Question

Over the ycars, the thermite reaction has been used for welding railroad rails, in incendiary bombs, and to ignite solid fuel rocket motors. The reaction is $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \rightarrow 2 \mathrm{Fe}(l)+\mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ What mass of iron(III) oxide must be used to produce \(25.69 \mathrm{~g}\) of iron? b. What mass of aluminum must be used to produce \(25.69 \mathrm{~g}\) of iron? c. What is the maximum mass of aluminum oxide that could be produced along with \(25.69 \mathrm{~g}\) of iron?

Short answer

To produce 25.69 g of Iron, 36.7 g of iron(III) oxide is required, and 12.4 g of aluminum is needed. The maximum mass of aluminum oxide produced along with 25.69 g of Iron is 23.4 g.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation for the thermite reaction is: \[ Fe_2O_3(s) + 2Al(s) \rightarrow 2Fe(l) + Al_2O_3(s) \]

Calculate the moles of produced Iron.

To find the amount of iron(III) oxide required, first, we need to calculate the moles of produced Iron. We can do this using the molar mass of Iron: \(1 \ mol \ \mathrm{Fe} = 55.85 \ g\) \[ \text{moles of Fe} = \frac{25.69 \ g}{55.85 \ g/mol} = 0.46 \ mol \]

Calculate the moles of iron(III) oxide required.

According to the balanced chemical equation, 1 mole of \(Fe_2O_3\) reacts to form 2 moles of Fe. Now, we will find out how many moles of \(Fe_2O_3\) are required to produce 0.46 mol of Fe: \[ \text{moles of}\ Fe_2O_3 = \frac{0.46 \ mol}{2} = 0.23 \ mol \]

Calculate the mass of iron(III) oxide required.

To calculate the mass of iron(III) oxide required, we will multiply the moles of \(Fe_2O_3\) with its molar mass: \(1 \ mol \ Fe_2O_3 = (2 \times 55.85 + 3 \times 16.00) = 159.7\ g\) \[ \text{mass of}\ Fe_2O_3 = 0.23 \ mol \times 159.7 \frac{g}{mol} = 36.7 \ g \] So, 36.7 g of iron(III) oxide must be used to produce 25.69 g of Iron. b. Mass of aluminum required to produce 25.69 g of Iron

Calculate the moles of aluminum required.

According to the balanced chemical equation, 2 moles of Al react to form 2 moles of Fe. Now, we will find out how many moles of Al are required to produce 0.46 mol of Fe: \[ \text{moles of Al} = 0.46 \ mol \]

Calculate the mass of aluminum required.

To calculate the mass of aluminum required, we will multiply the moles of Al with its molar mass: \(1 \ mol \ \mathrm{Al} = 26.98 \ g\) \[ \text{mass of Al} = 0.46 \ mol \times 26.98 \frac{g}{mol} = 12.4 \ g \] So, 12.4 g of aluminum must be used to produce 25.69 g of Iron. c. Maximum mass of aluminum oxide produced along with 25.69 g of Iron

Calculate the moles of aluminum oxide produced.

According to the balanced chemical equation, 2 moles of Al react to produce 1 mole of \(Al_2O_3\). Now, we will find out how many moles of \(Al_2O_3\) are produced when 0.46 mol of Al reacts: \[ \text{moles of}\ Al_2O_3 = \frac{0.46 \ mol}{2} = 0.23 \ mol \]

Calculate the mass of aluminum oxide produced.

To calculate the mass of aluminum oxide produced, we will multiply the moles of \(Al_2O_3\) with its molar mass: \(1 \ mol \ \mathrm{Al}_2\mathrm{O}_3 = 101.96\) g \[ \text{mass of}\ Al_2O_3 = 0.23 \ mol \times 101.96 \frac{g}{mol} = 23.4 \ g \] So, the maximum mass of aluminum oxide produced along with 25.69 g of Iron is 23.4 g.

Key concepts

Iron(III) Oxide in the Thermite Reaction

Iron(III) oxide, also known as ferric oxide, plays a key role in the highly exothermic thermite reaction. This reaction can produce molten iron when iron(III) oxide reacts with aluminum powder. Besides its industrial uses in welding and creating incendiary devices, this reaction provides an excellent example of a redox reaction where iron(III) oxide is reduced to iron while aluminum is oxidized to aluminum oxide.

In this reaction, the chemical formula for iron(III) oxide is \(Fe_2O_3\), which consists of two iron (Fe) atoms and three oxygen (O) atoms. Understanding the composition of iron(III) oxide is essential in predicting both qualitative and quantitative aspects of the reaction it participates in, including the stoichiometry calculations required to determine the reactants' masses for a desired amount of iron.

Understanding Stoichiometry in Chemical Reactions

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the substances involved in chemical reactions. In the context of the thermite reaction, stoichiometry allows us to calculate the exact amounts of reactants needed to produce a certain quantity of products.

The balanced chemical equation provides the mole ratio between reactants and products: \(Fe_2O_3 + 2Al \rightarrow 2Fe + Al_2O_3\). This equation indicates that two moles of aluminum are needed for every mole of iron(III) oxide to produce two moles of iron and a mole of aluminum oxide. It's through these ratios that chemists can predict how much of each substance will react, so that none of the reactants go to waste, and safety is ensured when handling the exothermic nature of the thermite reaction.

From Moles to Mass Calculation

The conversion from moles to mass is a foundational concept in chemistry and a vital part of stoichiometry. To perform a moles to mass calculation for a chemical reaction, you need two key pieces of information: the number of moles of the substance and its molar mass.

Molar mass is a constant that represents the mass of one mole of a substance and is expressed in grams per mole (g/mol). It can be found by adding the atomic masses of each element in the compound, as featured in the periodic table. Once the moles of a substance are known, as determined through stoichiometry based on balanced chemical equations, the mass can be calculated by multiplying the number of moles by its molar mass. For the thermite reaction, these calculations allow us to determine the precise masses of iron(III) oxide and aluminum needed to yield a specific mass of iron, as well as the resulting mass of aluminum oxide produced.