles of sulfur in SO₂ based on the compound's formula.
Calculate mass of the element: We converted moles of sulfur to grams to find the mass of sulfur.
Calculate moles of oxygen: We found the moles of oxygen needed to match the mass of sulfur.
Determine moles of the target compound (N₂O): We identified the moles of N₂O required based on the moles of oxygen.
Convert moles to grams: Finally, we converted moles of N₂O to grams using its molar mass.

By breaking down the problem into manageable steps and using molar masses as conversion factors, we were able to solve this stoichiometry problem efficiently. These skills are super important in chemistry, so keep practicing!

Practice Makes Perfect

To really nail these types of problems, practice is key! Try solving similar problems with different compounds and masses. You can change the given mass of SO₂ or ask for a different target gas. The more you practice, the more comfortable you'll become with these calculations.

Example Practice Question:

How many grams of CO₂ contain the same mass of oxygen as the mass of carbon in 10 grams of CH₄? (C: 12, H: 1, O: 16 g/mol)

Give it a shot and see if you can apply the steps we discussed. Good luck, and happy calculating!