Problem 54 - Chemistry: The Central Science in SI Units, Global Edition

Question

Consider the following equation: $$ \mathrm{Al}^{3+}(g)+e^{-} \longrightarrow \mathrm{Al}^{2+}(g) $$ Which of the following statements are true? (i) The energy change for this process is the second electron affinity of Al atom since \(\mathrm{Al}^{2+}(g)\) is formed. (ii) The energy change for this process is the negative of the third ionization energy of the Al atom. (iii) The energy change for this process is the electron affinity of the \(\mathrm{Al}^{2+}\) ion.

Step-by-Step Solution

Answer

In conclusion, of the three provided statements, only statement (ii) is true. The energy change for the given process is equal to the negative of the third ionization energy of the Al atom, as it represents the reverse process of the third ionization energy of the Al atom. Statements (i) and (iii) are false, as they refer to electron affinities which are typically associated with neutral atoms instead of ions.

Step 1: Understand the equation

In the given equation, an Al³⁺ ion gains an electron and is reduced to Al²⁺ ion: \[ \mathrm{Al}^{3+}(g) + e^{-} \longrightarrow \mathrm{Al}^{2+}(g) \]

Step 2: Analyze statement (i)

Statement (i) says that the energy change for this process is the second electron affinity of Al atom since Al²⁺ is formed. Electron affinity is defined as the energy change when an atom gains an electron to form an anion. However, in this case, we are dealing with ions, not neutral atoms. Moreover, we are given a process where the Al³⁺ ion is gaining an electron instead of its neutral atom state. Therefore, statement (i) is false.

Step 3: Analyze statement (ii)

Statement (ii) says that the energy change for this process is the negative of the third ionization energy of the Al atom. Ionization energy is defined as the energy required to remove an electron from an atom or ion. The third ionization energy is the energy required to remove the third electron from Al: \[ \mathrm{Al^{2+}} \longrightarrow \mathrm{Al^{3+}} + e^- \] Comparing this with the given equation, we can see that the given equation is the reverse of the process of the third ionization energy of the Al atom. This means that statement (ii) is true since the energy change for this process is equal to the negative of the third ionization energy of the Al atom.

Step 4: Analyze statement (iii)

Statement (iii) says that the energy change for this process is the electron affinity of the Al²⁺ ion. Since the reduction of Al³⁺ to Al²⁺ involves gaining an electron and electron affinity is the energy change when an atom gains an electron, it seems reasonable that the energy change for this process matches the definition for electron affinity. However, it is important to note that electron affinity typically refers to neutral atoms in their ground state that initially gain an electron to form a negatively charged species. In this case, we are dealing with the electron affinity of Al²⁺ ion and not a neutral Al atom. Thus, the energy change is more accurately described as the electron gain process for the Al²⁺ ion, making statement (iii) false. In conclusion, of the three provided statements, only statement

Step 5: (ii) is true

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Key Concepts

Electron Affinity

Electron affinity refers to the energy change that occurs when an electron is added to a neutral atom, forming an anion. In simple terms, it measures the tendency of an atom to accept an additional electron.

• Generally, a greater electron affinity indicates a stronger attraction for an added electron.
• A positive electron affinity means the atom releases energy when it gains an electron, while a negative value indicates that energy is required for the addition.
• Typically, electron affinity is applicable to atoms, not ions, which is important when considering chemical reactions involving ions.

In the context of the exercise where Al³⁺ gains an electron to become Al²⁺, it's crucial to note that this process does not fit the usual definition of electron affinity. Instead, it describes an electron gain process specific to aluminum ions.

Aluminum Ions

Aluminum, a member of the boron group, typically forms a final charge of 3+, noted as Al³⁺. Understanding its ion behavior is crucial to analyzing reactions involving aluminum:

• Aluminum loses three electrons to achieve a stable electron configuration, commonly forming Al³⁺ ions.
• The process of removing electrons results in ionization energy, with the third ionization energy being particularly significant for this element.
• Conversely, when an Al³⁺ ion gains an electron, reversing this energy change, we observe an ion transforming to a less charged state, such as Al²⁺.

In the exercise, when analyzing the equation \[\mathrm{Al}^{3+}(g) + e^{-} \longrightarrow \mathrm{Al}^{2+}(g),\] note that it illustrates an aluminum ion (Al³⁺) gaining an electron, a process relevant to understand aluminum ion behavior.

Energy Change Analysis

Energy changes during chemical processes are fundamental in understanding the nature of reactions. In the given exercise, such changes play a crucial role:

• The equation involves a reduction, where the Al³⁺ ion gains an electron to form Al²⁺. This involves energy changes as the electron integrates into the ion structure.
• Ionization energy, particularly the third ionization energy, involves the energy needed to remove an electron. Thus, the reverse process aligns with an energy release when gaining an electron, relevant in this exercise.
• Here, understanding that the process reflects the negative of the third ionization energy clarifies the correct choice among given statements.

Grasping these energy change concepts helps distinguish between different ionization and affinity processes in reactions, shaping accurate interpretations.