Question

Which of the following reactions (equations unbalanced) would be expected to be spontaneous at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ? (a) \(\mathrm{PbO}(s)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{Pb}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{NaOH}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{Al}(s)\) (d) \(2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)\)

Short answer

Reactions (a) and (b) would be expected to be spontaneous at 25C and 1 atm.

Step-by-step solution

Evaluate the Changes in Entropy and Enthalpy

For a reaction to be spontaneous at a given temperature and pressure, the overall free energy change (Gibbs free energy, \( \Delta G \) ) must be negative. \( \Delta G \) is related to enthalpy (\(\Delta H\)), entropy (\(\Delta S\)), and temperature (\(T\)), by the equation \( \Delta G = \Delta H - T\Delta S \) where \( T \) is in Kelvin. A negative \( \Delta H \) and a positive \( \Delta S \) typically suggest a reaction might be spontaneous. We need to analyze each reaction qualitatively to predict if the reaction is spontaneous considering enthalpy and entropy changes.

Assess Reaction (a)

The reaction \(\mathrm{PbO}(s)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{Pb}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) changes from one solid and one gas to one solid and two gases. Considering entropy, the production of more gas molecules suggests an increase in disorder, hence, \(\Delta S > 0\). If the enthalpy change is also negative due to the reaction being exothermic, this reaction could be spontaneous.

Assess Reaction (b)

The reaction \(\mathrm{NaOH}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) goes from one solid and one gas to a solid and a liquid. This would lead to a decrease in entropy (\(\Delta S < 0\)) since gases have higher entropy than liquids or solids. However, the reaction is known to be highly exothermic (\(\Delta H < 0\)), which could drive the spontaneity.

Assess Reaction (c)

The reaction \(\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{Al}(s)\) features solids throughout. There is unlikely to be a significant change in entropy. Without additional data on the enthalpy change, we cannot easily predict the spontaneity; however, thermodynamically, solid-state reactions without a gas-phase component tend not to have large entropy changes.

Assess Reaction (d)

The reaction \(2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)\) starts with one type of gas molecule and produces two different types. The change in entropy could be positive; however, knowing the hydrocarbon reactions tend to be endothermic (unless combustion), we could expect an enthalpy increase (\(\Delta H > 0\)), which would not favor spontaneity at room temperature.

Predict the Spontaneous Reaction

Given the qualitative analysis, reaction (a) seems likely to be spontaneous due to increased disorder and potential for being exothermic. Reaction (b) also seems likely to be spontaneous due to its exothermic nature outweighing the decrease in entropy. Reaction (c) is uncertain without further data, and reaction (d) appears not spontaneous at room temperature because it likely requires input of energy (endothermic). Therefore, reactions (a) and (b) are expected to be spontaneous at \(25^\circ \mathrm{C}\) and \(1 \mathrm{~atm}\).

Key concepts

Gibbs Free Energy

Gibbs free energy (G) is the cornerstone of predicting chemical spontaneity. It represents the maximum amount of energy available to a system to perform useful work when the system is at a constant temperature and pressure. The formula to calculate the change in Gibbs free energy, \( \Delta G \), for a chemical reaction is \( \Delta G = \Delta H - T\Delta S \). Here, \( \Delta H \) refers to the enthalpy change, \( T \) stands for the temperature in Kelvin, and \( \Delta S \) is the entropy change.
If \( \Delta G \) comes out to be negative, the reaction is predicted to be spontaneous, meaning it will proceed without any external energy input. Conversely, if it’s positive, the reaction is nonspontaneous. A \( \Delta G \) of zero indicates the system is at equilibrium, meaning there's no net change occurring.
When we provide explanations for chemical reactions' spontaneity, we simplify a complex ensemble of molecular interactions to whether there's a net release or consumption of energy. This energy consideration is crucial for students in understanding why certain reactions occur without any external intervention.

Entropy and Enthalpy

Entropy (S) and enthalpy (H) are crucial in assessing the behavior of chemical reactions. Entropy measures the degree of disorder or randomness in a system, with higher entropy reflecting greater disorder. An increase in entropy is favorable for spontaneity, as systems naturally progress towards disorder.

Understanding Entropy

Chemistry students learn that gas has higher entropy than liquids and solids due to its molecular freedom, and reactions producing more gas generally lead to an increase in entropy (\( \Delta S > 0 \)).

What Is Enthalpy?

Enthalpy represents the heat content of a system at constant pressure. A reaction that releases heat, known as exothermic (\( \Delta H < 0 \)), increases the likelihood of being spontaneous, whereas endothermic reactions (\( \Delta H > 0 \)) absorb heat and are less likely to be spontaneous. It’s the interplay between these changes in heat and disorder that tells us whether a process will naturally occur or not. Teaching these concepts involves not only conveying definitions but also helping students visualize the energy and disorder changes that accompany chemical reactions.

Chemical Spontaneity

Chemical spontaneity is a way to describe whether a reaction will proceed on its own without being driven by outside forces. The two main factors that determine spontaneity are changes in enthalpy and entropy, contextualized by the reaction's temperature. Spontaneity is therefore a balance: a reaction could have a decrease in entropy (become more ordered) but still be spontaneous if it releases enough heat (\( \Delta H \) is sufficiently negative) to overcome this change.
By grappling with these concepts, students gain a holistic view of how chemical reactions work and what factors influence them. Simplified, we can think of spontaneous reactions as processes that nature 'prefers' due to their inherent energy favorability or increase in disorder, or both. Diving deeper includes understanding that reaction spontaneity is not an absolute concept but depends on conditions such as temperature and concentrations.

Temperature and Reaction Spontaneity

The role of temperature in reaction spontaneity cannot be overstated. Its significance lies in its relationship with entropy within the Gibbs free energy formula. As temperature increases, the value of \( T\Delta S \) becomes more substantial, which can shift a reaction from nonspontaneous to spontaneous if entropy increases (\( \Delta S > 0 \)). What this means for students is that a nonspontaneous reaction at low temperature could very well become spontaneous at higher temperatures.
For example, when evaluating the spontaneity of a reaction, the ambient conditions, such as room temperature, are critical. If a reaction is endothermic with a small increase in entropy, it may require high temperatures to become spontaneous. Visualizing this interaction helps students understand why certain reactions may only occur under specific thermal conditions and also reinforces the often counterintuitive nature of entropy in chemical processes.