Question

Which of the following statements is(are) true? a. F has a larger first ionization energy than does Li. b. Cations are larger than their parent atoms. c. The removal of the first electron from a lithium atom (electron configuration is \(1 s^{2} 2 s^{1}\) ) is exothermic - that is, removing this electron gives off energy. d. The He atom is larger than the \(\mathrm{H}^{+}\) ion. e. The Al atom is smaller than the Li atom.

Short answer

Statements a, d, and e are true. Statement a is true because F has a higher electronegativity than Li, resulting in a larger first ionization energy. Statement d is true as the He atom is larger than the \(\mathrm{H}^{+}\) ion, which has no measurable atomic size. Statement e is true because Al has a larger effective nuclear charge than Li, resulting in a smaller atomic size for Al compared to Li.

Step-by-step solution

Statement a. Comparison of Ionization Energies

To determine whether fluorine (F) has a larger first ionization energy than lithium (Li), we need to consider their positions on the periodic table. Fluorine is in Group 17 (halogens) and has a higher electronegativity than lithium, which is in Group 1 (alkali metals). Since ionization energy increases from left to right across a period, and from bottom to top within a group, Fluorine will indeed have a larger first ionization energy than lithium. Therefore, statement a is true.

Statement b. Size of Cations and Their Parent Atoms

A cation is an atom that has lost one or more electrons, resulting in a net positive charge. The removal of electrons causes the electron cloud around the nucleus to shrink, as there is now less electron-electron repulsion. Consequently, the remaining electrons are drawn closer to the positively charged nucleus. Thus, cations are generally smaller than their parent atoms, making statement b false.

Statement c. Energy Change in Removing the First Electron from Lithium

When an electron is removed from a neutral atom, energy is always required to overcome the attraction between the negatively charged electron and the positively charged nucleus. This energy is known as ionization energy. In the case of lithium (1s²2s¹), the removal of the first electron is endothermic, meaning that it requires energy input, not the exothermic process that releases energy as stated. Therefore, statement c is false.

Statement d. Size Comparison of Helium Atom and Hydrogen Ion

The helium (He) atom has an electron configuration of \(1s^{2}\), whereas the hydrogen ion (\(\mathrm{H}^{+}\)) is just a proton with no electrons. Since there is no electron cloud in \(\mathrm{H}^{+}\) to determine its size, it is considered to have no measurable atomic size. Therefore, the helium atom is larger than the \(\mathrm{H}^{+}\) ion, making statement d true.

Statement e. Size Comparison of Aluminum and Lithium Atoms

Aluminum (Al) and lithium (Li) are both in Group 13 and Group 1, respectively, of the periodic table. Atomic size generally increases as you move down a group and from right to left within a period. Since aluminum is located further down and to the right, we would expect it to be larger than lithium. However, aluminum has a larger effective nuclear charge than lithium due to the higher number of protons in its nucleus. This increased effective nuclear charge pulls the electron cloud of aluminum closer to the nucleus, which results in a smaller atomic size for aluminum compared to lithium. Thus, statement e is true. In summary: - Statement a is true. - Statement b is false. - Statement c is false. - Statement d is true. - Statement e is true.

Key concepts

Atomic Structure

The concept of atomic structure is fundamental in chemistry and involves the arrangement of subatomic particles—protons, neutrons, and electrons—within an atom. The core of the atom, the nucleus, contains protons and neutrons. Electrons, considerably less massive, are located in orbitals around the nucleus, with energy levels increasing at greater distances from the nucleus.

Understanding atomic structure is crucial when considering ionization energy—the energy required to remove an electron. Each electron in an atom is bound to the nucleus due to the electrostatic force between negatively charged electrons and positively charged protons. Removing an electron disrupts this balance, and the amount of energy needed to do so varies depending on an electron's position within the structure. For example, removing the first electron from lithium, which has the electron configuration of \(1s^2 2s^1\), involves overcoming the attraction of this electron to the lithium nucleus.

Periodic Trends

Periodic trends in the periodic table are patterns that predict the behavior of the elements. For example, ionization energy tends to increase across a period (left to right) due to electrons being added to the same energy level while effective nuclear charge increases. This means that as we move across a period, each added electron is held more tightly by the nucleus, thus requiring more energy to remove one.

Conversely, ionization energy decreases down a group (top to bottom), as electrons are being placed into higher and more distant orbitals from the nucleus, increasing the shielding effect and making them easier to remove. These trends explain why fluorine has a higher ionization energy than lithium. When students visualize the periodic table and understand these trends, they can more readily grasp concepts such as the energy required to form cations or the relative sizes of ions and atoms.

Cation Size

Cation size refers to the radius of a positively charged ion, which is known as a cation. This radius is smaller than that of its parent atom because the removal of an electron results in a reduced repulsion among the remaining electrons and a stronger attraction to the nucleus due to the decrease in shielding.

The size of a cation is influenced by the atomic structure; as electrons are removed—for instance, from the valence shell—the electron cloud contracts because there are fewer electrons to spread out the repulsive force between them. As a direct consequence of this contraction, the cation becomes smaller than its parent atom. This can also be attributed to the increased effective nuclear charge experienced by the remaining electrons. Understanding the concept of cation size is crucial for predicting and explaining various chemical behaviors, particularly during the formation of ionic compounds and the consequences on the properties of those compounds.