Question

Rank the following in order of increasing ionization energy: \(\mathrm{Cl}, \mathrm{Ca}^{2+},\) and \(\mathrm{Cl}^{-} .\) Briefly explain your answer.

Short answer

Increasing ionization energy order: Cl^-, Cl, Ca^{2+}.

Step-by-step solution

Understand Ionization Energy

Ionization energy refers to the energy required to remove an electron from a neutral atom in the gaseous state. Generally, the higher the nuclear charge and the smaller the atomic radius, the higher the ionization energy of an atom or ion.

Consider Chlorine (Cl)

The chlorine atom is neutral with an atomic number of 17, which translates to having 17 protons and 17 electrons. The outermost electron is less tightly held due to electron-electron repulsion and shielding, which provides it with moderate ionization energy.

Evaluate Chloride Ion (Cl-)

The chloride ion ( Cl^- ) is formed when a chlorine atom gains an additional electron, resulting in a negative charge. This added electron increases electron-electron repulsion, lowering the effective nuclear charge felt by the outer electrons. Thus, Cl^- has a lower ionization energy compared to neutral Cl due to the increased shielding.

Analyze Calcium Ion (Ca2+)

Calcium ion ( Ca^{2+} ) has lost two electrons compared to a neutral calcium atom, resulting in a +2 charge. This loss of electrons reduces electron shielding significantly, causing the remaining electrons to be more tightly bound to the nucleus and increasing its ionization energy relative to neutral atoms or anions.

Arrange in Order of Increasing Ionization Energy

Considering the ionization principles—protons in the nucleus, electron shielding, and resultant nuclear charge—the order of increasing ionization energy is: Cl^-, Cl, Ca^{2+}.

Key concepts

Nuclear Charge

Nuclear charge is a fundamental concept that plays a significant role in determining an element's ionization energy. It refers to the total positive charge within an atom's nucleus, attributed to the protons present. This positive charge attracts electrons, keeping them bound to the nucleus.
The more protons an atom contains, the stronger the nuclear charge. This results in a greater pull on the electrons, making it harder to remove them and increasing ionization energy. For instance, between chlorine and its ion forms, the nuclear charge remains essentially the same, but how it's effectively "felt" by the electrons shifts due to other factors such as electron shielding and electron repulsion.
Understanding the distribution of nuclear charge can help explain why electrons in some atoms are more tightly bound than in others, providing insights into the relative ionization energies of different elements and ions.

Atomic Radius

The atomic radius is the distance from the nucleus of an atom to its outermost electron shell. It is a crucial factor when discussing ionization energy. A smaller atomic radius typically corresponds to higher ionization energy. This is because electrons are closer to the nucleus, experiencing a stronger attraction and thus more difficult to remove.
Conversely, a larger atomic radius means the electrons are farther from the nucleus. This results in a weaker attractive force, lowering the ionization energy.
Comparing chlorine with the chloride ion, the added electron in the chloride ion increases the atomic radius, spreading the electrons over a greater volume. This increased radius in turn lowers its ionization energy compared to neutral chlorine.

Electron-Electron Repulsion

Electron-electron repulsion occurs when negatively charged electrons in an atom repel each other. This phenomenon impacts the atom's ionization energy because increased repulsion can "loosen" electrons, making them easier to remove.
In ions such as Cl^- , the addition of electrons enhances electron-electron repulsion, reducing the force keeping the outer electrons in place. This can lead to a lower ionization energy compared with the neutral atom. The added repulsion counters the attractive force from the nucleus, especially in a closed shell system which does not have extra space to accommodate increased electron density.
Hence, more electrons in the same shell without a corresponding increase in nuclear charge make it energetically easier to remove an electron.

Electron Shielding

Electron shielding occurs when inner-shell electrons partly block the nuclear charge from being felt by the outer-shell electrons. This effect significantly influences the effective nuclear charge, which is the perceived nuclear charge by an electron in the outer shell.
Depending on how many inner electrons are present, the outer electrons might experience a weaker pull from the nucleus. This makes them easier to remove, thus lowering ionization energy. In ions like Ca^{2+} , losing outer electrons greatly reduces the shielding effect, allowing the nuclear charge to hold the remaining electrons more tightly, increasing the ionization energy.
In summary, the balance of electron shielding and nuclear attraction is key in determining how tightly bound the outer electrons are, ultimately affecting ionization energy.