Problem 68 - Chemistry The Central Science

Question

Silver and rubidium both form \(+1\) ions, but silver is far less reactive. Suggest an explanation, taking into account the ground-state electron configurations of these elements and their atomic radii.

Step-by-Step Solution

Answer

Silver (Ag) is far less reactive than rubidium (Rb) because, although they both form +1 ions and have one valence electron in the 5s orbital, the atomic radius of rubidium is larger than that of silver. This means the valence electron in rubidium is easier to remove compared to silver, and hence, rubidium is more chemically reactive than silver.

Step 1: Determine the electron configurations of silver and rubidium atoms

In order to determine the electron configurations of silver and rubidium, we can refer to the periodic table where their atomic numbers are given. Silver (Ag) has an atomic number of 47, while rubidium (Rb) has an atomic number of 37. Using the atomic numbers, we can write the electron configurations for both elements as follows: Silver (Ag): \( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^1 \) Rubidium (Rb): \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 \) It is important to analyze the outermost electrons, also known as valence electrons. Silver has one valence electron in the 5s orbital, while rubidium has one valence electron in the 5s orbital as well.

Step 2: Analyze the atomic radii of silver and rubidium atoms

The other factor that can be taken into account is the atomic radii. In the periodic table, atoms increase in size as you move down a group (vertical column) and decrease in size as you move across a period (horizontal row). Rubidium is located in the alkali metals group and found in period 5. Silver is located in the transition metals group and found in period 5 as well. Since rubidium is on the far left of the period and silver is several elements to the right, we can conclude that rubidium has a larger atomic radius compared to silver.

Step 3: Discuss the reactivity of silver and rubidium

The reactivity of an element is mainly determined by the ease with which it loses or gains electrons. Since both silver and rubidium have one valence electron in the 5s orbital, forming +1 ions, the atomic radius becomes an important factor to consider. Rubidium, with a larger atomic radius, means that its 5s valence electron is located farther from its nucleus and is less tightly bound, making it easier to be removed. On the other hand, silver's valence electron is closer to the nucleus due to its smaller atomic radius, resulting in a stronger attraction making it harder to be removed.

Step 4: Conclusion

Silver (Ag) is far less reactive than rubidium (Rb) because, although they both form +1 ions and have one valence electron in the 5s orbital, the atomic radius of rubidium is larger than that of silver. This means the valence electron in rubidium is easier to remove compared to silver, and hence, rubidium is more chemically reactive than silver.

Key Concepts

Electron Configuration

The electron configuration of an atom describes the distribution of electrons in its orbitals. For the elements in question, silver (Ag) and rubidium (Rb), understanding their electron configurations helps explain differences in their chemical reactivity.

- **Silver (Ag)** has an atomic number of 47. Its configuration is: \( 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6 4d^{10} 5s^1 \). The outermost electron, or valence electron, is found in the 5s orbital. - **Rubidium (Rb)** has an atomic number of 37, with a configuration of: \( 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 \). Similarly, its valence electron is also in the 5s orbital.

Although both elements have a single electron in the 5s orbital, their placement in different groups on the periodic table affects their electron configuration at the deeper levels, influencing their chemical properties and reactivity.

Atomic Radii

Atomic radius refers to the size of an atom, more specifically, the distance from the nucleus to the outermost electron shell. As a rule of thumb, the atomic radius increases down a group and decreases across a period in the periodic table.

Rubidium has a larger atomic radius than silver. In the periodic table, rubidium is situated in the alkali metal group, while silver is a transition metal. Both are located in period 5, but since rubidium lies to the far left and silver towards the center, rubidium's atoms are larger.

- **Bigger Radius & Easier Reactivity**: In rubidium, the increased size means its valence electron is farther from the nucleus, held with less energy, and therefore more easily lost. - **Smaller Radius & Harder Reactivity**: Conversely, in silver, the closer proximity of the valence electron to the nucleus due to a smaller radius creates a stronger attraction, making it harder to remove this electron, thus reducing its reactivity.

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom. These are the ones primarily involved in bonding and chemical reactions.

Silver and rubidium both have one valence electron in the 5s orbital. The way these electrons interact with the surrounding environment plays a vital role in determining the reactivity of the element.
- In **rubidium**, this electron is more loosely bound because of its larger atomic radius. Therefore, rubidium can easily lose its electron to form a +1 ion. This ease of electron removal makes rubidium highly reactive. - In **silver**, the valence electron is more tightly bound due to the relatively smaller atomic radius, meaning more energy is required to remove it. This results in silver being less reactive than rubidium.

The easy loss or retention of the valence electron significantly influences these elements' chemical behavior, contributing to the distinct difference in their reactivity despite having similar valence shell configurations.