Stoichiometry Problems: Calculating Percentage And Mass

Oct 16, 2025 by ADMIN 56 views

Hey guys! Let's dive into some stoichiometry problems that often pop up in chemistry. We're going to break down how to calculate the percentage of an element in a compound and how to determine the mass of a substance in a chemical formula. So, grab your calculators and let's get started!

Problem 1: Finding the Percentage of Iron (Fe) in a Compound

Let's tackle this question first: If Mr Fex(SO₄) = 400 and Ar Fe = 56, what is the percentage (%) of Fe in the compound?

This is a classic stoichiometry problem where we need to find the percentage of iron (Fe) in a compound with a given molecular weight. Here's how we can solve it, step by step:

Step 1: Understand the Basics

Before we jump into calculations, let's clarify a few terms:

Mr (Relative Molecular Mass): This is the sum of the atomic masses of all atoms in a molecule. In our case, Mr Fex(SO₄) = 400.
Ar (Relative Atomic Mass): This is the mass of an atom relative to 1/12th the mass of a carbon-12 atom. Here, Ar Fe = 56.
Percentage Composition: This tells us the percentage by mass of each element in a compound.

Step 2: Determine the Number of Iron Atoms

The formula Fex(SO₄) tells us that there are 'x' atoms of iron (Fe) in the compound. We need to figure out what 'x' is. Since we know the total Mr of the compound and the Ar of Fe, we can set up an equation.

The molecular formula given is Fex(SO₄). To determine the number of iron atoms (x), we need to consider the molar mass of the entire compound and the atomic mass of iron. The molar mass of the compound, Mr Fex(SO₄), is given as 400, and the atomic mass of iron (Ar Fe) is 56. We'll also need to account for the molar mass of the sulfate (SO₄) group.

Step 3: Calculate the Molar Mass of the Sulfate (SO₄) Group

To find the molar mass of the sulfate group (SO₄), we need to add the atomic masses of sulfur (S) and oxygen (O) in the correct proportions. The atomic mass of sulfur (Ar S) is approximately 32, and the atomic mass of oxygen (Ar O) is 16. There are four oxygen atoms in the sulfate group, so we calculate the molar mass as follows:

Molar mass of SO₄ = (1 × Ar S) + (4 × Ar O) = (1 × 32) + (4 × 16) = 32 + 64 = 96

Step 4: Set Up the Equation

Now we can set up an equation to solve for x. The molar mass of the entire compound (Mr Fex(SO₄)) is the sum of the masses of all its components:

Mr Fex(SO₄) = (x × Ar Fe) + Molar mass of SO₄

We know Mr Fex(SO₄) = 400, Ar Fe = 56, and the molar mass of SO₄ = 96. Plugging these values into the equation, we get:

400 = (x × 56) + 96

Step 5: Solve for x

Now, let's solve for x:

Subtract 96 from both sides of the equation:

400 - 96 = 56x

304 = 56x

Divide both sides by 56:

x = 304 / 56

x ≈ 5.43

Since x represents the number of iron atoms, it must be a whole number. There seems to be a discrepancy in the provided data or the molar mass calculation. We'll proceed assuming x is meant to be a whole number for the purpose of this problem, and we'll use x = 1 for demonstration. If we use x = 1:

400 = (1 × 56) + Molar mass of SO₄

Molar mass of SO₄ = 400 - 56 = 344

This is inconsistent with the known molar mass of SO₄ (96), indicating an issue with the initial data. For the sake of completing the problem-solving process, we will assume the compound is FeSO₄ (x = 1) and recalculate the percentage of iron based on this assumption.

Step 6: Calculate the Mass of Iron in the Compound

The mass of iron in the compound is simply the number of iron atoms (x) multiplied by the atomic mass of iron (Ar Fe):

Mass of Fe = x × Ar Fe

If we assume x = 1:

Mass of Fe = 1 × 56 = 56

Step 7: Calculate the Percentage of Iron

Now we can calculate the percentage of iron in the compound:

Percentage of Fe = (Mass of Fe / Mr Fex(SO₄)) × 100

Assuming x = 1:

Percentage of Fe = (56 / 400) × 100

Percentage of Fe = 0.14 × 100

Percentage of Fe = 14%

So, based on our assumption that the compound is FeSO₄, the percentage of iron in the compound is 14%.

Therefore, the correct answer is A. 14%

Problem 2: Determining the Mass of Oxygen in a Compound

Now, let's move on to the second question: A compound with the formula CxHyOz contains 72 grams of carbon, and what amount of oxygen? (Ar H=1, C=12, O=16)

This problem requires us to find the mass of oxygen in a compound given the mass of carbon and the atomic masses of the elements involved. Here's how we can approach it:

Step 1: Find the Number of Moles of Carbon

The first step is to determine the number of moles of carbon in the compound. We can use the formula:

Moles = Mass / Ar

Where:

Mass = 72 grams (given)
Ar (C) = 12 (atomic mass of carbon)

So,

Moles of C = 72 g / 12 g/mol = 6 moles

Step 2: Understand the Stoichiometry

The formula CxHyOz tells us the ratio of the elements in the compound. We know that there are 6 moles of carbon (C), but we need more information to determine the exact moles of oxygen (O). Without knowing the values of x, y, and z, we can’t directly calculate the moles of oxygen.

However, we can proceed if we make an assumption or are given additional information, such as the molar mass of the compound or the mass of another element in the compound. Let's assume for a moment that we have additional information that allows us to relate the moles of carbon to the moles of oxygen.

Step 3: Assume a Relationship Between Carbon and Oxygen

For the sake of demonstration, let’s assume that the compound is a simple carbohydrate, and the ratio of carbon to oxygen is 1:1. This would mean that for every mole of carbon, there is one mole of oxygen. In this case:

Moles of O = Moles of C = 6 moles

Step 4: Calculate the Mass of Oxygen

Now we can calculate the mass of oxygen using the formula:

Mass = Moles × Ar

Where:

Moles of O = 6 moles
Ar (O) = 16 (atomic mass of oxygen)

So,

Mass of O = 6 moles × 16 g/mol = 96 grams

Step 5: General Approach with Insufficient Information

In a real scenario, if we don't have enough information to directly relate carbon to oxygen (like in our assumption), we would need additional data such as the molar mass of the compound or the mass of hydrogen. If, for instance, we knew the compound's molar mass, we could set up equations to solve for the unknowns (x, y, z).

For example, if the molar mass of CxHyOz is M, we could write:

(x × 12) + (y × 1) + (z × 16) = M

And we would need at least two more independent pieces of information to solve for x, y, and z. Without this, we can't find a unique solution.

Conclusion

If we assume a 1:1 ratio of carbon to oxygen (based on the hypothetical scenario that the compound is a simple carbohydrate), the mass of oxygen is 96 grams. However, without additional information, this problem cannot be definitively solved.

Therefore, we can tentatively say that if there's a 1:1 ratio, the answer is 96 grams, but we need more data for a conclusive answer.

Key Takeaways

To find the percentage of an element in a compound, calculate the mass of the element and divide it by the molar mass of the compound, then multiply by 100.
To find the mass of an element in a compound, you need to know the moles of that element and its atomic mass. If you're missing information, look for relationships or additional data.

Stoichiometry can seem tricky at first, but with practice, you'll get the hang of it! Keep practicing, and you'll be solving these problems like a pro in no time. Good luck, guys!