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

01

Write the unbalanced chemical equation

Here's the unbalanced chemical equation given in the problem statement: \(Fe_2O_3 + Al \rightarrow Al_2O_3 + Fe\)

02

Balance the chemical equation

To balance the equation, we need equal numbers of atoms for each element on both sides. Our balanced equation is: \(_{2}Fe_2O_3 + _{3}Al \rightarrow Al_2O_3 + _{4}Fe\)

03

Identify the states of matter

We know that iron(III) oxide and aluminum are solid (s), and aluminum oxide is also a solid. Iron is a solid as well when not melted. So the balanced equation with states of matter is: \(_{2}Fe_2O_3(s) + _{3}Al(s) \rightarrow Al_2O_3(s) + _{4}Fe(s)\) #b) Calculating the grams of aluminum to react completely with 500.0 g of iron oxide#

04

Calculate the moles of iron oxide

Given 500.0 grams of \(Fe_2O_3\), we can determine the moles by dividing by its molar mass: Moles of iron oxide = \(\frac{500.0 g}{(2 \times 55.8) + (3 \times 16)} = 2.96 moles\)

05

Determine the stoichiometry between iron oxide and aluminum

From the balanced equation, we see that 2 moles of iron oxide react with 3 moles of aluminum.

06

Calculate the moles of aluminum needed

Using the stoichiometry, we get the moles of aluminum needed: Moles of aluminum = \(\frac{3 moles}{2 moles} \times 2.96 moles = 4.44 moles\)

07

Calculate the grams of aluminum needed

Multiplying by aluminum's molar mass, we get: Grams of aluminum = \(4.44 moles \times 26.98 g/mole = 119.9 g\) #c) Finding the grams of iron oxide required to produce 1.00 x 10^4 kJ of heat#

08

Calculate the moles of iron oxide needed for 1.00 x 10^4 kJ heat

We are given that 852 kJ of heat is produced per mole of \(Fe_2O_3\). Solving for the moles, we get: Moles of iron oxide = \(\frac{1.00 \times 10^4 kJ}{852 kJ/mole} = 11.7 moles\)

09

Calculate the grams of iron oxide needed

Using the molar mass of \(Fe_2O_3\), we can calculate the grams needed as follows: Grams of iron oxide = \(11.7 moles * 159.7 g/mole = 1868 g\) #d) Identifying if the reverse reaction has heat as a reactant or product#

10

Determine if heat is a reactant or product in the reverse reaction

In the given thermite reaction, heat is produced (an exothermic reaction). For the reverse reaction, heat would be absorbed since the chemical process would require energy to proceed. As a result, heat would be a reactant for the reverse reaction (an endothermic reaction).

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