Problem 5 - Chemistry: The Central Science

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 \(\mathrm{A}\), 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? [Sections \(7.4\) and 7.5]

Step-by-Step Solution

Answer

The energy change for the electron transfer reaction is \(\Delta E = IE - EA\), where \(IE\) is the ionization energy, and \(EA\) is the electron affinity of atom A. For Chlorine (nonmetal), \(\Delta E = 1599.8 \mathrm{kJ/mol}\), and for Sodium (metal), \(\Delta E = 548.6 \mathrm{kJ/mol}\). In both cases, the energy change is positive, indicating that the reaction is not exothermic.

Step 1: Write down the given electron transfer reaction

The given electron transfer reaction is: \[ \mathrm{A}(g) + \mathrm{A}(g) \longrightarrow \mathrm{A}^{+}(g) + \mathrm{A}^{-}(g) \]

Step 2: Identify the energy changes associated with the reaction

The reaction involves the following energy changes: 1. Ionization Energy (IE) - Required energy to remove an electron from a neutral atom A. 2. Electron Affinity (EA) - Energy released when an electron is added to a neutral atom A.

Step 3: Calculate the energy change for the reaction

The energy change for the reaction can be calculated by taking the difference between the ionization energy (energy required) and electron affinity (energy released): \[ \Delta E = IE - EA \] Now, let's determine if the process is exothermic for a nonmetal (chlorine) and a metal (sodium) using their ionization energies and electron affinities.

Step 4: Chlorine (nonmetal) energy change

Chlorine has the following ionization energy and electron affinity values: Ionization Energy (IE) \(= 1251.2 \mathrm{kJ/mol}\) Electron Affinity (EA) \(= -348.6 \mathrm{kJ/mol}\) Energy change for Chlorine: \[ \Delta E = 1251.2 - (-348.6) = 1251.2 + 348.6 = 1599.8 \mathrm{kJ/mol} \] Since the energy change is positive, the reaction is not exothermic for Chlorine (nonmetal).

Step 5: Sodium (metal) energy change

Sodium has the following ionization energy and electron affinity values: Ionization Energy (IE) \(= 495.8 \mathrm{kJ/mol}\) Electron Affinity (EA) \(= -52.8 \mathrm{kJ/mol}\) Energy change for Sodium: \[ \Delta E = 495.8 - (-52.8) = 495.8 + 52.8 = 548.6 \mathrm{kJ/mol} \] Since the energy change is positive, the reaction is not exothermic for Sodium (metal). #Conclusions# The electron transfer reaction is not exothermic for both Chlorine (nonmetal) and Sodium (metal).

Key Concepts

Understanding Ionization Energy

Ionization energy is a fundamental concept in chemistry that refers to the amount of energy needed to remove an electron from an atom or ion in its gaseous state. It's an important property because it tells us how tightly an electron is bound to its nucleus. Higher ionization energy means that more energy is required to remove the electron from the atom.

When discussing ionization energy:

• It's typically expressed in kilojoules per mole (kJ/mol).
• Generally, nonmetals have higher ionization energies compared to metals.
• The first ionization energy refers to the energy required to remove only the first electron.

Bringing this back to electron transfer reactions, ionization energy represents the energy input needed to initiate the process, as seen in the conversion from a neutral atom to an ion (e.g., A to \(\mathrm{A}^{+}\)). Understanding this is crucial for analyzing whether such electron transfer is energetically favorable.

What is Electron Affinity?

Electron affinity is another crucial term in the context of atomic interactions. It measures the amount of energy released when an electron is added to a neutral atom, forming an anion in its gaseous state. This process indicates how strongly an atom can attract and hold an extra electron.

Some key points about electron affinity include:

• It is usually expressed in kilojoules per mole (kJ/mol).
• Nonmetals, like halogens, generally exhibit high electron affinities.
• Electron affinity values can be negative, indicating that energy is released during the process.

During an electron transfer, electron affinity accounts for the energy released as a new electron is added to a neutral atom creating a negative ion (e.g., A to \(\mathrm{A}^{-}\)). This release of energy can make certain reactions more spontaneous and energetically favorable, contrasting the energy input required by ionization energy.

Examining Exothermic Reactions

An exothermic reaction is defined as a chemical reaction that releases energy, generally in the form of heat, into its surroundings. This release happens because the total energy of the products is less than the total energy of the reactants.

Here's how to identify if a reaction is exothermic:

• A negative energy change (\(\Delta E\)) often points to an exothermic process, indicating that energy is lost from the system.
• Common everyday exothermic reactions include combustion and oxidation.
• Exothermic reactions usually feel warm or hot.

In the context of ionization energy and electron affinity, a reaction can only be exothermic if the energy released during electron affinity is higher than the energy absorbed during ionization. The specific example of electron transfer in metals like sodium or nonmetals like chlorine helps illustrate cases where the aforementioned balance is not achieved, hence making these not exothermic reactions. Understanding these principles can predict whether certain chemical reactions will spontaneously release energy or not.