Problem 103 - Chemistry: The Central Science in SI Units, Global Edition

Question

Elemental barium reacts more violently with water than does elemental calcium. Which of the following best explains this difference in reactivity? (i) Calcium has greater metallic character than does barium. (ii) The electron affinity of calcium is smaller than that of barium. (iii) The first and second ionization energies of barium are less than those of calcium. (iv) The atomic radius of barium is smaller than that of calcium. (v) The ionic radius of the barium ion is larger than that of the calcium ion.

Step-by-Step Solution

Answer

The best explanation for the difference in reactivity between elemental barium and elemental calcium is Explanation (iii): The first and second ionization energies of barium are less than those of calcium. This makes it easier for barium to lose electrons and react with water, resulting in its more violent reaction.

Step 1: Explanation (i) - Metallic character

Metallic character refers to the propensity of an element to lose electrons and form positive ions. If calcium had a greater metallic character than barium, it would be more likely to lose electrons and react with water. However, barium is more reactive than calcium. Therefore, this explanation is not valid.

Step 2: Explanation (ii) - Electron affinity

Electron affinity is the energy change associated with the process of an atom gaining an electron. A smaller electron affinity means that an element is less likely to gain electrons. Here, we are concerned with the elements losing electrons and reacting with water. So, electron affinity is not relevant to this situation, and this explanation is not valid.

Step 3: Explanation (iii) - Ionization energies

Ionization energy refers to the amount of energy required to remove an electron from an atom. The explanation states that both the first and second ionization energies of barium are less than those of calcium. Since the ionization energies are lower for barium, it means that it is easier for barium to lose electrons in comparison to calcium. This would indeed make barium more reactive with water, so this explanation is valid.

Step 4: Explanation (iv) - Atomic radius

The atomic radius is a measure of the size of an atom. A smaller atomic radius would mean that the electrons are closer to the nucleus, making it harder to lose electrons. Since barium is more reactive than calcium, its atomic radius should be larger and not smaller. Thus, this explanation is not valid.

Step 5: Explanation (v) - Ionic radius

The ionic radius refers to the size of an atom's ion. A larger ionic radius would suggest that the atom forms a more stable ion, making it more likely to lose electrons and react with water. However, this characteristic is not directly related to the inherent reactivity of elemental barium and calcium, making this explanation less relevant to the problem. Conclusion: Therefore, among the given explanations, Explanation (iii) - "The first and second ionization energies of barium are less than those of calcium" - best explains the difference in reactivity between elemental barium and elemental calcium.

Key Concepts

Metallic Character

Metallic character is a fundamental property of elements, especially metals. It refers to how easily an element can lose electrons, a key aspect of its ability to form positive ions. Elements with higher metallic character tend to have lower ionization energies. This means they can lose their outermost electrons with less energy and therefore react more easily, particularly with non-metals like oxygen and water.

Barium has a greater metallic character than calcium because as you move down a group in the periodic table, elements tend to become more metallic. This is because the outer electrons are further from the nucleus and less tightly held, allowing them to be lost more readily.

• Elements with high metallic character are often metals.
• They typically have high electrical conductivity.
• They usually exhibit a shiny luster and are malleable.

Thus, in terms of metallic character, barium's higher tendency to lose electrons makes it more reactive than calcium.

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion. The lower the ionization energy, the easier it is for the element to lose an electron, which influences its reactivity.

In barium, the first and second ionization energies are lower than in calcium. This means barium can lose its electrons more easily compared to calcium, which contributes to its higher reactivity. Lower ionization energy in an element often leads to greater reactivity because the removal of electrons facilitates chemical reactions, particularly those that involve electron transfer.

• First ionization energy refers to removing the first outermost electron.
• Successive ionization energies are generally higher than the previous one.
• Elements with lower ionization energies are often highly reactive.

Therefore, the difference in ionization energies between barium and calcium explains why barium reacts more violently with water.

Atomic Radius

The atomic radius is the distance from the nucleus to the outermost shell of an electron. In the periodic table, atomic radius generally increases as you move down a group. This occurs because each row down adds a new electron shell, making the atom larger.

For barium, its larger atomic radius compared to calcium means that its outer electrons are farther away from the nucleus. This increased distance reduces the effective nuclear charge on these electrons, allowing them to be lost more easily during chemical reactions.

• As you go down a group, the atomic radius increases.
• The increased atomic size often means lower ionization energies.
• Atoms with larger radii can lose their electrons more easily, resulting in higher reactivity.

Hence, barium's larger atomic radius is one reason it is more reactive than calcium.

Electron Affinity

Electron affinity refers to the energy change that occurs when an atom gains an electron. It is a measure of how strongly an atom can attract and hold onto an added electron.

In the context of metal reactivity, electron affinity is not as relevant because metals typically lose rather than gain electrons during reactions. However, understanding electron affinity provides insight into non-metal behavior or reactions involving electron gain.

• Electron affinity values are generally more negative for non-metals.
• High electron affinity means an atom eagerly attracts electrons.
• In metals, electron affinity values typically have less influence on their typical reactivity.

In the case of barium and calcium, electron affinity does not significantly explain why barium is more reactive, since their reactivity primarily involves electron loss rather than gain.