Problem 78 - Chemistry The Molecular Science

Question

For each of these reactions at \(25^{\circ} \mathrm{C}\), indicate whether the entropy effect, the energy effect, both, or neither favors the reaction. (a) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{~F}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NF}_{3}(\mathrm{~g}) \quad \Delta_{1} H^{\circ}=-249 \mathrm{~kJ} / \mathrm{mol}\) (b) \(\mathrm{N}_{2} \mathrm{~F}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NF}_{2}(\mathrm{~g})\) \(\Delta_{t} H^{\circ}=93.3 \mathrm{~kJ} / \mathrm{mol}\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NCl}_{3}(\mathrm{~g}) \quad \Delta_{1} H^{\circ}=460 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

(a) Energy effect favors; (b) Entropy effect favors; (c) Neither effect favors.

Step 1: Analyze the Entropy Change for Reaction (a)

In reaction (a), the reactants are one mole of nitrogen gas and three moles of fluorine gas, totaling four moles of gaseous reactants. The product is two moles of nitrogen trifluoride gas. Therefore, the number of moles of gas decreases from four to two. This suggests that entropy decreases, as there is a lower dispersion of energy. Thus, the entropy effect does not favor the reaction.

Step 2: Analyze the Enthalpy Change for Reaction (a)

The reaction given has an enthalpy change \(\Delta_{1} H^{\circ} = -249 \, \text{kJ/mol}\), which is negative. A negative enthalpy change indicates that the reaction is exothermic and releases energy to the surroundings. This energy release favors the reaction.

Step 3: Conclusion for Reaction (a)

For reaction (a), the entropy effect does not favor the reaction (since entropy decreases), but the energy effect does favor the reaction (since the reaction is exothermic).

Step 4: Analyze the Entropy Change for Reaction (b)

In reaction (b), one mole of dinitrogen tetrafluoride gas decomposes into two moles of difluoroamine gas. The increase in the number of gaseous moles from one to two suggests an increase in entropy, which favors the reaction.

Step 5: Analyze the Enthalpy Change for Reaction (b)

The enthalpy change is given as \(\Delta_{t} H^{\circ} = 93.3 \, \text{kJ/mol}\). This positive value indicates that the reaction is endothermic and requires energy. This energy effect does not favor the reaction.

Step 6: Conclusion for Reaction (b)

For reaction (b), the entropy effect favors the reaction (due to increased entropy), but the energy effect does not favor it (as it is endothermic).

Step 7: Analyze the Entropy Change for Reaction (c)

In reaction (c), one mole of nitrogen gas and three moles of chlorine gas form two moles of nitrogen trichloride gas. The number of gas molecules decreases from four to two, suggesting a decrease in entropy. Hence, the entropy effect does not favor the reaction.

Step 8: Analyze the Enthalpy Change for Reaction (c)

The enthalpy change \(\Delta_{1} H^{\circ} = 460 \, \text{kJ/mol}\) is positive, indicating an endothermic reaction requiring energy input. This energy effect does not favor the reaction.

Step 9: Conclusion for Reaction (c)

For reaction (c), neither the entropy effect (decreased number of moles) nor the energy effect (endothermic reaction) favors the reaction.

Key Concepts

Entropy Change

Entropy change speaks to how energy is dispersed in a system. When reactions occur, the number of molecules or"moles" can change, impacting how disorderly or orderly the system is. If a process increases the number of gas molecules, it often increases entropy and disorder, thus favoring the reaction. Conversely, when the number of gas molecules decreases, entropy typically drops, leading to less disorder and a less favorable reaction. Let's apply this to our examples. In Reaction (a), there’s a decrease in gaseous molecules from four to two, indicating a reduction in entropy. This reduced disorder suggests that the entropy change does not favor the reaction. However, in Reaction (b), the conversion of one gas molecule into two means increased entropy. This increase in disorder favors the reaction. Lastly, for Reaction (c), like in Reaction (a), there's again a decrease from four moles to two moles of gas, so the entropy effect does not favor the reaction.

Enthalpy Change

Enthalpy change measures the heat exchange associated with a chemical reaction at constant pressure. It reflects the energy content of the reactants and products. If the enthalpy change (\(\Delta H^{\circ}\)) is negative, the reaction is exothermic, meaning it releases heat into the surroundings and is generally favorable. When \(\Delta H^{\circ}\) is positive, the reaction is endothermic, absorbing heat, which often makes it less favorable.
Analyzing our reactions: In Reaction (a), \(\Delta_1 H^{\circ} = -249 \, \text{kJ/mol}\) indicates that the reaction releases energy, making it exothermic and thereby favorable. Reaction (b) has a positive \(\Delta_{t} H^{\circ} = 93.3 \, \text{kJ/mol}\), suggesting it requires energy input to proceed, making it endothermic and less favorable. Similarly, for Reaction (c), the positive enthalpy change of \(\Delta_1 H^{\circ} = 460 \, \text{kJ/mol}\) indicates an endothermic reaction, where the energy effect does not favor the reaction.

Exothermic and Endothermic Reactions

Understanding whether a reaction is exothermic or endothermic is crucial to predicting a reaction's feasibility. Exothermic reactions, characterized by negative enthalpy changes, release energy, often making them more spontaneous and favorable. They are common in combustion processes.- Example: Reaction (a) with \(\Delta_1 H^{\circ}\) being negative is exothermic.
On the flip side, endothermic reactions absorb energy, having positive enthalpy changes, and usually require an energy source to proceed. These reactions are less likely to occur spontaneously but are essential in processes like photosynthesis.- Reaction (b) and (c), with positive enthalpy changes, are both endothermic.
Thus, analyzing whether a reaction releases or absorbs heat helps us understand the overall energy balance and its likelihood to occur naturally. Whether a reaction is exothermic or endothermic ties back to its enthalpy change, playing a key role in determining its energetics and favorability.