Problem 87 - Chemistry The Central Science

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 reaction 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.

Step-by-Step Solution

Answer

a) False. The feasibility depends on the value of \(\Delta G = \Delta H - T\Delta S\). b) True. The reaction is highly exothermic and spontaneous. c) False. A spontaneous process can be conducted irreversibly. d) False. Spontaneous processes do not require work to be done to force them to proceed. e) False. Spontaneous processes are those for which \(\Delta G\) is negative.

Step 1: Statement 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 \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) This statement is FALSE. The feasibility of a reaction depends not only on \(\Delta H\), but also on \(\Delta S\) and temperature. The true statement would be: The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends on the value of \(\Delta G\) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\), where \(\Delta G = \Delta H - T\Delta S\). #b)

Step 2: Statement b

The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. This statement is TRUE. The reaction of Sodium and Chlorine to form Sodium chloride (NaCl) is a highly exothermic reaction and is spontaneous. #c)

Step 3: Statement c

A spontaneous process can in principle be conducted reversibly. This statement is FALSE. A reversible process must satisfy \(\Delta G = 0\), however, a spontaneous process has \(\Delta G < 0\). The correct statement would be: A spontaneous process can in principle be conducted IRREVERSIBLY. #d)

Step 4: Statement d

Spontaneous processes in general require that work be done to force them to proceed. This statement is FALSE. Spontaneous processes do not require external work to proceed, as they tend to proceed in the direction of lower energy on their own. The correct statement would be: Spontaneous processes in general DO NOT require work to be done to force them to proceed. #e)

Step 5: Statement e

Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system. This statement is FALSE. Although spontaneous processes often involve exothermic reactions and an increase in order, this is not always the case. The true criterion for spontaneity is that the Gibbs Free Energy change, \(\Delta G\), is negative. Thus, the correct statement would be: Spontaneous processes are those for which the Gibbs Free Energy change, \(\Delta G\), is negative.

Key Concepts

Gibbs Free Energy (ΔG)

When we talk about chemical reactions and processes, one of the most crucial concepts is the Gibbs Free Energy, represented by ΔG. It's a thermodynamic potential that helps us determine the spontaneity of a process. If the change in Gibbs Free Energy (ΔG) is negative, it indicates that the process can occur spontaneously, without the need for additional energy input. ΔG is calculated using the formula ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy of the system.

For instance, when we examine the formation of ammonia (NH_{3}) from nitrogen (N_{2}) and hydrogen (H_{2}), we cannot rely solely on the enthalpy change (ΔH) to determine feasibility. Both entropy (ΔS) and temperature play a critical role. A process may have a positive ΔH (endothermic) and still be spontaneous at high temperatures if it's accompanied by a significant increase in entropy (ΔS). This interplay between enthalpy, entropy, and temperature makes the Gibbs Free Energy a reliable indicator of a process's spontaneous nature.

Enthalpy (ΔH)

Enthalpy, symbolized as ΔH, is a measure of the total heat content in a thermodynamic system. It's associated with pressure-volume work and is a state function, meaning its value depends only on the initial and final states of the system, not on the path taken. When a reaction releases heat, we consider it exothermic (ΔH < 0), and when it absorbs heat, it's endothermic (ΔH > 0).

While enthalpy is an essential factor in understanding chemical reactions, it's not the sole determinant of spontaneity. For example, the highly exothermic reaction of sodium (Na) with chlorine gas (Cl_{2}) to form sodium chloride (NaCl) indeed has a negative ΔH, which means it's a driving factor in the spontaneity of the reaction. However, to evaluate spontaneity fully, we need to consider enthalpy in conjunction with entropy and the system's temperature.

Entropy (ΔS)

Entropy is a measure of the disorder or randomness within a thermodynamic system and is denoted by ΔS. It's a fundamental concept in understanding how systems evolve over time. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. In the context of chemical reactions, an increase in entropy generally favors spontaneity.

A spontaneous process can result in either an increase or decrease in order, but it must always lead to an increase in the entropy of the universe, which includes the system and its surroundings. For instance, while some spontaneous processes are exothermic and increase order within the system, they must be offset by a greater increase in disorder elsewhere—in the surroundings or by a large enough entropic increase within the system itself.

Reversible Processes

In thermodynamics, the concept of reversible processes is an idealization that serves as a standard for real-world processes. Reversible processes are theoretical scenarios where changes happen infinitesimally slowly, allowing the system to remain in equilibrium at all times. In reality, no process is perfectly reversible due to innate inefficiencies and frictions.

For a process to be reversible, the change in Gibbs Free Energy (ΔG) must be zero, and the system must be in a state of dynamic equilibrium. This is distinctly different from spontaneous processes where ΔG is negative. Understanding the distinction between reversible and spontaneous processes helps clarify that a spontaneous process, such as the mixing of gases or the expansion of a gas into a vacuum, occurs naturally and irreversibly due to a favorable Gibbs Free Energy change.