Problem 115 - Chemistry The Central Science

Question

The thermite reaction, $$ \mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{Al} \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3}+\mathrm{Fe} $$ produces so much heat that the Fe product melts. This reaction is used industrially to weld metal parts under water, where a torch cannot be employed. It is also a favorite chemical demonstration in the lecture hall (on a small scale). (a) Balance the chemical equation for the thermite reaction, and include the proper states of matter. (b) Calculate how many grams of aluminum are needed to completely react with 500.0 g of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in this reaction. (c) This reaction produces 852 kJ of heat per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) reacted. How many grams of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) are needed to produce \(1.00 \times 10^{4} \mathrm{kJ}\) of heat? (d) If you performed the reverse reaction aluminum-oxide plus iron makes iron oxide plus aluminum-would that reaction have heat as a reactant or a product?

Step-by-Step Solution

Answer

The balanced chemical equation for the thermite reaction is: 2 Al (s) + Fe₂O₃ (s) → Al₂O₃ (s) + 2 Fe (l). To completely react with 500.0 g of Fe₂O₃, 168.9 g of aluminum is needed. To produce 1.00 x 10⁴ kJ of heat, 1874 g of Fe₂O₃ is needed. In the reverse reaction, heat would be a reactant.

Step 1: (a) Balancing the chemical equation

First, let's balance the given chemical equation: Fe₂O₃ (s) + Al (s) → Al₂O₃ (s) + Fe (l) To balance this equation, we notice that there are 2 Fe atoms on the left side and only 1 Fe atom on the right side. Similarly, there are 3 O atoms on the left side and 2 O atoms on the right side. Thus, we need to balance the equation as follows: 2 Al (s) + Fe₂O₃ (s) → Al₂O₃ (s) + 2 Fe (l) Now, our balanced equation has the same number of each element on both sides.

Step 2: (b) Calculating grams of aluminum

To calculate the grams of aluminum that would completely react with 500.0 g of Fe₂O₃, we will use stoichiometry. First, find the molar mass of Fe₂O₃ and Al: Molar mass of Fe₂O₃ = 2(55.85 g/mol) + 3(16.00 g/mol) = 159.7 g/mol Molar mass of Al = 26.98 g/mol Now, convert grams of Fe₂O₃ to moles, then use the stoichiometric ratio (2 moles of Al for every 1 mole of Fe₂O₃) and finally convert moles of Al back to grams. moles of Fe₂O₃ = 500.0 g / 159.7 g/mol = 3.13 moles moles of Al = 3.13 moles * (2 moles Al / 1 mole Fe₂O₃) = 6.26 moles grams of Al = 6.26 moles * 26.98 g/mol = 168.9 g So, 168.9 g of aluminum is needed to completely react with 500.0 g of Fe₂O₃.

Step 3: (c) Calculating grams of Fe₂O₃ to produce heat

We are given that the reaction produces 852 kJ of heat per mole of Fe₂O₃ reacted. To calculate the grams of Fe₂O₃ needed to produce 1.00 x 10⁴ kJ of heat, we will first convert the kJ to moles of Fe₂O₃ and then convert to grams. 1.00 x 10⁴ kJ * (1 mole Fe₂O₃ / 852 kJ) = 11.737 moles Fe₂O₃ grams of Fe₂O₃ = 11.737 moles * 159.7 g/mol = 1874 g Therefore, 1874 g of Fe₂O₃ is needed to produce 1.00 x 10⁴ kJ of heat.

Step 4: (d) Heat as a reactant or product in the reverse reaction

Heat is released in the given reaction (endothermic), which means that if we were to perform the reverse reaction (Al₂O₃ + Fe → Al + Fe₂O₃), heat would be absorbed (exothermic). Hence, in the reverse reaction, heat would be a reactant.

Key Concepts

Chemical Equation Balancing

Understanding the process of balancing chemical equations is crucial for studying chemical reactions like the thermite reaction. Balancing an equation ensures that the law of conservation of matter is respected, meaning the same number of atoms for each element must be present on both the reactant and product sides of the equation.

In the case of the thermite reaction, the unbalanced equation is \[\mathrm{Fe}_2 \mathrm{O}_3 + \mathrm{Al} \rightarrow \mathrm{Al}_2\mathrm{O}_3 + \mathrm{Fe}\]. To balance this, we observe the number of atoms of each element and adjust the coefficients accordingly. The correct balanced equation is: \[2 \mathrm{Al} (s) + \mathrm{Fe}_2\mathrm{O}_3 (s) \rightarrow \mathrm{Al}_2\mathrm{O}_3 (s) + 2 \mathrm{Fe} (l)\]. The balancing of this equation is key, as it will determine the stoichiometry used for further calculations, such as determining how much reactant is needed to produce a certain amount of product.

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It is derived from a balanced chemical equation and allows scientists to predict the amounts of substances consumed and produced in a given reaction. In the thermite reaction, we use stoichiometry to calculate, for example, how much aluminum is needed for the reaction with a known mass of iron(III) oxide (Fe₂O₃).

By using the molar mass of Fe₂O₃ and Al, we convert grams to moles and then apply the stoichiometric coefficients from the balanced equation to find the corresponding amount of aluminum. In the exercise, a calculation based on stoichiometry showed that \(168.9\) grams of aluminum are required to react with \(500.0\) grams of Fe₂O₃. These quantitative relations are foundational for predicting how chemicals will react in both experimental and industrial settings.

Thermochemistry

Thermochemistry involves the study of the heat energy associated with chemical reactions. The thermite reaction is highly exothermic, releasing a considerable amount of heat. In a thermochemical equation, the amount of energy produced or consumed during the reaction is indicated alongside the chemical equation.

For instance, the thermite reaction produces \(852\) kJ of heat per mole of Fe₂O₃ reacted. Understanding these energy changes is essential for several applications, such as material welding, where the heat released is used to meld materials. Moreover, it allows scientists to calculate the amount of a reactant needed to produce a specific amount of energy, which was demonstrated in the exercise by determining that \(1874\) grams of Fe₂O₃ is required to produce \(1.00 \times 10^{4} \mathrm{kJ}\) of heat. Using thermochemistry principles, we can predict not only the amount of substance involved in a reaction but also the energy changes that occur.