Question

The thermite reaction, \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+2 \mathrm{Al}(\mathrm{s}) \longrightarrow 2 \mathrm{Fe}(\mathrm{s})+\) \(\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})\), is one of the most exothermic reactions known. The heat released is sufficient to melt the iron product; consequently, the thermite reaction is used to weld metal under the ocean. \(\Delta H^{\circ}\) for the thermite reaction is \(-851.5 \mathrm{~kJ} / \mathrm{mole}\). What is the mass change per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) that accompanies this reaction?

Short answer

The mass change per mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) during the thermite reaction is -1.00 g/mol.

Step-by-step solution

Determine the molar masses

First, let's find the molar masses of each reactant and product involved in the thermite reaction. We can refer to the periodic table to find the atomic masses: For \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})\): - Molar mass of Fe = 55.845 g/mol - Molar mass of O = 16.00 g/mol Molar mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3} = 2 \times 55.845 + 3 \times 16.00 = 159.69 \,\mathrm{g/mol}\) For \(\mathrm{Al}(\mathrm{s})\): - Molar mass of Al = 26.98 g/mol For \(\mathrm{Fe}(\mathrm{s})\): - Molar mass of Fe = 55.845 g/mol For \(\mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})\): - Molar mass of Al = 26.98 g/mol - Molar mass of O = 16.00 g/mol Molar mass of \(\mathrm{Al}_{2} \mathrm{O}_{3} = 2 \times 26.98 + 3 \times 16.00 = 101.96 \,\mathrm{g/mol}\)

Calculate the mass change per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\)

Now let's calculate the mass change per mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) during the thermite reaction using the molar masses. For the balanced equation, 1 mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) reacts with 2 moles of \(\mathrm{Al}\) to produce 2 moles of \(\mathrm{Fe}\) and 1 mole of \(\mathrm{Al}_{2} \mathrm{O}_{3}\). Mass change per mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) = (Initial mass of reactants - Final mass of products) / moles of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) Initial mass of reactants = Mass of 1 mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3} + 2 \times\) mass of 1 mole of \(\mathrm{Al}\) = \(159.69\,\mathrm{g/mol} + 2 \times 26.98\,\mathrm{g/mol} = 213.65\,\mathrm{g/mol}\) Final mass of products = Mass of 2 moles of \(\mathrm{Fe} + 1 \times\) mass of 1 mole of \(\mathrm{Al}_{2}\mathrm{O}_{3}\) = \(2 \times 55.845\,\mathrm{g/mol} + 101.96\,\mathrm{g/mol} = 214.65\,\mathrm{g/mol}\) Mass change per mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3} = \cfrac{213.65\,\mathrm{g/mol} - 214.65\,\mathrm{g/mol}}{1\,\mathrm{mol}} = -1.00\,\mathrm{g/mol}\) The mass change per mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) during the thermite reaction is -1.00 g/mol.

Key concepts

Enthalpy Change

Enthalpy change, or \(\Delta H\), is a critical concept in thermodynamics that represents the heat absorbed or released during a chemical reaction at constant pressure. The significance of this measurement lies in its ability to indicate whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).

In the context of the thermite reaction, \(\Delta H^{\circ}\) is given as -851.5 kJ/mol. This value tells us that the reaction is highly exothermic; more specifically, it informs us that 851.5 kJ of energy is released for every mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) that reacts. This large release of heat is what makes the iron product melt—making the thermite reaction ideal for applications that require a high-heat source, like underwater welding.

Molar Mass Calculation

Understanding molar mass calculation is essential for delving into the stoichiometry of a reaction. The molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol), and it is a fundamental property used in various chemical calculations.

For the thermite reaction, the molar mass of each compound must be known to determine the mass change during the reaction. Molar mass is calculated by summing the atomic masses of the elements in the compound, which are consistent values found in the periodic table. For instance, the molar mass of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) includes 2 moles of iron and 3 moles of oxygen, combining to 159.69 g/mol.

Chemical Reactions

A chemical reaction is a process that transforms one or more substances into different substances. The substances that undergo change are called reactants, and the new substances produced are called products.

The thermite reaction, expressed as \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s}) + 2 \mathrm{Al}(\mathrm{s}) \longrightarrow 2 \mathrm{Fe}(\mathrm{s}) + \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{~s})\), showcases a transformation from iron oxide and aluminum to iron and aluminum oxide. It is a redox reaction where aluminum is oxidized, and iron oxide is reduced—a critical concept in understanding the electron transfer that takes place during the reaction.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. The principle of stoichiometry is based on the law of conservation of mass, which states that matter cannot be created or destroyed in an ordinary chemical reaction.

In the step-by-step solution, stoichiometry is used to calculate the mass change per mole of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) by considering the molar masses and the balanced chemical equation. It requires an understanding of the stoichiometric coefficients, which, in this chemical equation, tell us for every 1 mole of iron(III) oxide that reacts, 2 moles of aluminum are consumed, and 2 moles of iron and 1 mole of aluminum oxide are produced. The final calculation reveals the mass change involved in the reaction.