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

For the given reactions, we have the following relationships between ΔH and ΔE: a. In the reaction \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\), the number of moles of gaseous particles remains the same. Therefore, \(\Delta H = \Delta E\). b. In the reaction \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\), the number of moles of gaseous particles decreases. Therefore, \(\Delta H < \Delta E\). c. In the reaction \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2}\mathrm{O}(g)\), the number of moles of gaseous particles increases. Therefore, \(\Delta H > \Delta E\).

Step-by-step solution

Count number of moles of gaseous particles

On the reactants side, there are 2 moles of HF(g). On the products side, there's 1 mole each of H₂(g) and F₂(g), summing up to 2 moles. So the number of moles of gaseous particles on both sides is equal.

Use the equation ΔH=ΔE+PΔV

Since the number of moles of gaseous particles is the same on both sides, the ΔV(volume change) is zero. Therefore, our equation will look like this: ΔH = ΔE + P(0) ⟹ ΔH = ΔE. In this reaction, \(\Delta H = \Delta E\). b. Predicting the relationship between ΔH and ΔE for reaction: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\)

Count number of moles of gaseous particles

On the reactants side, there are 1 mole of N₂(g) and 3 moles of H₂(g) - total 4 moles. On the products side, there are 2 moles of NH₃(g). So the number of moles of gaseous particles decreases in this reaction.

Use the equation ΔH=ΔE+PΔV

Since the number of moles of gaseous particles decreases, the ΔV will be negative. Therefore, our equation will look like this: ΔH = ΔE + P(-ΔV) ⟹ ΔH < ΔE. In this reaction, \(\Delta H < \Delta E\). c. Predicting the relationship between ΔH and ΔE for reaction: $4 NH_{3}(g)+5 O_{2}(g) \longrightarrow 4 NO(g)+6 H_{2} O(g)$

Count number of moles of gaseous particles

On the reactants side, there are 4 moles of NH₃(g) and 5 moles of O₂(g) - total 9 moles. On the products side, there are 4 moles of NO(g) and 6 moles of H₂O(g) - total 10 moles. So the number of moles of gaseous particles increases in this reaction.

Use the equation ΔH=ΔE+PΔV

Since the number of moles of gaseous particles increases, the ΔV will be positive. Therefore, our equation will look like this: ΔH = ΔE + P(ΔV) ⟹ ΔH > ΔE. In this reaction, \(\Delta H > \Delta E\).

Key concepts

Enthalpy

Enthalpy, often symbolized as \(H\), is a thermodynamic quantity that represents the total heat content of a system. It is an important concept that indicates whether heat is absorbed or released during a chemical reaction when measured at constant pressure.
In practical terms, you can consider enthalpy as the energy required to create a system plus the energy needed to make room for it by displacing its environment. The change in enthalpy (\(\Delta H\)) indicates the amount of energy released or consumed in a process that involves both the internal energy change and the work done by the system.
It's important to remember that enthalpy is a state function, which means its change depends on the initial and final states, not the path between them. By using enthalpy, scientists can predict heat flow during reactions.

Internal Energy

Internal energy, denoted as \(E\), is a measure of all the energy contained within a system. This includes kinetic energy due to molecule motion and potential energy due to intermolecular forces.
Internal energy is central to understanding how energy is transferred in processes. It is used to determine whether energy is added to or released from a system. Unlike enthalpy, internal energy does not consider the work done by pressure-volume changes.

• When gases expand or compress, changes in internal energy occur.
• In chemical reactions, the internal energy change is correlated with changes in chemical bonds.

Internal energy can be calculated via the first law of thermodynamics, \(\Delta E = q + w\), where \(q\) is heat and \(w\) is work.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics and chemistry that relates four properties of an ideal gas: pressure (\(P\)), volume (\(V\)), temperature (\(T\)), and number of moles (\(n\)). The equation is expressed as \(PV = nRT\), where \(R\) is the ideal gas constant.
This law helps us understand how gases behave under varying conditions and is crucial in predicting the outcome of reactions involving gaseous reactants or products.
Although no gas is truly ideal, many gases approximate this behavior under standard conditions. Using the Ideal Gas Law makes it possible to interrelate the changes in gas properties during reactions or physical transformations.

• Predict changes in pressure or volume when temperature changes.
• Estimate the amount of gas produced or consumed in a reaction.

This concept explains why certain reactions result in a change in enthalpy and internal energy.

Chemical Reactions

Chemical reactions are processes where one set of chemical substances transforms into another. This involves breaking and forming chemical bonds, resulting in changes in energy and chemical structure.
Understanding reactions is crucial for determining energy changes, like enthalpy (\(\Delta H\)) and internal energy (\(\Delta E\)). Reactions can be classified based on how they release or absorb energy:

• Exothermic reactions release energy, causing \(\Delta H\) to be negative.
• Endothermic reactions absorb energy, resulting in positive \(\Delta H\).

The relationship between the enthalpy change and internal energy change is often determined by the shift in the number of moles of gas, as seen in many reaction equations.
By analyzing these shifts, one can predict energy flow within the system, providing insights into reaction spontaneity and feasibility.