Question

For the following reactions at constant pressure, predict if \(\Delta H>\) \(\Delta E, \Delta H<\Delta E\), or \(\Delta H=\Delta E\) a. \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

a. \(\Delta H = \Delta E\) b. \(\Delta H < \Delta E\) c. \(\Delta H > \Delta E\)

Step-by-step solution

Count the moles of gas on both sides of the reaction

Count the number of moles of gaseous reactants and products in the balanced chemical equation.

Determine the change in volume

Use the differences in the number of moles of gases on the reactants and products sides to determine the change in volume, \(\Delta V\).

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Using the equation \(\Delta H = \Delta E + P\Delta V\) and the value of \(\Delta V\), determine whether \(\Delta H > \Delta E\), \(\Delta H < \Delta E\), or \(\Delta H = \Delta E\). a. \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\)

Count the moles of gas on both sides

Reactants: 2 moles of HF (g) Products: 1 mole of H2 (g) + 1 mole of F2 (g)

Determine the change in volume

Since the number of gas moles is the same on both sides (2 moles), we have no change in volume: \(\Delta V=0\).

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Since \(\Delta V = 0\), the equation simplifies to \(\Delta H = \Delta E\). Hence, \(\Delta H = \Delta E\). b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2\mathrm{NH}_{3}(g)\)

Count the moles of gas on both sides

Reactants: 1 mole of N2 (g) + 3 moles of H2 (g) Products: 2 moles of NH3 (g)

Determine the change in volume

There are 4 moles of gas in the reactants and 2 moles of gas in the products, resulting in a decrease in volume: \(\Delta V < 0\).

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Since \(\Delta V < 0\), then \(\Delta H < \Delta E + P\Delta V\) (with \(P\Delta V<0\)). Hence, \(\Delta H < \Delta E\). c. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4\mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Count the moles of gas on both sides

Reactants: 4 moles of NH3 (g) + 5 moles of O2 (g) Products: 4 moles of NO (g) + 6 moles of H2O (g)

Determine the change in volume

There are 9 moles of gas in the reactants and 10 moles of gas in the products, resulting in an increase in volume: \(\Delta V > 0\).

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Since \(\Delta V > 0\), then \(\Delta H > \Delta E + P\Delta V\) (with \(P\Delta V>0\)). Hence, \(\Delta H > \Delta E\).

Key concepts

Enthalpy (ΔH)

Enthalpy is a crucial concept in thermodynamics, representing the total heat content of a system. When studying chemical reactions, particularly at constant pressure, enthalpy changes help us understand heat transfer. This is denoted by the symbol \( \Delta H \). It reflects changes in energy during a reaction.

The expression \( \Delta H = \Delta E + P\Delta V \) connects enthalpy with internal energy \( (\Delta E) \) and the pressure-volume work \( (P\Delta V) \). In simple terms, this equation illustrates how enthalpy accounts for both the change in internal energy and the work done by or on the substance due to volume changes.

Comprehending \( \Delta H \) allows us to predict whether a reaction will either absorb or release heat. When \( \Delta H \) is positive, heat is absorbed (endothermic process). On the contrary, when \( \Delta H \) is negative, heat is released (exothermic process). This insight helps in anticipating the thermal dynamic behavior of reactions.

Internal Energy (ΔE)

The concept of internal energy \( (\Delta E) \) in thermodynamics refers to the total energy contained within a system. This includes both kinetic and potential energy at the molecular level. Changes in internal energy occur during chemical reactions and physical processes and are influenced by factors such as temperature and phase changes.

Fundamentally, the change in internal energy is tied to the system's heat exchange and work done, represented by the equation \( \Delta E = q + w \), where \( q \) is heat and \( w \) is work. However, at constant volume, all the heat changes translate directly to internal energy changes because the volume work \( (P\Delta V) \) is zero.

In the broader context of gaseous reactions, understanding \( \Delta E \) is vital. It helps in describing how reaction conditions impact energy transformations. It is especially relevant when comparing it to \( \Delta H \), as it provides insights into whether the energy change primarily involves heat or if work also has a significant role.

Gaseous Reactions

Gaseous reactions are particularly notable because they often involve significant changes in volume and pressure. These changes are crucial in calculating enthalpy changes and determining the energetic outcome of a reaction.

In a gaseous reaction, the number of moles of reactants compared to the number of moles of products can change, leading to a change in volume \( (\Delta V) \). According to the Ideal Gas Law, changes in moles affect the volume significantly, impacting the system's pressure-volume work \( (P\Delta V) \).

For example, between reactants and products, an increase in gaseous moles results in \( \Delta V > 0 \). Conversely, a reduction results in \( \Delta V < 0 \). This variation is key when predicting whether \( \Delta H \) will be greater, lesser, or equal to \( \Delta E \), with \( \Delta H \) incorporating these volume changes alongside internal energy. This understanding provides clear insights into thermodynamic predictions and efficiencies in chemical processes.

Mole Concept

The mole is a fundamental measurement unit in chemistry essential for quantifying substances in chemical reactions. It allows scientists to count particles in a given amount of matter, linking microscopic observations to macroscopic measurements.

One mole equates to Avogadro's number, approximately \( 6.022 \times 10^{23} \) entities (atoms, molecules). Using the mole concept in reactions like gaseous ones helps to keep track of reactants and products efficiently by converting mass values to quantities that reflect the actual number of particles participating in the reaction.

In the context of gaseous reactions, counting the moles of gaseous reactants and products is crucial. It helps in determining changes in volume \( (\Delta V) \) and plays a vital role in evaluating enthalpic changes and internal energy differences. Additionally, it offers insights into reaction progress and completion, allowing for a more detailed understanding of stoichiometric balances and energy transformations in chemical reactions.