Question

Which of the following thermochemical equations can have \(\Delta H_{\mathrm{f}}^{\circ}\) for the heat of the reaction? If it cannot, then why not? (a) \(\mathrm{Na}_{2} \mathrm{SO}_{4}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(l)+2 \mathrm{NaCl}(s)\) (b) \(\mathrm{H}_{2}(g)+\mathrm{S}(s)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(l)\) (c) \(2 \mathrm{H}+\mathrm{S}+4 \mathrm{O} \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(l)\) (d) \(\frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{~S}(s)+\mathrm{O}_{2}(g) \longrightarrow \frac{1}{2} \mathrm{H}_{2} \mathrm{SO}_{4}(l)\)

Short answer

(b) Can have \(\Delta H_{\mathrm{f}}^{\circ}\) because it shows the formation of sulfuric acid from its elements in their standard states. (a), (c), and (d) cannot because they either do not start with the elements in their standard states, or do not form one mole of product.

Step-by-step solution

Definition of \(\Delta H_{\mathrm{f}}^{\circ}\)

Understand that \(\Delta H_{\mathrm{f}}^{\circ}\) represents the standard heat of formation, which is the change in enthalpy when one mole of a compound is formed from its elements in their standard states at 1 atm pressure and 298.15 K.

Check if compounds are formed from their elements in standard states

Review the given equations to determine if the products of each reaction are being formed from their respective elements in their standard states.

Analyze Equation (a)

The equation \(\mathrm{Na}_{2} \mathrm{SO}_{4}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(l)+2 \mathrm{NaCl}(s)\) does not represent the formation of a compound from its elements in their standard states, since \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and \(\mathrm{HCl}\) are compounds, not elements.

Analyze Equation (b)

The equation \(\mathrm{H}_{2}(g)+\mathrm{S}(s)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(l)\) represents the formation of sulfuric acid from its elements hydrogen, sulfur, and oxygen in their standard states, which qualifies for \(\Delta H_{\mathrm{f}}^{\circ}\).

Analyze Equation (c)

The equation \(2 \mathrm{H}+\mathrm{S}+4 \mathrm{O} \longrightarrow \mathrm{H}_{2}\mathrm{SO}_{4}(l)\) does not mention the physical state of hydrogen and oxygen, which implies they are not in their standard states (\mathrm{H}_{2}(g) and \mathrm{O}_{2}(g), respectively). Therefore, this equation cannot have a \(\Delta H_{\mathrm{f}}^{\circ}\) for the heat of the reaction.

Analyze Equation (d)

The equation \(\frac{1}{2} \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{~S}(s)+\mathrm{O}_{2}(g) \longrightarrow \frac{1}{2} \mathrm{H}_{2} \mathrm{SO}_{4}(l)\) involves the correct standard states of the elements, but the coefficients indicate that it describes the formation of \(\frac{1}{2}\) mole of sulfuric acid, not 1 mole, which does not conform to the definition of standard heat of formation.

Key concepts

Understanding Thermochemistry

Thermochemistry is a branch of thermodynamics focused on the study of energy changes during chemical reactions, particularly the heat exchange with the surroundings. The key principle behind thermochemistry is the conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed.

Every chemical reaction involves breaking and forming bonds, processes that either absorb or release energy, typically in the form of heat. Thermochemistry quantifies these energy changes and binds them to stoichiometric coefficients, providing us with a deeper understanding of reaction dynamics and energy efficiency.

Heat of Reaction

The heat of reaction, or enthalpy change for a reaction, indicates whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat). By studying thermochemical equations, we can predict the energy requirements or releases when chemicals interact, essential for industries like pharmaceuticals and material science, safety, and environmental impact assessments.

Enthalpy Change and Its Significance

Enthalpy change, denoted by \( \Delta H \), is the amount of heat absorbed or released by a system at constant pressure during a chemical reaction. It's one of the most prevalent forms of energy change studied in chemistry because it accounts directly for the heats involved in reactions.

When \( \Delta H \) is negative, it signifies an exothermic process; energy is being released to the surroundings, and the products have lower energy than the reactants. Conversely, a positive \( \Delta H \) suggests an endothermic process; energy is absorbed, and the products are at a higher energy level than the reactants.

Standard Heat of Formation

A pivotal concept in thermochemistry is the standard heat of formation (\(\Delta H_{\mathrm{f}}^{\circ}\)), which is defined for the formation of one mole of a compound from its elements in their standard states. This value is crucial as it serves as a benchmark for comparing the energy profiles of different substances and reactions, allowing the calculation of \( \Delta H \) for an overall reaction from tabulated standard heats of formation.

Chemical Reactions and Energy Profiles

Chemical reactions are the processes by which substances, the reactants, transform into different substances, the products. Each reaction is accompanied by an energy profile that describes the energy changes throughout the process. Understanding these profiles is crucial for predicting the behavior and control of chemical reactions.

During a reaction, reactants must overcome an energy barrier known as the activation energy to form the transition state, which then leads to the formation of products. The difference between the energy of the reactants and the products results in the enthalpy change, contributing to the reaction's energy profile.

Exothermic vs. Endothermic

Exothermic reactions are characterized by a decrease in enthalpy, releasing heat to the environment and oftentimes generating warmth or light as byproducts. Endothermic reactions require an input of heat, so the products have higher energy levels than the reactants, and they are typically observed with cooling effects. In the context of the provided exercise, identifying whether a chemical equation embodies a standard heat of formation involves determining if the reactants are in their standard states and if the product formation aligns with the definition of \(\Delta H_{\mathrm{f}}^{\circ}\).