Question

Answer each of the following questions: (a) Which of the elements \(P, A s,\) and \(S\) has the largest atomic radius? (b) Which of the following has the smallest radius: \(\mathrm{Xe}, \mathrm{O}^{2-}, \mathrm{N}^{3-},\) or \(\mathrm{F}^{-} ?\) (c) Which should have the largest difference between the first and second ionization energy: \(\mathrm{Al}, \mathrm{Si}, \mathrm{P},\) or \(\mathrm{Cl} ?\) (d) Which has the largest ionization energy: \(\mathrm{C}, \mathrm{Si}\), or \(\mathrm{Sn}\) ? (e) Which has the largest electron affinity: \(\mathrm{Na}, \mathrm{B}\) \(\mathrm{Al},\) or \(\mathrm{C} ?\)

Short answer

The answers are: (a) P, (b) \(F^{-}\), (c) Al, (d) C, (e) C.

Step-by-step solution

Identify the trends

In general, atomic radius increases from top to bottom in a group, and decreases from left to right across a period. Ionization energy decreases from top to bottom in a group, and increases from left to right across a period. Electron affinity decreases from top to bottom in a group, and increases from left to right across a period.

Answer question (a)

Given the elements P (Phosphorus), As (Arsenic), and S (Sulfur), use the atomic radius trend. As these elements are found in the same period but different groups, the atomic radius decreases from left to right. So, the element with the largest atomic radius is P (Phosphorus).

Answer question (b)

When looking at Xe, \(O^{2-}\), \(N^{3-}\), and \(F^{-}\), consider that ions are generally larger when they have a negative charge because they have gained electrons. Among the ions, \(N^{3-}\) has the greatest negative charge and hence the largest size. Xe is a neutral atom and is larger than an oxygen or fluorine ion. So \(F^{-}\) has the smallest radius.

Answer question (c)

Regarding the largest difference between the first and second ionization energies, it's important to understand that the second ionization energy is always larger than the first. However, if removing the second electron means breaking a stable electron configuration, the difference will be huge. Between Al, Si, P, and Cl, Al has an electron configuration ending in \(3p^1\). Removing one electron results in a stable \(3s^2\) configuration, so removing a second one will involve more energy. Thus, Al should have the largest difference between the first and second ionization energies.

Answer question (d)

For the greatest ionization energy among C, Si, and Sn, you need to consider the trend that ionization energy decreases from top to bottom and increases from left to right. C is above Si and Sn in the same group, so C has the greatest ionization energy.

Answer question (e)

For the largest electron affinity among Na, B, Al, and C, use the trend that electron affinity generally increases from left to right across a period. Thus, C, being furthest to the right, has the highest electron affinity.

Key concepts

Atomic Radius

The atomic radius is a measure of the size of an atom. It is determined by the distance from the nucleus to the outer boundary of the surrounding cloud of electrons. As you go down a group in the periodic table, atomic radius increases. This is because each row adds an electron shell, making the atoms larger. Conversely, as you move from left to right across a period, atomic radius decreases. This occurs due to an increase in nuclear charge, as protons are added to the nucleus, pulling the electrons closer.

• For example, when comparing phosphorous (P), arsenic (As), and sulfur (S), As has the largest atomic radius as it is lower in the same group.
• This trend helps explain why certain elements are more reactive or have different physical properties.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom in its gaseous state. As you move from left to right across the periodic table, ionization energy increases due to stronger nuclear pull on the electrons. As you descend a group, ionization energy decreases because the outer electrons are further away from the nucleus and are shielded by inner electrons. This makes them easier to remove. Also, when considering the first and second ionization energies, there is often a significant increase if removal of the second electron disrupts a stable electron configuration.

• For instance, aluminum (Al) has a marked jump from first to second ionization energy because the second removal disturbs a noble gas-like core.
• Carbon (C) has higher ionization energy than its group members silicon (Si) and tin (Sn) since it is at the top of the group, facing less electron shielding.
• Understanding ionization energy trends is crucial for predicting how an element will react during chemical reactions.

Electron Affinity

Electron affinity measures the energy change that occurs when an atom gains an electron in its gaseous state. It reflects how much an atom wants to add an extra electron, which is often linked to stability achieved by gaining a full electron shell. Typically, electron affinity becomes more negative (indicating greater affinity) as you move from left to right across a period. As you go down a group, electron affinity values can vary but generally decrease because the added electron is entering a shell farther from the nucleus.

• Carbon (C) has the highest electron affinity among Na, B, Al, and C because it is furthest to the right in its period.
• This trend impacts how elements bond with each other and their resulting compounds.

Elemental Properties

The properties of elements depend on their electron configurations, which dictate trends like atomic radius, ionization energy, and electron affinity. These trends help predict how elements behave and interact in chemical reactions. Elements in the same group often have similar chemical properties due to their comparable valence electron configurations, but they vary as you move up or down the group.

• For example, noble gases are known for their lack of reactivity due to having full electron shells.
• Exploring these periodic trends can provide insight into why some elements, such as chlorine, react vigorously with others, such as sodium, forming stable compounds.

Grasping these properties not only helps in understanding chemistry but also aids in predicting the behavior and characteristics of new elements discovered. Understanding these trends is a cornerstone of chemistry as it provides a systematic approach to organizing and understanding elements and their interactions.