Problem 71 - Chemistry: An Atoms-Focused Approach

Question

If a reaction vessel contains equal masses of \(\mathrm{Fe}\) and \(\mathrm{S}, \mathrm{a}\) mass of FeS corresponding to which of the following could theoretically be produced? a. the sum of the masses of \(\mathrm{Fe}\) and \(\mathrm{S}\) b. more than the sum of the masses of Fe and \(S\) c. less than the sum of the masses of Fe and \(S\)

Step-by-Step Solution

Answer

Question: In a reaction vessel containing equal masses of iron (Fe) and sulfur (S), the theoretical mass of iron sulfide (FeS) formed in the reaction is (a) equal to the sum of the masses of Fe and S, (b) more than the sum of the masses of Fe and S, (c) less than the sum of the masses of Fe and S. Explain your answer. Answer: The correct answer is (c) less than the sum of the masses of Fe and S. This is because the mass of FeS produced is determined by the limiting reactant in a 1:1 ratio, which will always be less than the sum of the masses of Fe and S.

Step 1: Write the balanced chemical equation for the reaction

The chemical equation for the reaction between iron (Fe) and sulfur (S) to form iron sulfide (FeS) is: Fe + S → FeS Notice that this equation is already balanced.

Step 2: Calculate the molar mass of all reactants and products

Using the periodic table, we can find the molar mass of each substance involved in the reaction: Iron (Fe): 55.85 g/mol Sulfur (S): 32.07 g/mol Iron sulfide (FeS): 55.85 g/mol + 32.07 g/mol = 87.92 g/mol

Step 3: Identify the limiting reactant

Since both Fe and S are present in equal masses, we can divide the mass of each reactant by its respective molar mass to compare the number of moles of each reactant: moles of Fe = mass of Fe / molar mass of Fe moles of S = mass of S / molar mass of S Since the stoichiometry of the reaction is 1:1 (one mole of Fe reacts with one mole of S), the reactant with fewer moles will be the limiting reactant.

Step 4: Calculate the theoretical mass of FeS based on the limiting reactant

Using the limiting reactant, we can calculate the theoretical mass of FeS produced by multiplying the moles of the limiting reactant by the molar mass of FeS: theoretical mass of FeS = moles of limiting reactant * molar mass of FeS Since the mass of FeS produced will be determined by the reactant present in the smallest amount (the limiting reactant), we can compare this theoretical mass of FeS to the sum of the masses of Fe and S present in the original reaction vessel to determine the correct answer.

Step 5: Compare the theoretical mass of FeS with the sum of masses of Fe and S

If the theoretical mass of FeS is equal to the sum of the masses of Fe and S, then option (a) is correct. If it is more than the sum of the masses of Fe and S, then option (b) is correct. If it is less than the sum of the masses of Fe and S, then option (c) is correct. Since the mass of FeS is based on the limiting reactant in a 1:1 ratio, it can be concluded that the theoretical mass of FeS will always be less than the sum of the masses of Fe and S. Therefore, the correct answer is (c) less than the sum of the masses of Fe and S.

Key Concepts

Chemical Equation Balancing

Chemical equation balancing is a crucial step in understanding how substances react with each other. It involves ensuring that the number of atoms for each element is the same on both sides of the equation. This represents the conservation of mass principle, which dictates that matter cannot be created or destroyed in a chemical reaction.
For the formation of iron sulfide (FeS), the reaction can be represented by:

• \[\text{Fe} + \text{S} \rightarrow \text{FeS}\]

In this equation, each side has one iron (Fe) atom and one sulfur (S) atom, making it already balanced.
This equilibrium is important because it allows us to accurately predict the amount of product produced given the amounts of reactants used. Balancing equations is foundational in chemical calculations, such as finding limiting reactants or calculating theoretical yields.

Molar Mass Calculation

Molar mass allows chemists to convert between a substance's mass and the moles present, which is pivotal when solving chemical equations. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol).
To calculate the molar mass of

• Iron (Fe): Refer to the periodic table and find that Fe has a molar mass of approximately 55.85 g/mol.
• Sulfur (S): Similarly, the molar mass is 32.07 g/mol.
• Iron sulfide (FeS): Add the molar masses of iron and sulfur: 55.85 g/mol + 32.07 g/mol, resulting in 87.92 g/mol.

These values are essential for determining the number of moles of each reactant and product, providing a quantitative basis for reaction stoichiometry. Knowing the molar mass helps in calculations involving limiting reactants and theoretical yields.

Theoretical Yield Calculation

Theoretical yield refers to the maximum amount of product that can be formed from a given amount of reactants, assuming complete reaction under ideal conditions. It's calculated by using the balanced equation and involves finding the limiting reactant first.
The steps to calculate the theoretical yield are:

• Identify the reactant that will run out first, known as the limiting reactant. Compare the number of moles of each reactant to determine this.
• Use the balanced equation to determine how many moles of product each mole of the limiting reactant produces. In the reaction \(\text{Fe} + \text{S} \rightarrow \text{FeS},\)

1 mole of Fe reacts with 1 mole of S to produce 1 mole of FeS.

• Calculate the theoretical mass of FeS that can be produced by multiplying moles of the limiting reactant by the molar mass of FeS, which we found to be 87.92 g/mol.

The theoretical yield helps predict whether the amount of product will be equal to, less than, or more than the combined masses of reactants used. In this scenario, the result will always be less due to the limiting reactant principle.