Problem 103 - Chemistry An Atoms First Approach

Question

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

Step-by-Step Solution

Answer

In summary, - For Reaction a (2 HF(g) → H₂(g) + F₂(g)), ΔH = ΔE since ΔV = 0. - For Reaction b (N₂(g) + 3 H₂(g) → 2 NH₃(g)), ΔH < ΔE since ΔV < 0. - For Reaction c (4 NH₃(g) + 5 O₂(g) → 4 NO(g) + 6 H₂O(g)), ΔH > ΔE since ΔV > 0.

Step 1: The given reaction is: \( 2 \mathrm{HF}(g) \rightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \) On the reactants' side, there are 2 moles of HF gas, while on the products' side, there are 1 mole of H₂ gas and 1 mole of F₂ gas. So, the change in volume (ΔV) is the difference in moles of gas: ΔV = moles of gas products - moles of gas reactants = (1 + 1) - 2 = 0 #Step 2: Determine the relationship between ΔH and ΔE for Reaction a#

Since ΔV equals 0 for Reaction a, we can use the following relationship: ΔH = ΔE #Step 3: Determine the change in volume for Reaction b#

Step 2: The given reaction is: \( \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g) \) On the reactants' side, there is 1 mole of N₂ gas and 3 moles of H₂ gas, while on the products' side, there are 2 moles of NH₃ gas. So, the change in volume (ΔV) is: ΔV = moles of gas products - moles of gas reactants = 2 - (1 + 3) = -2 #Step 4: Determine the relationship between ΔH and ΔE for Reaction b#

Since ΔV is less than 0 for Reaction b, we can use the following relationship: ΔH < ΔE #Step 5: Determine the change in volume for Reaction c#

Step 3: The given reaction is: \( 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \) On the reactants' side, there are 4 moles of NH₃ gas and 5 moles of O₂ gas, while on the products' side, there are 4 moles of NO gas and 6 moles of H₂O gas. So, the change in volume (ΔV) is: ΔV = moles of gas products - moles of gas reactants = (4 + 6) - (4 + 5) = 1 #Step 6: Determine the relationship between ΔH and ΔE for Reaction c#

Since ΔV is greater than 0 for Reaction c, we can use the following relationship: ΔH > ΔE In summary, - For Reaction a, ΔH = ΔE - For Reaction b, ΔH < ΔE - For Reaction c, ΔH > ΔE

Key Concepts

Enthalpy Change ({ΔH})

Enthalpy change, symbolized as {ΔH}, represents the heat exchange in a system at constant pressure. It plays a crucial role in determining the energy dynamics of chemical reactions. When a reaction occurs, energy is either released or absorbed, and this is measured as the enthalpy change.

Understanding {ΔH} is critical for predicting whether a process is exothermic (releasing heat) or endothermic (absorbing heat). For example, in an exothermic reaction, {ΔH} is negative because heat is being released to the surroundings. Conversely, in an endothermic reaction, {ΔH} is positive due to the absorption of heat.

When comparing {ΔH} to changes in internal energy ({ΔE}), the role of pressure and volume changes becomes apparent, as evidenced by the solutions provided for the reactions in the exercise.

Internal Energy Change ({ΔE})

Internal energy change, denoted as {ΔE}, refers to the total change in energy within a system. This includes all forms of energy such as thermal, chemical, and nuclear. In the context of chemical reactions, {ΔE} signifies the sum of potential and kinetic energy changes of the molecules involved.

The relationship between enthalpy ({ΔH}) and internal energy ({ΔE}) is elegantly summarized by the equation {ΔH = ΔE + PΔV}, where {P} is pressure and {ΔV} is the change in volume. Thus, the internal energy change encompasses more than just heat exchange; it also accounts for work done by the system due to volume changes.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through bond-breaking and bond-forming processes. Every chemical reaction is accompanied by energy changes due to the rearrangement of atoms and molecules. These energy changes can be quantified by measures like enthalpy ({ΔH}) and internal energy ({ΔE}).

Understanding the direction of energy flow in a reaction is essential for predicting product stability and reaction spontaneity. The energy profile of a reaction, which includes the endothermic and exothermic stages, can provide insights into the reaction kinetics and thermodynamics. Whether a reaction releases heat or requires energy input can drastically affect its feasibility and the conditions under which it will proceed.

Change in Volume ({ΔV})

Change in volume ({ΔV}) is a pivotal factor when considering work done by or on a system during a chemical reaction under constant pressure. When a reaction produces more gas molecules, {ΔV} is positive, and the system does work on the surroundings as it expands. Conversely, if a reaction results in fewer gas molecules, {ΔV} is negative, and the surroundings do work on the system.

As seen in the exercise solutions, the value of {ΔV} affects the relationship between enthalpy and internal energy. A zero change in volume indicates that {ΔH} and {ΔE} are equal, as there's no work associated with volume change. However, a non-zero {ΔV} leads to {ΔH} and {ΔE} diverging, depending on whether the reaction is associated with expansion or compression of the system.