Problem 34 - Chemistry Matter and Change

Question

Apply In an experiment, you combine 83.77 \(\mathrm{g}\) of iron with an excess of sulfur and then heat the mixture to obtain iron(lil) sulfide. $$2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{S}(\mathrm{s}) \rightarrow \mathrm{Fe}_{2} \mathrm{S}_{3}(\mathrm{s})$$ What is the theoretical yield, in grams, of iron(III) sulfide?

Step-by-Step Solution

Answer

The theoretical yield of iron(III) sulfide is 155.93 g.

Step 1: Determine the Molar Mass of Iron

First, calculate the molar mass of iron (Fe). The atomic mass of iron is approximately 55.85 g/mol. Therefore, the molar mass of iron is 55.85 g/mol.

Step 2: Convert Mass of Iron to Moles

Using the molar mass of iron, convert the given mass of iron used in the reaction to moles. The formula to find moles is: \[ \text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}} = \frac{83.77 \, \text{g}}{55.85 \, \text{g/mol}} = 1.50 \, \text{moles of Fe} \]

Step 3: Use Stoichiometry to Find Moles of Fe2S3 Produced

According to the balanced chemical equation, 2 moles of Fe produce 1 mole of Fe2S3. Therefore, the moles of Fe2S3 formed are calculated as follows: \[ \text{moles of Fe}_2\text{S}_3 = \frac{1.50 \, \text{moles of Fe}}{2} = 0.75 \, \text{moles of Fe}_2\text{S}_3 \]

Step 4: Determine the Molar Mass of Fe2S3

Calculate the molar mass of Fe2S3. The formula consists of 2 Fe atoms and 3 S atoms. Using the atomic masses 55.85 g/mol for Fe and 32.07 g/mol for S, calculate: \[ \text{Molar mass of Fe}_2\text{S}_3 = 2(55.85) + 3(32.07) = 207.9 \, \text{g/mol} \]

Step 5: Convert Moles of Fe2S3 to Grams

Finally, convert the moles of Fe2S3 to grams using the molar mass of Fe2S3: \[ \text{mass of Fe}_2\text{S}_3 = 0.75 \, \text{moles of Fe}_2\text{S}_3 \times 207.9 \, \text{g/mol} = 155.93 \, \text{g} \]

Step 6: Conclusion

The theoretical yield of iron(III) sulfide, Fe2S3, when 83.77 g of iron is used with excess sulfur is 155.93 g.

Key Concepts

Molar Mass Calculation

In chemistry, the molar mass is a critical concept, representing the mass of one mole of a substance. To perform a molar mass calculation, you need to know the atomic masses of the elements involved. The atomic mass of iron (Fe) is approximately 55.85 g/mol. This value is derived from the periodic table and represents the mass of one mole of iron atoms. If you are calculating the molar mass of a compound, like iron (III) sulfide (Fee2Se3), you must sum the molar masses of all the atoms present:

• For Fee2Se3, you need two Fe atoms and three S atoms.
• The sulfur (S) atom has an atomic mass of about 32.07 g/mol.
• Thus, the calculation is: \(2 \times 55.85 + 3 \times 32.07 = 207.9 \, \text{g/mol}\).

This calculated molar mass is crucial for further calculations involving this compound.

Stoichiometry

Stoichiometry is the bridge between the quantities of reactants and products in chemical reactions. It is rooted in the concept of the mole, which allows chemists to relate amounts of substances. Through stoichiometry, we determine the proportions of elements and compounds involved in reactions. For example, in the balanced equation:\[2 \text{Fe}(\text{s}) + 3 \text{S}(\text{s}) \rightarrow \text{Fe}_2\text{S}_3(\text{s})\]The stoichiometric coefficients (2, 3, and 1, respectively) tell us that 2 moles of iron react with 3 moles of sulfur to form 1 mole of iron(III) sulfide. This tells us the mole ratio critical to calculating how much product we can obtain from a given amount of reactant. Using the example, 1.5 moles of iron based on stoichiometry produce 0.75 moles of Fee2Se3, as shown in our calculation steps.

Chemical Reaction Balancing

Chemical reaction balancing is essential to ensure that mass and charge are conserved in a reaction. Essentially, it involves making sure that the number of atoms of each element is the same on both sides of the equation. For instance, consider this equation:\[2 \text{Fe}(\text{s}) + 3 \text{S}(\text{s}) \rightarrow \text{Fe}_2\text{S}_3(\text{s})\]Balance is achieved by adjusting coefficients before formulas and NOT by changing subscripts within formulas. Ul>

The process begins by listing all components involved.

Then, adjust coefficients to ensure that each element has the same number of atoms on both sides.

This balanced equation shows that 2 Fe atoms and 3 S atoms react to form 1 molecule of Fee2Se3.

Balancing is key to accurately predicting reaction yields and performing stoichiometric calculations.

Moles to Grams Conversion

Converting moles to grams is a fundamental step in many chemical calculations. This conversion uses the molar mass as a bridge between the amount of substance in moles and its mass. Here's the basic formula used:\[\text{mass} = \text{moles} \times \text{molar mass}\]Consider the example where we found 0.75 moles of Fee2Se3, and we determined its molar mass to be 207.9 g/mol. To convert the amount to grams, simply multiply:\[\text{mass of Fe}_2\text{S}_3 = 0.75 \, \text{moles} \times 207.9 \, \text{g/mol} = 155.93 \, \text{g}\]Understanding this conversion is crucial because it allows chemists to predict the mass of products in a reaction, given the amount of reactants used. This is directly tied to calculating a reaction's theoretical yield, such as in our example where 155.93 g is the predicted mass of iron(III) sulfide synthesized.