Problem 93 - Chemistry: The Central Science in SI Units, Global Edition

Question

In the chemical process called electron transfer, an electron is transferred from one atom or molecule to another. (We will talk about electron transfer extensively in Chapter 20.) A simple electron transfer reaction is $$ \mathrm{A}(g)+\mathrm{A}(g) \longrightarrow \mathrm{A}^{+}(g)+\mathrm{A}^{-}(g) $$ In terms of the ionization energy and electron affinity of atom A, what is the energy change for this reaction? For a representative nonmetal such as chlorine, is this process exothermic? For a representative metal such as sodium, is this process exothermic?

Step-by-Step Solution

Answer

The energy change for the given electron transfer reaction can be calculated as: Energy change = Ionization energy of A - Electron affinity of A. For chlorine (a representative nonmetal), the process is endothermic with an energy change of 1600 kJ/mol. For sodium (a representative metal), the process is also endothermic with an energy change of 549 kJ/mol. Therefore, the process is not exothermic for both chlorine and sodium.

Step 1: Define ionization energy and electron affinity

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. Electron affinity is the energy change that occurs when an electron is added to an atom in its gaseous state.

Step 2: Calculate the energy change for the electron transfer reaction

The energy change for the reaction can be determined by considering the ionization energy and electron affinity: Energy change = Ionization energy of A - Electron affinity of A

Step 3: Determine if the process is exothermic for a representative nonmetal (chlorine)

For chlorine (a representative nonmetal), the ionization energy is 1251 kJ/mol and the electron affinity is -349 kJ/mol. Using the energy change equation, we can calculate the energy change for the electron transfer reaction: Energy change = 1251 kJ/mol - (-349 kJ/mol) = 1600 kJ/mol Since the energy change is positive, the process is endothermic for chlorine, not exothermic.

Step 4: Determine if the process is exothermic for a representative metal (sodium)

For sodium (a representative metal), the ionization energy is 496 kJ/mol and the electron affinity is -53 kJ/mol. Using the energy change equation, we can calculate the energy change for the electron transfer reaction: Energy change = 496 kJ/mol - (-53 kJ/mol) = 549 kJ/mol Since the energy change is positive, the process is also endothermic for sodium, not exothermic. In conclusion, the energy change for the electron transfer reaction can be calculated using the ionization energy and electron affinity of atom A. The process is endothermic for both a representative nonmetal (chlorine) and a representative metal (sodium), meaning the process is not exothermic for these examples.

Key Concepts

Ionization Energy

Imagine needing to pack energy into an atom to pry away one of its electrons. This energy is known as ionization energy. It's like the entrance fee needed to pull an electron out from its cozy spot within an atom.
The ionization energy varies across elements. Some atoms tightly hold onto their electrons, demanding a hefty amount, while others surrender their electrons more easily, requiring less energy. Generally, you see higher ionization energy in nonmetals compared to metals.

• Why is ionization energy important?
  Understanding it helps us predict how an atom behaves in terms of forming ions and compounds. For example, a metal's lower ionization energy is why it's more willing to give up electrons and form positive ions.

Ionization energy is a fundamental concept that shows the inherent nature of elements to resist or yield their electrons based on their chemical environments.

Electron Affinity

Welcoming an electron into an atom's embrace is accompanied by something known as electron affinity. While ionization energy talks about losing electrons, electron affinity deals with gaining them.
It's the change in energy that occurs when an electron is added to a neutral atom. For some elements, this process releases energy, making it exothermic, while for others, it demands energy input, making it endothermic.

• Key Insights:
  1. Nonmetals typically have a more notable electron affinity as they love gaining electrons to achieve full valence shells.
  2. Metals, on the contrary, often resist addition since they prefer giving away electrons.

When calculating the electron transfer involving electron affinity, you're essentially assessing an element's eagerness or reluctance to adopt a new electron into its fold.

Energy Change in Reactions

When electrons waltz from one atom to another, there's an energy shift occurring behind the scenes. This phenomenon is described as the energy change during reactions.
In the given exercise, the energy dynamics are influenced by both ionization energy (the cost to remove an electron) and electron affinity (the benefit of gaining one). The formula for the energy change in electron transfer is represented as: \[ \text{Energy change} = \text{Ionization energy of A} - \text{Electron affinity of A} \]Using specific element examples like chlorine and sodium:

• Chlorine shows a high ionization energy compared to its electron affinity. The positive outcome in energy change calculations shows the process is endothermic.
• Similarly, sodium's lower electron affinity than its ionization energy also results in endothermic reactions.

Understanding these energy changes enhances predictions about reaction spontaneity and the propensity of particular elemental reactions.