Question

When iron and steam react at high temperatures, the following reaction takes place. $$ 3 \mathrm{Fe}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{H}_{2}(g) $$ How much iron must react with excess steam to form \(897 \mathrm{~g}\) of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) if the reaction yield is \(69 \%\) ?

Short answer

The mass of iron needed is approximately 938.83 grams.

Step-by-step solution

Convert grams of Fe3O4 to moles

Using the molar mass of Fe3O4, we can convert grams to moles. The molar mass of Fe3O4 is: \(1 Fe_3O_4 = 3(55.8 g/mol) + 4(16.0 g/mol) = 231.6 g/mol\) So, the moles of Fe3O4 formed are: \(moles\,of\,Fe_3O_4 = \frac{897 \,g\,of\,Fe_3O_4}{231.6\, g/mol} = 3.871\,moles\)

Determine moles of iron needed

From the balanced chemical equation, we know that 3 moles of iron react with 1 mole of Fe3O4: \(3 Fe(s) \longrightarrow 1 Fe_3O_4(s)\) Using the mole ratio, we find the moles of iron required: \(moles\,of\,Fe = 3.871\,moles\,of\,Fe_3O_4 \times \frac{3\,moles\,of\,Fe}{1\,mole\,of\,Fe_3O_4} = 11.613\,moles\)

Convert moles of iron to grams

Now, we will convert moles of iron to grams, using the molar mass of iron (55.8 g/mol): \(mass\,of\,Fe = 11.613\,moles\,of\,Fe \times 55.8\,g/mol = 647.83\,g\,of\,Fe\)

Account for the reaction yield

Since the reaction yield is 69%, we need to find the actual mass of iron required by dividing the mass found in step 3 by the percentage yield: \(actual\,mass\,of\,Fe = \frac{647.83\,g\,of\,Fe}{0.69} = 938.833\,g\) The mass of iron needed to react with excess steam to yield 897 grams of Fe3O4 with a reaction yield of 69% is approximately 938.83 grams.

Key concepts

Chemical Reaction Yield

Understanding the chemical reaction yield is crucial when performing experiments or producing chemicals. The yield is the quantity of product obtained from a chemical reaction, usually expressed as a percentage of the theoretical amount. The actual yield is the amount of product actually produced, while the theoretical yield is the amount predicted by stoichiometry.

For example, if a reaction has a 69% yield, this means that only 69% of the theoretical amount was obtained. To determine how much reactant is required for a desired amount of product, we must adjust our calculations to account for the efficiency of the reaction, which includes factors like incomplete reactions or side reactions. To do this, we would divide the mass of the product we aim to produce by the reaction yield (as a decimal), which gives us the adjusted amount of reactant needed.

Mole-to-Mass Conversion

The process of mole-to-mass conversion is a fundamental step in stoichiometry, bridging the gap between the microscopic scale of atoms and the macroscopic world we can measure. A mole is a unit that represents a massive number of particles, 6.022 × 10²³, commonly referred to as Avogadro's number.

To convert moles to grams, we multiply by the molar mass, which is the mass of one mole of a substance. For instance, to find the mass of iron required to produce a specific amount of iron oxide, we'd multiply the moles of iron by the molar mass of iron. Similarly, to go from grams to moles, we divide the mass of the substance by its molar mass.

Balancing Chemical Equations

Every stoichiometry problem starts with a balanced chemical equation, which represents the conservation of mass in a chemical reaction. Balancing a chemical equation involves adjusting the coefficients in front of chemicals until the number of atoms of each element is the same on both sides of the equation. For instance, the equation for the reaction between iron and steam needs to have equal numbers of iron, oxygen, and hydrogen atoms before and after the reaction.

To balance the equation, we might initially count the atoms of each element and iteratively adjust the coefficients. In the provided example, there are three iron atoms on both sides, four water molecules produce four hydrogen molecules and one iron oxide compound, which is how we know the equation is balanced. Accurate balancing is essential for correct stoichiometric calculations.

Stoichiometric Calculations

Finally, we must master stoichiometric calculations to predict how much of each reactant is needed and how much product will be formed in a chemical reaction. These calculations are based on the balanced chemical equation, which provides the mole ratios needed to convert between amounts of reactants and products.

Starting with a known mass or moles of one substance, we utilize the mole ratios to find the corresponding moles of another substance in the reaction. These calculations also help us scale up from a small trial reaction to larger amounts needed for industrial processes, or vice versa. Whether you need to calculate reactant quantities or amounts of products formed, stoichiometry is a foundational tool in chemistry that links quantitative information in a balanced chemical equation to physical masses in the real world.