Problem 127 - Chemistry An Atoms First Approach

Question

Write equations corresponding to the following: a. the fourth ionization energy of Se b. the electron affinity of \(S^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of \(\mathrm{Mg}\)

Step-by-Step Solution

Answer

a. \[ \mathrm{Se}^{3+}(g) \rightarrow \mathrm{Se}^{4+}(g) + e^{-} \] b. \[ S^{-}(g) + e^{-} \rightarrow S^{2-}(g) \] c. \[ \mathrm{Fe}^{3+}(g) + e^{-} \rightarrow \mathrm{Fe}^{2+}(g) \] d. \[ \mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g) + e^{-} \]

Step 1: Identify the chemical for ionization

Selenium (Se) is a chemical element with atomic number 34.

Step 2: Determine the new charge after ionization

We are asked for the fourth ionization energy, indicating we need to remove the fourth electron, taking a neutral Se atom to an ion with a +4 charge.

Step 3: Write the equation

The fourth ionization energy equation for Se is: \[ \mathrm{Se}^{3+}(g) \rightarrow \mathrm{Se}^{4+}(g) + e^{-} \] b. the electron affinity of \(S^{-}\)

Step 1: Identify the chemical for electron addition

The chemical given is the sulfide ion, \(S^{-}\).

Step 2: Determine the new charge after electron addition

We will add one electron to \(S^{-}\), resulting in \(S^{2-}\).

Step 3: Write the equation

The electron affinity equation for \(S^{-}\) is: \[ S^{-}(g) + e^{-} \rightarrow S^{2-}(g) \] c. the electron affinity of \(\mathrm{Fe}^{3+}\)

Step 1: Identify the chemical for electron addition

The chemical given is the iron(III) ion, \(\mathrm{Fe}^{3+}\).

Step 2: Determine the new charge after electron addition

We will add one electron to \(\mathrm{Fe}^{3+}\), resulting in \(\mathrm{Fe}^{2+}\).

Step 3: Write the equation

The electron affinity equation for \(\mathrm{Fe}^{3+}\) is: \[ \mathrm{Fe}^{3+}(g) + e^{-} \rightarrow \mathrm{Fe}^{2+}(g) \] d. the ionization energy of \(\mathrm{Mg}\)

Step 1: Identify the chemical for ionization

Magnesium (Mg) is a chemical element with atomic number 12.

Step 2: Determine the new charge after ionization

Removing one electron from a neutral Mg atom results in a \(\mathrm{Mg}^{+}\) ion.

Step 3: Write the equation

The ionization energy equation for Mg is: \[ \mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g) + e^{-} \]

Key Concepts

Chemical Ionization

Chemical ionization is a process where ions are formed from a substance through the addition or removal of charged particles, particularly electrons. This process is essential in various fields, including chemistry and physics, as it relates to the formation of ions which are pivotal in electrical conductivity and chemical reactions.

For example, the fourth ionization energy of selenium (Se) involves removing a fourth electron from a selenium ion that already has a +3 charge. This is represented by the equation \[ \mathrm{Se}^{3+}(g) \rightarrow \mathrm{Se}^{4+}(g) + e^{-} \].
In this equation, a positively charged selenium ion (the reactant) loses an electron to form a more positively charged ion, illustrating the energy required to remove an electron from a positively charged ion.

Electron Affinity

Electron affinity refers to the amount of energy released when an electron is added to a neutral atom or molecule in the gaseous state to form a negative ion. It is an important concept in understanding how elements form compounds and participate in chemical bonds.

The electron affinity of the sulfide ion (\(S^{-}\)) involves adding an electron to form a disulfide ion (\(S^{2-}\)), as represented by the equation \[ S^{-}(g) + e^{-} \rightarrow S^{2-}(g) \]. Similarly, an iron(III) ion (\(\mathrm{Fe}^{3+}\)) can gain an electron to form an iron(II) ion (\(\mathrm{Fe}^{2+}\)), as shown by \[ \mathrm{Fe}^{3+}(g) + e^{-} \rightarrow \mathrm{Fe}^{2+}(g) \].
These equations help to illustrate the process of gaining an electron and the energy implications associated with it.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. It is a critical concept in chemistry that helps us understand the reactivity of elements and their tendency to form chemical bonds.

The ionization energy of magnesium (\(\mathrm{Mg}\)) is demonstrated by the equation \[ \mathrm{Mg}(g) \rightarrow \mathrm{Mg}^{+}(g) + e^{-} \], which shows the energy input necessary to remove an electron from a neutral magnesium atom, resulting in a positively charged magnesium ion. Each successive ionization energy is higher than the last, which means it takes more energy to remove each subsequent electron.
This concept explains why certain elements are more likely to lose electrons and form cations, playing a crucial role in the periodic trends observed across the elements.