Question

Three elements have the electron configurations \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2}\), \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{4}\), and \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2}\). The first ionization en- ergies of these elements (not in the same order) are \(0.590,0.999\), and \(0.738 \mathrm{MJ} / \mathrm{mol}\). The atomic radii are 104,160 , and \(197 \mathrm{pm}\). Identify the three elements, and match the appropriate values of ionization energy and atomic radius to each configuration. Complete the following table with the correct information.

Short answer

Element A is Magnesium (Mg) with an electron configuration of \(1s^{2} 2s^{2} 2p^{6} 3s^{2}\), an ionization energy of 0.590 MJ/mol, and an atomic radius of 160 pm. Element B is Sulfur (S) with an electron configuration of \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{4}\), an ionization energy of 0.999 MJ/mol, and an atomic radius of 104 pm. Element C is Calcium (Ca) with an electron configuration of \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2}\), an ionization energy of 0.738 MJ/mol, and an atomic radius of 197 pm.

Step-by-step solution

Identify the elements from their electron configurations

To identify each element, we can map the electron configurations to their respective periods and groups in the periodic table: Element A: \(1s^{2} 2s^{2} 2p^{6} 3s^{2}\) This element is in period 3 and group 2 (alkaline earth metals) since the last electron entered the 3s shell. Element B: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{4}\) This element is in period 3 and group 16 (chalcogens) since the last electron entered the 3p shell and there are 4 electrons in that shell. Element C: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2}\) This element is in period 4 and group 2 (alkaline earth metals) since the last electron entered the 4s shell. Now let's identify elements A, B, and C: Element A: Period 3, Group 2 - Magnesium (Mg) Element B: Period 3, Group 16 - Sulfur (S) Element C: Period 4, Group 2 - Calcium (Ca)

Match the ionization energies to the elements

We know that ionization energy generally increases across a period and decreases down a group. Given the ionization energies (0.590, 0.999, and 0.738 MJ/mol), we can assign them to the elements: Magnesium (Mg) - Being in period 3 and in an earlier group than sulfur, its ionization energy should be lower than sulfur's. So, it pairs with the lowest ionization energy, 0.590 MJ/mol. Sulfur (S) - Being in period 3 and having a higher ionization energy than magnesium (due to its position further across the period), it pairs with the highest ionization energy, 0.999 MJ/mol. Calcium (Ca) - Being in period 4, its ionization energy should be lower than magnesium's (the element in the same group but in an earlier period). So, it pairs with the remaining ionization energy, 0.738 MJ/mol.

Match the atomic radii to the elements

We know that atomic radius generally decreases across a period and increases down a group. Given the atomic radii (104, 160, and 197 pm), we can assign them to the elements: Magnesium (Mg) - Being in period 3 and in the same group as calcium, but in an earlier period, its atomic radius should be smaller than calcium's. It should also be larger than sulfur's, as the atomic radius decreases across the period. So, it pairs with the middle atomic radius, 160 pm. Sulfur (S) - Being in period 3 and further across the period than magnesium, it should have a smaller atomic radius than magnesium. So, it pairs with the smallest atomic radius, 104 pm. Calcium (Ca) - Being in period 4 and in the same group as magnesium but in a later period, its atomic radius should be larger than magnesium's. So, it pairs with the largest atomic radius, 197 pm. Now, we can complete the table: - Element: Magnesium (Mg) - Electron Configuration: \(1s^{2} 2s^{2} 2p^{6} 3s^{2}\) - Ionization Energy: 0.590 MJ/mol - Atomic Radius: 160 pm - Element: Sulfur (S) - Electron Configuration: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{4}\) - Ionization Energy: 0.999 MJ/mol - Atomic Radius: 104 pm - Element: Calcium (Ca) - Electron Configuration: \(1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2}\) - Ionization Energy: 0.738 MJ/mol - Atomic Radius: 197 pm

Key concepts

Ionization Energy

Ionization energy refers to the energy required to remove the outermost electron from an atom in its gaseous state. This is a key concept when studying elements since it helps us understand how easily an atom can lose an electron.
Ionization energy generally shows a clear trend across a period and down a group in the periodic table. As we move across a period from left to right, ionization energy tends to increase. This happens because the increase in positive charge in the nucleus attracts the electrons more strongly, making them harder to remove. Conversely, as we move down a group, the ionization energy typically decreases. This decrease occurs because the outermost electrons are farther from the nucleus due to additional electron shells, and thus are less tightly held.
These trends help explain the observations in the exercise:

• Magnesium, with an ionization energy of 0.590 MJ/mol, has a relatively low ionization energy as it is on the left side of period 3 (group 2).
• Sulfur, with the highest ionization energy of 0.999 MJ/mol, sits further across the same period (group 16) where electrons are held more tightly.
• Calcium, located below magnesium in group 2 of period 4, has a lower ionization energy (0.738 MJ/mol) due to its increased atomic size and additional electron shell.

Understanding these principles can assist in predicting an element’s behavior in chemical reactions and its tendency to form positive ions.

Atomic Radius

Atomic radius represents the size of an atom, usually measured from the nucleus to the outer boundary of the surrounding cloud of electrons. It is an important factor in understanding the arrangement and properties of atoms in the periodic table.
When examining atomic radius trends, we see that atomic size decreases across a period from left to right. The reason is that as we add more protons to the nucleus, the more the electrons are pulled towards the center, slightly reducing the size of the atom. On the other hand, moving down a group, the atomic radius increases because each successive element has an additional electron shell, offering more space for electrons to occupy.
These patterns correlate with the data in the exercise:

• Sulfur has the smallest atomic radius at 104 pm. This makes sense as it is further across period 3, leading to a tighter electron cloud.
• Magnesium, located earlier in the same period, has a larger atomic radius of 160 pm.
• Calcium, being one period down in the periodic table, has the largest atomic radius of 197 pm due to another added electron shell.

Atomic radius trends can help predict how atoms interact, bond, or contribute to the overall chemical nature of the element.

Periodic Table

The periodic table serves as a comprehensive chart that organizes all known elements by increasing atomic number. It reflects the periodic system created by Dmitri Mendeleev, which highlights recurring patterns in the properties of the elements. Familiarity with the periodic table is essential because it unveils significant relationships between properties such as ionization energy and atomic radius.
Each row of the table is known as a "period," and it marks the sequential filling of electron shells. As you move horizontally across a period, elements gain protons and electrons, leading to various trends. Meanwhile, vertical columns, termed "groups," categorize elements with similar characteristics and the same number of valence electrons.
In the exercise, understanding the position of magnesium, sulfur, and calcium on the periodic table is vital:

• Magnesium belongs to group 2 and period 3 where alkaline earth metals reside. These elements tend to have relatively low ionization energies and larger atomic radii than their neighbors further in the period.
• Sulfur finds its home in group 16 and period 3, representing chalcogens. They hold electrons more tightly due to their position further across the period, thus having higher ionization energies.
• Calcium, located in group 2 but in period 4, follows a similar pattern of group 2 elements but exhibits differences in properties due to its placement in a subsequent period.

The periodic table not only arranges elements logically but also aids predictions about chemical behaviors and bonding propensities, making it an invaluable tool for students and scientists alike.