Problem 115 - Chemistry The Central Science In Si Units

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 \(500.0 \mathrm{~g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in this reaction. (c) This reaction produces \(852 \mathrm{~kJ}\) 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

a) The balanced equation is: \( \mathrm{Fe}_2 \mathrm{O}_3 \mathrm{(s)} + 2 \mathrm{Al(s)} \rightarrow \mathrm{Al}_2 \mathrm{O}_3 \mathrm{(s)} + 2 \mathrm{Fe(l)} \). b) 169.0 g of Al is needed. c) 1874.53 g of \( \mathrm{Fe}_2 \mathrm{O}_3 \) is needed. d) Heat would be a reactant.

Step 1: Balance the Chemical Equation

First, identify the elements in the equation: Fe, O, and Al. Write down the unbalanced equation: \[ \mathrm{Fe}_2 \mathrm{O}_3 \mathrm{(s)} + \mathrm{Al(s)} \rightarrow \mathrm{Al}_2 \mathrm{O}_3 \mathrm{(s)} + \mathrm{Fe(l)} \]Balance the equation by making sure the number of atoms for each element is equal on both sides. Balance Fe first: 2 Fe on each side. Then balance Al: 2 Al on each side. Lastly, balance O: 3 O on each side. The balanced reaction becomes:\[ \mathrm{Fe}_2 \mathrm{O}_3 \mathrm{(s)} + 2 \mathrm{Al(s)} \rightarrow \mathrm{Al}_2 \mathrm{O}_3 \mathrm{(s)} + 2 \mathrm{Fe(l)} \]

Step 2: Calculate Grams of Aluminum Needed

Given 500.0 g of \( \mathrm{Fe}_2 \mathrm{O}_3 \), determine the grams of Al needed. First, find the molar mass of \( \mathrm{Fe}_2 \mathrm{O}_3 \) (159.69 g/mol) and \( \mathrm{Al} \) (26.98 g/mol). Calculate moles of \( \mathrm{Fe}_2 \mathrm{O}_3 \):\[ \text{Moles of } \mathrm{Fe}_2 \mathrm{O}_3 = \frac{500.0 \text{ g}}{159.69 \text{ g/mol}} = 3.13 \text{ moles} \]Using the balanced equation, convert moles of \( \mathrm{Fe}_2 \mathrm{O}_3 \) to moles of Al needed (1:2 stoichiometry):\[ 3.13 \text{ moles } \mathrm{Fe}_2 \mathrm{O}_3 \times 2 = 6.26 \text{ moles Al} \]Now convert moles of Al to grams:\[ 6.26 \text{ moles } \mathrm{Al} \times 26.98 \text{ g/mol} = 169.0 \text{ g Al} \]

Step 3: Calculate Grams of \( \mathrm{Fe}_2 \mathrm{O}_3 \) for Energy Production

The reaction produces 852 kJ/mol of \( \mathrm{Fe}_2 \mathrm{O}_3 \). Calculate moles of \( \mathrm{Fe}_2 \mathrm{O}_3 \) needed to produce 10,000 kJ:\[ \text{Moles needed} = \frac{1.00 \times 10^4 \text{ kJ}}{852 \text{ kJ/mol}} = 11.74 \text{ moles} \]Convert moles to grams using the molar mass of \( \mathrm{Fe}_2 \mathrm{O}_3 \) (159.69 g/mol):\[ 11.74 \text{ moles} \times 159.69 \text{ g/mol} = 1874.53 \text{ g} \]

Step 4: Reverse Reaction Heat Requirement

In the reverse reaction, \( \mathrm{Al}_2 \mathrm{O}_3 \) + \( \mathrm{Fe} \rightarrow \mathrm{Fe}_2 \mathrm{O}_3 \) + \( \mathrm{Al} \), the heat would be absorbed to break the newly formed bonds, making heat a reactant, not a product. This reaction would be endothermic.

Key Concepts

Thermochemistry

Thermochemistry is a fascinating branch of chemistry that focuses on the heat energy changes during chemical reactions. One of the classic examples demonstrating thermochemistry is the thermite reaction. In this process, aluminum reacts with iron(III) oxide producing molten iron and aluminum oxide, releasing a substantial amount of heat. The reaction is represented by the equation: \( \mathrm{Fe}_2 \mathrm{O}_3(\mathrm{s}) + 2 \mathrm{Al(s)} \rightarrow \mathrm{Al}_2 \mathrm{O}_3(\mathrm{s}) + 2 \mathrm{Fe(l)} \). This reaction is highly exothermic, making it an essential illustration of how chemical reactions can release energy, often in the form of heat, which in industrial applications like welding can be incredibly useful. In thermochemistry, the energy exchanged during a reaction is measured in kilojoules (kJ), helping chemists understand both the energy costs and gains of reactions.

Stoichiometry

Stoichiometry is about the relationship between the amounts of reactants and products in a chemical reaction. In the thermite reaction, a fundamental stoichiometric calculation can determine how much aluminum is needed to react with a given amount of iron(III) oxide. For instance, with 500 grams of \( \mathrm{Fe}_2 \mathrm{O}_3 \), you need to convert this mass to moles using its molar mass, which is 159.69 g/mol. This gives approximately 3.13 moles of \( \mathrm{Fe}_2 \mathrm{O}_3 \). The balanced chemical equation shows that for each mole of iron(III) oxide, two moles of aluminum are required. Thus, 6.26 moles of aluminum are needed. Knowing the molar mass of aluminum ( 26.98 g/mol), you can calculate the mass of aluminum required, which is 169 grams. Stoichiometry allows chemists to predict the quantities of substances required or produced in a reaction, ensuring efficiency and balance in chemical processes.

Endothermic vs Exothermic Reactions

In chemical reactions, heat can either be released or absorbed, classifying them as either exothermic or endothermic. The thermite reaction is an excellent example of an exothermic reaction because it releases heat to the surroundings, hence \( 852 \text{kJ} \) of heat per mole of \( \mathrm{Fe}_2 \mathrm{O}_3 \) is produced. This immense heat production is why the iron melts during the reaction, making it crucial for industrial applications like welding. Conversely, if you were to perform the reverse reaction where aluminum oxide and iron combine to form iron oxide and aluminum, the process would need energy to break the bonds. This means heat must be added, categorizing the reverse reaction as endothermic, as it absorbs heat rather than releasing it. Understanding the heat changes in reactions helps industries to plan energy requirements and safety measures.

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry allowing the conservation of mass principle to be applied, meaning matter is neither created nor destroyed in a reaction. For the thermite reaction, the unbalanced equation is \( \mathrm{Fe}_2 \mathrm{O}_3(\mathrm{s}) + \mathrm{Al(s)} \rightarrow \mathrm{Al}_2 \mathrm{O}_3(\mathrm{s}) + \mathrm{Fe(l)} \). To balance it, count the atoms of each element on both sides. Start with iron (Fe), which requires 2 atoms on each side. Next, balance aluminum (Al) with 2 atoms on both sides. Finally, balance the oxygen (O), making sure there are 3 atoms per side. The balanced equation is \( \mathrm{Fe}_2 \mathrm{O}_3(\mathrm{s}) + 2 \mathrm{Al(s)} \rightarrow \mathrm{Al}_2 \mathrm{O}_3(\mathrm{s}) + 2 \mathrm{Fe(l)} \). Balancing equations ensures that the number of atoms for each element is maintained, reflecting the physical reality of the reaction and helping accurately predict product formation.