Question

Indicate whether each of the following statements is true or false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of \(\Delta H\) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .\) (b) The re- action of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Short answer

(a) False. The feasibility depends on the value of ΔG, not solely ΔH. (b) True. The Na and Cl₂ reaction to form NaCl is spontaneous. (c) False. Spontaneous processes are typically irreversible. (d) False. Spontaneous processes do not require work to be done to proceed. (e) False. Spontaneous processes have a negative ΔG.

Step-by-step solution

(a) Assess the statement on the feasibility of NH3 production

The given statement is: "The feasibility of manufacturing NH_3 from N_2 and H_2 depends entirely on the value of ΔH for the process N_2(g) + 3 H_2(g) → 2 NH_3(g)." This statement is false. Although ΔH (the change in enthalpy) is an essential factor in determining the feasibility of a reaction, it is not the only factor. The reaction Gibbs free energy (ΔG) determines the spontaneity of a reaction. ΔG considers both the enthalpy change (ΔH) and the change in entropy (ΔS) and is given by ΔG = ΔH - TΔS, where T is the temperature. Therefore, the correct statement would be: "The feasibility of manufacturing NH_3 from N_2 and H_2 depends on the value of ΔG for the process N_2(g) + 3 H_2(g) → 2 NH_3(g)."

(b) Assess the statement on Na and Cl2 reaction to form NaCl

The given statement is: "The reaction of Na(s) with Cl_2(g) to form NaCl(s) is a spontaneous process." This statement is true. The reaction of sodium (Na) and chlorine (Cl_2) to form sodium chloride (NaCl) is an exothermic process, which releases energy. Since both the enthalpy change (∆H) and the entropy change (∆S) are favorable, the reaction is spontaneous.

(c) Assess the statement on spontaneous processes being reversible

The given statement is: "A spontaneous process can, in principle, be conducted reversibly." This statement is false. A spontaneous process is one that occurs naturally and tends to move towards a state of equilibrium. In contrast, a reversible process is an idealized process that occurs infinitely slowly and can be reversed with no net change in the system or surroundings. Spontaneous processes are typically irreversible because they involve dissipative effects (such as friction, heat generation, or mixing) that are not recoverable when trying to reverse the process. The corrected statement would be: "A spontaneous process is typically irreversible."

(d) Assess the statement on work being required for spontaneous processes

The given statement is: "Spontaneous processes, in general, require that work be done to force them to proceed." This statement is false. Spontaneous processes do not require work to proceed; they occur naturally without the input of external energy or the performance of work. The corrected statement would be: "Spontaneous processes, in general, do not require work to be done to force them to proceed."

(e) Assess the statement on spontaneous processes being exothermic and leading to higher order

The given statement is: "Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system." This statement is false. A spontaneous process is determined by the change in Gibbs free energy (ΔG), which depends on both the change in enthalpy (ΔH) and the change in entropy (ΔS). While exothermic reactions and an increase in order (ΔS < 0) can contribute to the spontaneity of a process, a spontaneous process can also occur under other conditions. The corrected statement would be: "Spontaneous processes are those where the change in Gibbs free energy (ΔG) is negative."

Key concepts

Gibbs Free Energy

Gibbs free energy, symbolized as \(\Delta G\), is a thermodynamic quantity that is pivotal in predicting the spontaneity of a process at constant pressure and temperature. It combines the system's enthalpy, or heat content, symbolized by \(\Delta H\), and its entropy, or the measure of disorder, symbolized by \(\Delta S\), into a single value. The equation \(\Delta G = \Delta H - T\Delta S\) reveals that a negative value of \(\Delta G\) indicates a spontaneous process.

Gibbs free energy helps us understand why a process like the formation of ammonia from nitrogen and hydrogen doesn't rely solely on the heat change, but also on the temperature and entropy change. So, when we correct the given statement, we emphasize the role \(\Delta G\) plays in determining feasibility, which stems from the fundamental thermodynamic truth that a process with a negative \(\Delta G\) will occur without external input of energy.

Enthalpy Change (\(\Delta H\))

Enthalpy change or \(\Delta H\) represents the total heat change within a system at constant pressure. It's a central factor in predicting whether a process will release heat (exothermic) or absorb heat (endothermic).

For example, when sodium reacts with chlorine gas to form sodium chloride, the reaction is exothermic, which means it has a negative enthalpy change and releases energy. This release of energy usually favors the spontaneity of a reaction. However, as we clarified in the exercise, it is not solely the \(\Delta H\) that governs the spontaneity, but the combination of both \(\Delta H\) and \(\Delta S\), as encapsulated by the Gibbs free energy formula.

Entropy Change (\(\Delta S\))

Entropy change, or \(\Delta S\), quantifies the change in disorder or randomness within a system during a process. An increase in entropy, which carries the notion that molecules are spreading out or becoming more disordered, often drives processes towards spontaneity.

However, we should note that a decrease in system's entropy doesn't always prevent a process from being spontaneous. If the enthalpy change releases enough energy (negative \(\Delta H\)), it can compensate for the decrease in entropy to still result in a negative Gibbs free energy, making the process spontaneous. The spontaneous formation of water from hydrogen and oxygen gases is an example of this: it leads to a decrease in entropy but is highly exothermic.

Chemical Equilibrium

Chemical equilibrium occurs in a reversible process when the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time. It is a state that spontaneous processes approach, driven by changes in Gibbs free energy.

In the context of our ammonia synthesis example, equilibrium would be achieved when the rate of production of ammonia from nitrogen and hydrogen equals the rate of decomposition back into nitrogen and hydrogen. At this point, \(\Delta G\) for the process is zero, indicating that the system is at maximum entropy and no further net change occurs as long as external conditions are stable.

Reversible and Irreversible Processes

Understanding reversible and irreversible processes is crucial for grasping the nature of spontaneity. A reversible process is idealistic: it could, in theory, go forward and reverse without losing any energy because it is assumed to happen infinitely slowly. Practically, this is impossible, as real processes can't happen without some energy dissipation.

Irreversible processes are the real spontaneous processes occurring in nature that move a system towards equilibrium while dissipating some energy as heat, making them impossible to reverse perfectly. For instance, when you dissolve salt in water, the process is spontaneous and irreversible - you cannot retrieve the original salt and water without adding external energy to the system. Thus, the earlier concept that spontaneous processes require work to proceed is refuted, as we know that they, in fact, occur naturally due to energy dispersal.