Chem 351 Help — Ionization Potential and Electron Affinity

Ionization Potentials and Electron Affinities

Many chemical processes involve the transfer of electrons between atoms, ions, or molecules. The energy required to remove electrons and the energy released when electrons are added are therefore important thermodynamic quantities.

The ionization potential (or ionization energy) is defined as the enthalpy change for removing an electron from a gaseous species at \(0\ \mathrm{K}\):

\[ M(g) \rightarrow M^+(g) + e^- \]

\[ \Delta H \equiv IP_1 \]

Removing additional electrons gives the second, third, and higher ionization potentials:

\[ M^+(g) \rightarrow M^{2+}(g) + e^- \qquad IP_2 \]

Ionization potentials are always positive because energy must be supplied to remove an electron from a species.

The electron affinity is the enthalpy change associated with adding an electron to a gaseous species:

\[ X(g) + e^- \rightarrow X^-(g) \]

Electron affinities are commonly tabulated as positive quantities even though the process itself is often exothermic. Consequently,

\[ \Delta H = -EA \]

for the electron-capture process.

Why Are These Quantities Useful?

Ionization potentials and electron affinities allow thermodynamic cycles to be constructed for reactions involving ions. By combining these quantities with reaction enthalpies and Hess' Law, the energetics of electron-transfer processes can be determined even when the reaction itself is difficult to measure directly.

They are particularly important in Born-Haber cycles, electrochemistry, and the thermodynamics of ionic compounds.

Worked examples

Worked example: Reaction enthalpy from ionization potentials

Calculate the enthalpy change for the gas-phase electron-transfer reaction:

\[ Cu^{2+}(g) + 2K(g) \rightarrow Cu(g) + 2K^+(g) \]

Use the following ionization potentials:

Process	Enthalpy
\(K(g) \rightarrow K^+(g)+e^-\)	\(IP_1(K)=418.8\ \mathrm{kJ\,mol^{-1}}\)
\(Cu(g) \rightarrow Cu^+(g)+e^-\)	\(IP_1(Cu)=745.5\ \mathrm{kJ\,mol^{-1}}\)
\(Cu^+(g) \rightarrow Cu^{2+}(g)+e^-\)	\(IP_2(Cu)=1957.9\ \mathrm{kJ\,mol^{-1}}\)

Potassium is oxidized, so use the ionization process as written:

\[ 2K(g) \rightarrow 2K^+(g) + 2e^- \]

\[ \Delta H = 2 \left( 418.8\ \mathrm{kJ\,mol^{-1}} \right) \]

\[ \Delta H = 837.6\ \mathrm{kJ\,mol^{-1}} \]

Copper(II) is reduced to copper metal, so reverse the first and second ionization processes:

\[ Cu^{2+}(g) + 2e^- \rightarrow Cu(g) \]

\[ \Delta H = - \left( 745.5\ \mathrm{kJ\,mol^{-1}} + 1957.9\ \mathrm{kJ\,mol^{-1}} \right) \]

\[ \Delta H = -2703.4\ \mathrm{kJ\,mol^{-1}} \]

Adding the two processes gives the target reaction:

\[ Cu^{2+}(g) + 2K(g) \rightarrow Cu(g) + 2K^+(g) \]

\[ \Delta H_{\mathrm{rxn}} = 837.6\ \mathrm{kJ\,mol^{-1}} - 2703.4\ \mathrm{kJ\,mol^{-1}} \]

\[ \Delta H_{\mathrm{rxn}} = -1865.8\ \mathrm{kJ\,mol^{-1}} \]

Therefore,

\[ \boxed{ \Delta H_{\mathrm{rxn}} = -1.87\times10^3\ \mathrm{kJ\,mol^{-1}} } \]

Physical interpretation: Energy must be supplied to remove electrons from potassium atoms, but a much larger amount of energy is released when \(Cu^{2+}\) gains those electrons and becomes neutral copper. The energy released by reducing copper exceeds the energy required to ionize potassium, making the overall reaction strongly exothermic.

Practice

Question 1
Which process corresponds to the first ionization potential of sodium?
\(Na(g)\rightarrow Na^+(g)+e^-\)	\(Na^+(g)+e^-\rightarrow Na(g)\)	\(Na(s)\rightarrow Na(g)\)	\(Na(g)+e^-\rightarrow Na^-(g)\)

Question 2
Which statement about ionization potentials is generally true?
A. Ionization potentials are usually negative.	B. Ionization potentials measure the energy released when an electron is removed.	C. Ionization potentials are always positive because energy must be supplied to remove an electron.	D. The second ionization potential is always smaller than the first.

Question 3
For the reaction \[ Cu^{2+}(g)+2K(g)\rightarrow Cu(g)+2K^+(g) \] which process releases the majority of the energy?
A. Ionization of potassium	B. Reduction of copper(II) to copper	C. Sublimation of potassium	D. Electron affinity of potassium

Key points (one glance)

The ionization potential (ionization energy) is the enthalpy required to remove an electron from a gaseous species.
The first ionization potential is defined by \[ M(g) \rightarrow M^+(g) + e^- \] \[ \Delta H \equiv IP_1 \]
Additional electrons may be removed through successive ionization processes: \[ M^+(g) \rightarrow M^{2+}(g) + e^- \] \[ \Delta H \equiv IP_2 \]
Ionization potentials are always positive because energy must be supplied to remove an electron.
The electron affinity describes the enthalpy change associated with adding an electron to a gaseous species: \[ X(g) + e^- \rightarrow X^-(g) \]
Electron affinities are commonly tabulated as positive numbers, so \[ \Delta H = -EA \] for the electron-capture process.
Electron-transfer reactions can be analyzed using Hess' Law by combining ionization and electron-capture processes.
Reversing an ionization process changes the sign of the associated enthalpy: \[ M^+(g) + e^- \rightarrow M(g) \] \[ \Delta H = -IP_1 \]
The enthalpy of a multistep electron-transfer reaction is obtained by summing the enthalpy changes of the individual electron-removal and electron-addition steps.
Ionization potentials and electron affinities are important components of thermodynamic cycles, including Born-Haber cycles and many electrochemical calculations.

Big picture: Ionization potentials measure the energy required to remove electrons, while electron affinities describe the energetics of adding electrons. Together they allow electron-transfer reactions to be analyzed using Hess' Law and provide the foundation for understanding ionic bonding, lattice energies, and Born-Haber cycles.