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

In conclusion, Rubidium's reactivity is higher than Silver's due to its larger atomic radius (248 pm vs 144 pm), making its outermost electron easier to remove. Additionally, Silver has more inner electron shells providing shielding to the outer electrons, reducing the effective nuclear charge. Therefore, Rubidium's increased reactivity is primarily a result of its larger atomic radius and weaker effective nuclear charge compared to Silver.

Step 1: 1. Identify the electron configuration of silver and rubidium

To find the electron configuration of each element, we must look at the periodic table and determine their atomic numbers (number of protons). The atomic number also represents the number of electrons in a neutral atom. For silver (Ag), the atomic number is 47. Its electron configuration is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^9\] For rubidium (Rb), the atomic number is 37. Its electron configuration is: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1\]

Step 2: 2. Compare the atomic radii of silver and rubidium

The atomic radius is a measure of the size of an atom. Larger atomic radii imply that the electrons are further away from the nucleus. This can be important when looking at the reactivity of elements. In general, elements with larger atomic radii are more reactive since their outer electrons are less tightly bound by the nucleus. Rubidium has an atomic radius of 248 pm (picometers). Silver has an atomic radius of 144 pm.

Step 3: 3. Explain the difference in reactivity

When comparing their electron configurations, we can see that both elements contain a single electron in their outermost s-orbital (5s^1 for Rb and 5s^2 4d^9 for Ag). This is essential for forming a +1 ion, as the loss of an outer electron results in a stable, positively charged ion. However, the atomic radius of Rubidium is larger than that of Silver (248 pm vs 144 pm). This means that the outermost electron in Rubidium is further away from the nucleus, making it less tightly bound and easier to remove. That partly explains why Rubidium is more reactive than Silver. Another point worth considering is the shielding effect of the inner electron shells. Silver has more inner electron shells (full 4d orbitals) that shield the outer electrons from the positive charge of the nucleus. This means that Silver's outermost electron feels a smaller net positive charge. In conclusion, with a larger atomic radius and a weaker effective nuclear charge, Rubidium's outermost electron is more easily removed, making the element more reactive than Silver. This factor, combined with the shielding provided by additional inner electron shells in Silver, helps to explain the observed difference in reactivity between these two elements.