Problem 93 - 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 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

In the given electron transfer reaction, the energy change (ΔE) is expressed as the difference between the ionization energy (IE) and electron affinity (EA) of atom A: \[ \Delta E = IE - EA \] For a representative nonmetal like chlorine, this process is endothermic as it requires energy input (ΔE = 1600 kJ/mol). Similarly, for a representative metal like sodium, this process is also endothermic (ΔE = 549 kJ/mol).

Step 1: Write down the reaction

Given the electron transfer reaction: \[ \mathrm{A}(g) + \mathrm{A}(g) \longrightarrow \mathrm{A}^{+}(g) + \mathrm{A}^{-}(g) \]

Step 2: Energy change for this reaction

The energy change for this reaction can be found by considering the ionization energy (IE) to remove an electron from atom A and the electron affinity (EA) when an electron is added to atom A. Energy change (ΔE) = Ionization energy (IE) - Electron affinity (EA) \[ \Delta E = IE - EA \]

Step 3: Energy change for a representative nonmetal: Chlorine (Cl)

Chlorine is a representative nonmetal, having a high ionization energy and a high electron affinity. Ionization energy (IE) for Cl: 1251 kJ/mol Electron affinity (EA) for Cl: -349 kJ/mol Using the energy change formula: \[ \Delta E = IE - EA = 1251 - (-349) = 1600 \text{ kJ/mol} \] The positive energy change indicates that the process is endothermic for chlorine, as it requires energy input for the electron transfer to occur.

Step 4: Energy change for a representative metal: Sodium (Na)

Sodium is a representative metal, having a low ionization energy and a low electron affinity. Ionization energy (IE) for Na: 496 kJ/mol Electron affinity (EA) for Na: -53 kJ/mol Using the energy change formula: \[ \Delta E = IE - EA = 496 - (-53) = 549 \text{ kJ/mol} \] The positive energy change indicates that the process is also endothermic for sodium, as it requires energy input for the electron transfer to occur. In conclusion, the energy change for the given electron transfer reaction is given by: \[ \Delta E = IE - EA \] This process is endothermic (requires energy input) for both a representative nonmetal like chlorine and a representative metal like sodium.

Key Concepts

Ionization Energy

Ionization energy (IE) is the amount of energy required to remove an electron from an atom or molecule in its gaseous state. Imagine an atom as a tiny solar system, with the nucleus as the sun and electrons as planets orbiting around it. Just like it takes a lot of energy for a planet to leave its orbit, it takes a significant amount of energy for an electron to 'escape' from the pull of the nucleus.

Higher ionization energy implies a stronger attraction between the atom's nucleus and its electrons. Hence, nonmetals like chlorine have high ionization energies because their electrons are tightly held, required a lot of energy to remove. Conversely, metals such as sodium have lower ionization energies since their outer electrons are more loosely bound. The general equation to express ionization energy is:
\[ IE = -E_{final} + E_{initial} \]
In this formula, \(E_{initial}\) is the energy of the atom before ionization, and \(E_{final}\) is the energy of the resulting ion. Understanding ionization energy is crucial when studying electron transfer reactions as it directly affects the energy change during the reaction.

Electron Affinity

In contrast to ionization energy, electron affinity (EA) refers to the energy change that occurs when an electron is added to a neutral atom in the gaseous phase to form an anion. It is essentially the 'welcoming energy' of an atom, indicating how much an atom wants an extra electron.

Atoms with a high electron affinity are like homes with open doors, ready to welcome a new member with warmth (energy release). Chlorine, for instance, releases energy when it gains an electron due to its high electron affinity. On the flip side, metals like sodium, which have low electron affinities, are akin to homes that are not so welcoming; adding an electron doesn't release much energy. The electron affinity can be expressed by the equation:
\[ EA = E_{neutral} - E_{anion} \]
where \(E_{neutral}\) is the energy of the neutral atom and \(E_{anion}\) is the energy of the anion formed. It's important to note that a negative value for electron affinity means that energy is being released when the atom gains an electron.

Endothermic Process

An endothermic process is any reaction or phase change in which the system absorbs energy from its surroundings, usually in the form of heat. Visualizing an endothermic reaction, you can picture that you're pushing a boulder uphill; it requires extra effort (energy) from you for the task to be accomplished.

This concept is crucial when discussing electron transfer reactions. As seen with elements such as chlorine and sodium, the electron transfer reaction requires more energy to remove an electron (ionization) than is released when an electron is gained (electron affinity). Therefore, the overall process for these elements is endothermic. The formula for energy change in such a reaction is simply:
\[ \text{Energy Change} = IE - EA \]
When the calculated energy change (\(\text{Delta E}\)) value is positive, it indicates energy is being absorbed by the system, confirming the endothermic nature of the process. By understanding this concept, students can predict the energy requirements of chemical reactions and how atoms will behave during these interactions.