Question

Show how the sum of enthalpy of formation equations produces each of the following reactions. You do not need to look up and include ?H values a. \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) b. \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\)

Short answer

For reaction (a), we have: Step 1: Formation of NO: \( \frac{1}{2} N_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow NO(g) \) Step 2: Formation of NO2: \( \frac{1}{2} N_{2}(g) + O_{2}(g) \rightarrow NO_{2}(g) \) Combine Steps 1 & 2: \( 2 NO(g) + O_{2}(g) \rightarrow 2 NO_{2}(g) \) For reaction (b), we have: Step 1: Formation of SO3: \( S(s) + \frac{3}{2} O_{2}(g) \rightarrow SO_{3}(g) \) Step 2: Formation of H2O: \( H_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow H_{2}O(l) \) Step 3: Formation of H2SO4: \( H_{2}(g) + S(s) + 2 O_{2}(g) \rightarrow H_{2}SO_{4}(aq) \) Combine Steps 1-3: \( SO_{3}(g) + H_{2}O(l) \rightarrow H_{2}SO_{4}(aq) \)

Step-by-step solution

Reaction (a) Step 1: Formation of NO

To form NO, its constituent elements N and O need to combine: \( \frac{1}{2} N_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow NO(g) \)

Reaction (a) Step 2: Formation of NO2

For formation of NO2, its constituent elements N and O need to react: \( \frac{1}{2} N_{2}(g) + O_{2}(g) \rightarrow NO_{2}(g) \)

Reaction (a) Step 3: Combine Steps 1 & 2 to get reaction (a)

To get the reaction (a), we need to multiply the enthalpy of formation of NO by 2 and add the enthalpy of formation of O2, which should be equal to the enthalpy of formation of NO2 multiplied by 2: \( 2 \left[ \frac{1}{2} N_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow NO(g) \right] + O_{2}(g) \rightarrow 2 \left[ \frac{1}{2} N_{2}(g) + O_{2}(g) \rightarrow NO_{2}(g) \right] \) Simplifying this equation gives us the reaction (a): \( 2 NO(g) + O_{2}(g) \rightarrow 2 NO_{2}(g) \)

Reaction (b) Step 1: Formation of SO3

To form SO3, its constituent element S and O need to react: \( S(s) + \frac{3}{2} O_{2}(g) \rightarrow SO_{3}(g) \)

Reaction (b) Step 2: Formation of H2O

For formation of H2O, its constituent elements H and O need to react: \( H_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow H_{2}O(l) \)

Reaction (b) Step 3: Formation of H2SO4

For formation of H2SO4, its constituent elements H, S and O need to combine: \( H_{2}(g) + S(s) + 2 O_{2}(g) \rightarrow H_{2}SO_{4}(aq) \)

Reaction (b) Step 4: Combine Steps 1-3 to get reaction (b)

To get the reaction (b), the enthalpy of formation of SO3 and reverse of enthalpy of formation of H2O (since it is a reactant) should be equal to the enthalpy of formation of H2SO4: \( \left[ S(s) + \frac{3}{2} O_{2}(g) \rightarrow SO_{3}(g) \right] - \left[ H_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow H_{2}O(l) \right] \rightarrow H_{2}(g) + S(s) + 2 O_{2}(g) \rightarrow H_{2}SO_{4}(aq) \) Simplifying this equation gives us the reaction (b): \( SO_{3}(g) + H_{2}O(l) \rightarrow H_{2}SO_{4}(aq) \)

Key concepts

Chemical Reactions

A chemical reaction is a process where substances, known as reactants, are transformed into different substances, known as products. In the exercise provided, we're looking at the formation of different chemical compounds from their elemental forms, which is an essential concept in the study of chemical reactions.

For instance, in equation (a), nitrogen (N) and oxygen (O) combine to form nitrogen dioxide (NO₂). These transformations are governed by the laws of conservation of mass and energy, where atoms are neither created nor destroyed during a chemical reaction, meaning each atom of the reactants must be accounted for in the products.

In simplifying chemical reactions, as in the given solutions for NO and NO₂ formation, the original complexity of the step-by-step interactions between elements is reduced to stoichiometric coefficients that reflect the balanced equation. Understanding how these transformations occur and being able to balance the equations is fundamental to mastering chemical reactions.

Thermochemistry

Thermochemistry deals with the heat involved in chemical reactions. An important aspect of this is the concept of enthalpy (\( H \)), which represents the total heat content of a system. When dealing with enthalpies of reactions, the enthalpy of formation, which is the change in enthalpy when one mole of a compound is formed from its elements at standard conditions, becomes very relevant.

In the exercise, the focus is on the sum of enthalpy of formation equations. These equations help determine the overall heat change during the formation of compounds like NO₂ and H₂SO₄ from their respective elements. This is important because it gives insights into the energy requirements or release during the reaction, which has practical applications in industries such as materials synthesis and energy production.

By understanding how to combine the enthalpies of individual steps, as shown in the solutions to yield the enthalpies of overall reactions (a) and (b), students can predict whether a reaction will release heat (exothermic) or absorb heat (endothermic) without needing to memorize specific values.

Stoichiometry

Stoichiometry is the quantitative relationship between the amounts of reactants and products in a chemical reaction. It allows chemists to predict the quantities of substances consumed and produced in a reaction, based on the balanced chemical equation.

In our exercise, stoichiometry is applied to understand the formation of nitrogen dioxide (NO₂) and sulfuric acid (H₂SO₄). For example, the reaction forming NO₂ requires balancing the nitrogen and oxygen atoms on both sides of the reaction. This balancing act ensures that the equation adheres to the law of conservation of mass.

The provided solutions demonstrate how to scale the reactions for the formation of intermediates (NO and SO₃) and then how to sum them to arrive at the final balanced equation for the desired compounds. Mastering stoichiometry is crucial for a student's ability to perform calculations involving mass, moles, and gas volume in reactions, making it a cornerstone of chemical education.