Question

Below are data on the first four ionization energies for a fictitious element \(X\). First ionization energy \(=500 \mathrm{~kJ} / \mathrm{mol}\) Second ionization energy \(=2000 \mathrm{~kJ} / \mathrm{mol}\) Third ionization energy \(=3500 \mathrm{~kJ} / \mathrm{mol}\) Fourth ionization energy \(=25,000 \mathrm{~kJ} / \mathrm{mol}\) From the data, which of the following statements is(are) incorrect? (a) \(\mathrm{X}\) could belong to group IIIA. (b) The fourth ionization energy is so much greater than the third ionization energy because \(\mathrm{X}^{3+}\) consists of a noble-gas core or a pseudo- noble-gas core. (c) The third ionization energy is greater than the second ionization energy because \(\mathrm{X}^{2+}\) has a bigger charge than \(\mathrm{X}^{+}\). (d) \(\mathrm{X}\) could belong to group IIIB. (e) \(X\) could belong to group VA.

Short answer

Statements (d) and (e) are incorrect based on the ionization energy data provided.

Step-by-step solution

Assess Statement (a)

Statement (a) says that X could belong to group IIIA. The trend of ionization energies suggests that for elements of the same period, as we move across the period from left to right, the ionization energy increases. Also, there is a significant increase in ionization energy when moving from one group to the other. Based on the ionization energy data, we can see that there is a large jump of ionization energy between the third and fourth ionization energies (from 3500 to 25000 kJ/mol). Considering the periodic trend, this indicates X most likely belongs to group IIIA. So, statement (a) is correct.

Assess Statement (b)

Statement (b) says that the fourth ionization energy is so much greater than the third ionization energy because \(X^{3+}\) consists of a noble-gas core or a pseudo-noble-gas core. As we discussed in statement (a), the significant increase in ionization energy from the third to the fourth ionization energy supports this statement. When the element's electron configuration reaches a noble-gas core or pseudo-noble-gas core after the third ionization, it requires much more energy to remove another electron, which explains the significant jump in ionization energy. So, statement (b) is correct.

Assess Statement (c)

Statement (c) says that the third ionization energy is greater than the second ionization energy because \(X^{2+}\) has a bigger charge than \(X^+\). The increase in ionization energy from the second to the third ionization energy is due to the increased effective nuclear charge experienced by the outer electrons. This increase in effective nuclear charge makes it harder to remove an electron from \(X^{2+}\) compared to \(X^+\). So, statement (c) is correct.

Assess Statement (d)

Statement (d) says that X could belong to group IIIB. If X belonged to group IIIB, we would expect the ionization energy to increase significantly between the second and third ionization energies, not between the third and fourth as observed in the data. Consequently, statement (d) is incorrect.

Assess Statement (e)

Statement (e) states that X could belong to group VA. If X belonged to group VA, we would expect a large increase in ionization energy between the first and second ionization energies, not between the third and fourth ionization energies as observed in the data. Therefore, statement (e) is incorrect. According to the given data and our analysis, statements (d) and (e) are incorrect, while statements (a), (b), and (c) are correct.

Key concepts

Periodic Trends

Periodic trends are patterns observed within elements on the periodic table concerning their chemical and physical properties. One fundamental trend involves ionization energy, which is the energy required to remove an electron from a gaseous atom or ion.

Typically, the ionization energy increases from left to right across a period, owing to the increasing number of protons in the nucleus, which results in a stronger attraction between the nucleus and the electrons. This trend generally leads to a higher energy requirement to remove an electron because they are held more tightly due to this increased positive charge.

On the other hand, ionization energy decreases down a group as the outermost electrons are further from the nucleus and more shielded by inner-shell electrons. With increased distance and shielding, these outer electrons are less tightly bound to the atom, and thus, less energy is needed to remove them.

Effective Nuclear Charge

The concept of effective nuclear charge (\(Z_{\text{eff}}\)) helps explain the hold that the nucleus has on the outermost electrons. It is the net positive charge experienced by an electron in a multi-electron atom. The reason it’s not the full nuclear charge is due to shielding or screening by the inner electrons.

\(Z_{\text{eff}} = Z - S\) where \(Z\) is the atomic number and \(S\) is the average number of electrons between the nucleus and the electron in question (the shielding constant).

As an atom's nuclear charge becomes more substantial due to an increasing number of protons, if the shielding effect remains relatively constant, the effective nuclear charge increases. This increased attraction means that more energy will be needed to remove an electron, heightening the element's ionization energy.

Noble-Gas Core

A noble-gas core refers to the electron configuration of an atom that corresponds to that of a noble gas, indicating a full valence shell. This is a stable configuration because noble gases are famously inert and rarely form chemical bonds under normal conditions.

Atoms strive to reach this state of stability, which is described in the octet rule, where atoms prefer to have eight electrons in their valence shell. When an element achieves a noble-gas core, particularly after ionization, it indicates that all valence electrons have been removed, and those remaining are tightly held by the nucleus. This situation results in a drastic increase in ionization energy for the removal of the next electron, as observed in the exercise with the transition from the third ionization energy to the much larger fourth ionization energy for element X.