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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 \(\mathrm{Al}\) 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.

Short Answer

Expert verified
Statements (ii) and (iii) are true; statement (i) is false.

Step by step solution

01

Identify the Process

The equation given is \( \mathrm{Al}^{3+}(g) + e^{-} \longrightarrow \mathrm{Al}^{2+}(g) \), which indicates that an electron is being added to an aluminum ion with a +3 charge to form an ion with a +2 charge.
02

Analyze Statement (i)

Statement (i) claims that this process represents the second electron affinity of aluminum. Electron affinity typically refers to the energy change when an electron is added to a neutral atom, so the statement is a misdescription because the process involves cations.
03

Analyze Statement (ii)

Statement (ii) suggests that the energy change is the negative of the third ionization energy of aluminum. Ionization energy is the energy required to remove an electron, not add one. However, adding an electron to a +3 cation is related to the reverse process of removing the third electron, so this description is accurate but not always stated as negative ionization energy.
04

Analyze Statement (iii)

Statement (iii) states that the energy change is the electron affinity of the \( \mathrm{Al}^{2+} \) ion. This is correct because it involves adding an electron to the \( \mathrm{Al}^{2+} \) ion, which aligns with the definition of electron affinity for ions.
05

Draw Conclusions

Considering the analyses: Statement (i) is false because electron affinity traditionally refers to neutral atoms, and statement (ii) is technically correct if we consider the reverse of ionization. Statement (iii) correctly defines the process as electron affinity for an ion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electron Affinity
Electron affinity is a fundamental concept in chemistry that describes how much energy is released when an electron is added to a neutral atom or molecule in the gaseous state. It tells us how much an atom "wants" an extra electron.
This concept is critical when discussing ions and electron transfer. Usually, electron affinity refers to neutral atoms. However, in some contexts, it applies to ions, like the addition of an electron to the positively charged \( \mathrm{Al}^{2+} \) ion.
Understanding this helps evaluate the changes in energy during processes like electron addition or ion formation.
  • Higher electron affinity means the atom or ion strongly attracts new electrons.
  • For ions, an electron affinity process, as seen with the \( \mathrm{Al}^{2+} \) ion, aligns with how certain ions interact with added electrons.
By comprehending electron affinity, students can better grasp why certain reactions release energy when ions gain electrons.
Aluminum Ion
Aluminum ions play a significant role in chemical reactions and are commonly found in compounds and solutions. When aluminum loses electrons, it forms positively charged ions. The most notable is the \( \mathrm{Al}^{3+} \) ion.
This ionization happens when aluminum atoms lose three electrons to achieve a stable electron configuration, reaching a noble-gas-like state with a filled outer shell.
  • The \( \mathrm{Al}^{3+} \) ion is stable due to its electron configuration.
  • It has a high positive charge, influencing its interactions in solutions and compounds.
In the context of our exercise, we're looking at how this ion can gain an electron to form the \( \mathrm{Al}^{2+} \) ion, which involves understanding electron affinity in the context of charged species.
Electron Transfer
Electron transfer is a process essential to many chemical reactions. It occurs when electrons move from one atom or ion to another, and it is a cornerstone of many biological and industrial processes.
Understanding electron transfer involves grasping how energy changes during the movement of electrons, such as in redox reactions. This movement can either release or absorb energy, depending on the direction of transfer.
  • The transfer of electrons is driven by differences in charge and energy stability.
  • In the equation \( \mathrm{Al}^{3+}(g) + e^{-} \longrightarrow \mathrm{Al}^{2+}(g) \), an electron is transferred to the \( \mathrm{Al}^{3+} \) ion, demonstrating how ions can gain stability through electron acceptance.
Electron transfer is pivotal in forming cations and anions, driving the chemistry within solutions and compounds.
Cations
Cations are positively charged ions that form when atoms lose one or more electrons. This loss results in more protons than electrons, giving the ion its positive charge.
Cations are crucial for various chemical processes, including the conduction of electricity in solution and the formation of ionic compounds.
  • They are often involved in reactions where electrons are transferred, playing a key role in balancing charges.
  • The transition from \( \mathrm{Al}^{3+} \) to \( \mathrm{Al}^{2+} \) represents a cation becoming more stable through electron gain, highlighting the role of cations in electron transfer reactions.
In summary, cations are essential components in many areas of chemistry, influencing both the physical and chemical properties of substances.

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Most popular questions from this chapter

Identify each statement as true or false: (a) Cations are larger than their corresponding neutral atoms. (b) \(\mathrm{Li}^{+}\) is smaller than Li. (c) \(\mathrm{Cl}^{-}\) is bigger than I \(^{-}\).

Moseley established the concept of atomic number by studying \(X\) rays emitted by the elements. The \(X\) rays emitted by some of the elements have the following wavelengths: $$ \begin{array}{cc} \hline \text { Element } & \text { Wavelength (pm) } \\ \hline \text { Ne } & 1461 \\ \text { Ca } & 335.8 \\ \text { Zn } & 143.5 \\ \text { Zr } & 78.6 \\ \text { Sn } & 49.1 \\ \hline \end{array} $$ (a) Calculate the frequency, \(\nu,\) of the \(X\) rays emitted by each of the elements, in Hz. (b) Plot the square root of \(\nu\) versus the atomic number of the element. What do you observe about the plot? (c) Explain how the plot in part (b) allowed Moseley to predict the existence of undiscovered elements. (d) Use the result from part (b) to predict the X-ray wavelength emitted by iron. (e) A particular element emits X rays with a wavelength of \(98.0 \mathrm{pm}\). What element do you think it is?

Using only the periodic table, arrange each set of atoms in order from largest to smallest: \((\mathbf{a}) \mathrm{Ar}, \mathrm{As}, \mathrm{Kr} ;(\mathbf{b}) \mathrm{Cd}, \mathrm{Rb}, \mathrm{Te} ;(\mathbf{c})\) C, Cl, Cu.

Explain the following variations in atomic or ionic radii: (a) \(\mathrm{I}^{-}>\mathrm{I}>\mathrm{I}^{+}\) (b) \(\mathrm{Ca}^{2+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (c) \(\mathrm{Fe}>\mathrm{Fe}^{2+}>\mathrm{Fe}^{3+}\)

Little is known about the properties of astatine, At, because of its rarity and high radioactivity. Nevertheless, it is possible for us to make many predictions about its properties. (a) Do you expect the element to be a gas, liquid, or solid at room temperature? Explain. (b) Would you expect At to be a metal, nonmetal, or metalloid? Explain. (c) What is the chemical formula of the compound it forms with Na?

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