Problem 83 - 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. Corrected: The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends on both the value of \(\Delta H\) and \(\Delta S\) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\). (b) True. (c) True. (d) False. Corrected: Spontaneous processes, in general, do NOT require work to be done to force them to proceed. (e) False. Corrected: Spontaneous processes are those for which the change in Gibb's Free Energy (\(\Delta G\)) is negative and may include exothermic or endothermic reactions and a change in the degree of order in the system.

Step 1: (a) Evaluate the given statement

The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends on both the value of \(\Delta H\) for the process and the entropy change (\(\Delta S\)). The spontaneity of a reaction depends on the change in Gibb's Free Energy (\(\Delta G = \Delta H - T\Delta S\)) and not just the value of \(\Delta H\). Therefore, the statement is false. Corrected statement: The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends on both the value of \(\Delta H\) and \(\Delta S\) for the process \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\).

Step 2: (b) Evaluate the given statement

The reaction between \(\mathrm{Na}(s)\) and \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is the well-known reaction of sodium and chlorine gas. The reaction results in the formation of an ionic compound, which is thermodynamically favorable and exothermic. Thus, this reaction is indeed a spontaneous process. The statement is true.

Step 3: (c) Evaluate the given statement

A spontaneous process can proceed without external work, and the process will continue until it reaches equilibrium or its natural end state. A reversible process, on the other hand, is one where the reaction can be reversed by infinitesimally small changes to the surroundings. In principle, if the process is conducted at a slow enough rate and with minimal changes to the surrounding conditions, a spontaneous process can be conducted reversibly. The statement is true.

Step 4: (d) Evaluate the given statement

Spontaneous processes by definition proceed without the necessity of external work; they occur due to the system's natural tendency to reach equilibrium or a lower-energy state. This statement is false. Corrected statement: Spontaneous processes, in general, do NOT require work to be done to force them to proceed.

Step 5: (e) Evaluate the given statement

The spontaneity of a process is governed by Gibb's Free Energy (\(\Delta G = \Delta H - T\Delta S\)) and not solely based on exothermicity (\(\Delta H < 0\)) or an increase in order (negative \(\Delta S\)). A process can be spontaneous if it's exothermic and leads to a higher degree of order, or if it's endothermic and increases disorder. The statement is false. Corrected statement: Spontaneous processes are those for which the change in Gibb's Free Energy (\(\Delta G\)) is negative and may include exothermic or endothermic reactions and a change in the degree of order in the system.

Key Concepts

Gibb's Free Energy

Understanding the principles that govern the spontaneity of chemical reactions is central to the study of thermodynamics in chemistry. Gibb's Free Energy, represented by the symbol \(\Delta G\), is a thermodynamic quantity that is key to predicting whether a chemical process will proceed spontaneously. The change in free energy, \(\Delta G\), is defined by the equation \(\Delta G = \Delta H - T\Delta S\), where \(\Delta H\) represents the change in enthalpy, \(T\) stands for the temperature in Kelvin, and \(\Delta S\) denotes the change in entropy of the system.

A negative value of \(\Delta G\) indicates a spontaneous process under constant temperature and pressure, while a positive value suggests a non-spontaneous process. However, \(\Delta G\) on its own doesn't dictate the speed of the reaction—only its thermodynamic favorability. This distinction is crucial for students who might confuse spontaneity (a thermodynamic concept) with reaction rate (a kinetic concept).

Enthalpy Change (\textDelta H)

Enthalpy change, \(\Delta H\), is the amount of heat released or absorbed during a chemical reaction at constant pressure. It is an important part of the equation that determines Gibb's Free Energy. A negative \(\Delta H\), indicative of an exothermic reaction, means that the reaction releases heat and can potentially contribute to a spontaneous process. Conversely, a positive \(\Delta H\), associated with an endothermic reaction, means that the reaction absorbs heat from its surroundings.

Knowing the enthalpy change helps predict whether a reaction will be product- or reactant-favored at chemical equilibrium.

Key Point for Students:

It is important to remember that although exothermic processes are often spontaneous, \(\Delta H\) is only one factor. The overall spontaneity must take into account both \(\Delta H\) and \(\Delta S\), as well as the reaction temperature.

Entropy Change (\textDelta S)

Entropy, a measure of the disorder or randomness in a system, is a central concept in thermodynamics. The change in entropy, \(\Delta S\), during a chemical reaction provides insight into the degree of disorder resulting from the reaction. An increase in entropy (\textgreater 0) signifies that the system has become more disordered. Spontaneous processes often lead to an increase in entropy.

However, there can be spontaneous reactions where the entropy decreases (\textless 0), provided that the enthalpy change and temperature yield a negative value for Gibb's Free Energy (\textless 0). In the context of chemistry education, it’s essential to educate students on how changes in entropy impact the spontaneity of a reaction, making clear that both energy and disorder play roles in determining a reaction's natural tendency to occur.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical system become equal, and the concentrations of reactants and products remain constant over time, not necessarily equal. It is a dynamic state, with reactions still occurring, but with no net change in concentration. Equilibrium does not mean that the reactants and products are present in the same amounts. Instead, it depends on the specific reaction and conditions, characterized by the equilibrium constant (K).

Understanding equilibrium is crucial for students, as it is the balance point that many chemical reactions strive to reach. It's often mistakenly believed that processes at equilibrium are not spontaneous. However, for a reaction approaching equilibrium, the spontaneity can be assessed by Gibb's Free Energy, where \(\Delta G = 0\) at equilibrium. Moreover, the concept of Le Chatelier's Principle, which describes how a system at equilibrium responds to changes in concentration, temperature, or pressure, is a critical part for mastering equilibrium reasoning.

Thermodynamics in Chemistry

Thermodynamics in chemistry is a branch of science that deals with the study of energy changes accompanying chemical and physical processes. It is based on four fundamental laws, which define concepts such as internal energy, enthalpy, and entropy, helping us make predictions about the directionality of a reaction or process.

In the realm of chemistry education, it's significant to convey that thermodynamics helps us understand not just the energy aspects, but also the balance and movement of matter. Teaching students about the interplay between the laws of thermodynamics, the concepts of enthalpy, entropy, and Gibb’s Free Energy, and how they manifest in real-world chemical processes, like the formation of ammonia from nitrogen and hydrogen, helps demystify why reactions occur the way they do. Mastering these concepts is also essential for grasping advanced topics like electrochemistry, bioenergetics, and materials science.