Problem 22 - General Chemistry: Principles and Modern Applications

Question

Are there any atoms for which the second ionization energy \(\left(I_{2}\right)\) is smaller than the first \(\left(I_{1}\right) ?\) Explain.

Step-by-Step Solution

Answer

No, there are no atoms for which the second ionization energy (I2) is smaller than the first (I1). This is because the positive charge of an ion increases after the first ionization, attracting the remaining electrons more strongly and thus requiring more energy to remove them. Therefore, the second ionization energy is always greater than the first.

Step 1: Understanding ionization energy

The ionization energy of an atom is the energy required to remove an electron from a gaseous atom or ion. The first ionization energy is the energy needed to remove the first electron from the neutral atom. The second ionization energy is the energy needed to remove a second electron.

Step 2: Ionic charges and their effects on ionization energy

After the first ionization, the atom becomes positively charged creating an ion. This positive charge has a stronger pull on the remaining electrons. Therefore, It is always harder to remove electrons from a positively charged ion than from a neutral atom. As such, the second ionization energy is always greater than the first.

Step 3: Concluding the exercise

Because ionization energy increases as electrons are removed due to increasing positive charge, it can be concluded that no atom has a second ionization energy smaller than its first.

Key Concepts

First Ionization Energy

Ionization energy is a fundamental concept in chemistry which refers to the energy required to remove an electron from an atom or ion. The first ionization energy is specifically the amount of energy needed to remove the first electron from a neutral atom.
This initial electron is only weakly held by the atom, as the forces of attraction between the electron and the positively charged nucleus are often balanced by electron-electron repulsions. Hence, the first ionization energy gives us a sense of the atom's tendency to lose an electron and form a positively charged ion, or cation.

• The first ionization energy is unique to each element.
• It varies across the periodic table, generally increasing across a period and decreasing down a group.

Factors affecting the first ionization energy include the number of electron shells (energy levels), the effective nuclear charge (how strongly the nucleus pulls on outer electrons), and the electron configuration of the element. Understanding these trends helps in predicting the reactivity and chemical behavior of elements.

Second Ionization Energy

When we refer to second ionization energy, we're discussing the energy needed to remove a second electron from an already ionized atom. After the removal of the first electron, the atom becomes a positively charged ion. This positive ion has a stronger attraction to remaining electrons due to the overall positive charge.

• The second ionization energy is invariably higher than the first.
• This is because it requires more energy to remove an electron from a positively charged ion than from a neutral atom.

The second ionization energy is, therefore, a critical parameter in understanding the stability of ions and predicting the types of ions certain elements are likely to form. The tendency for a second ion to be formed is profoundly affected by the relative stability of the ion after the second electron is removed. For example, elements in group 1 of the periodic table typically have a high second ionization energy because removing a second electron destabilizes the atom significantly.

Atomic Charges

When electrons are removed from an atom, it results in a net charge imbalance, creating what is known as atomic charges. These charges play a crucial role in chemical reactions and bond formations by influencing the behavior of atoms and ions.
Each time an electron is removed, the atom's net positive charge increases. A +1 charge after the first ionization, and a +2 after the second, makes the ion more stable to keep existing electrons tightly bound.

• Positive charges result from electron removal, while negative charges result from electron addition.
• As electrons are sequentially removed, increasing positive charges make it harder to remove more electrons.

Understanding atomic charges is essential for visualizing how atoms interact, form bonds, and engage in electron exchange during chemical reactions. These interactions are key to the dynamic processes observed in everyday chemical reactions, from the rusting of iron to the functioning of batteries.