Problem 87 - Chemical Principles

Question

Arrange the elements in each of the following sets in order of decreasing atomic radius: (a) sulfur, chlorine, silicon; (b) cobalt, titanium, chromium; (c) zinc, mercury, cadmium; (d) antimony, bismuth, phosphorus.

Step-by-Step Solution

Answer

Set (a) Si > S > Cl, Set (b) Ti > Cr > Co, Set (c) Hg > Cd > Zn, Set (d) Bi > Sb > P

Step 1: Understanding Atomic Radius Trends

The atomic radius tends to decrease across a period from left to right, due to the increase in the number of protons resulting in a greater effective nuclear charge, pulling electrons closer to the nucleus. It increases down a group since the number of electron shells increases, making the atom's radius larger.

Step 2: Order for Set (a) - Sulfur (S), Chlorine (Cl), Silicon (Si)

These elements are in the same period of the periodic table. Sulfur, chlorine and silicon are in the 3rd period, with atomic numbers 16, 17, and 14 respectively. The atomic radius should decrease from silicon to chlorine, so the order is Si > S > Cl.

Step 3: Order for Set (b) - Cobalt (Co), Titanium (Ti), Chromium (Cr)

These elements are from the first two transition series. Across a period in the transition elements, atomic radius decreases slightly. With atomic numbers 27, 22, and 24 respectively, we can deduce the order is Ti > Cr > Co.

Step 4: Order for Set (c) - Zinc (Zn), Mercury (Hg), Cadmium (Cd)

These elements are all group 12 elements but from different periods. As you go down the group, the atomic radius increases. Hence, the order from largest to smallest is Hg > Cd > Zn.

Step 5: Order for Set (d) - Antimony (Sb), Bismuth (Bi), Phosphorus (P)

These elements belong to group 15. The atomic radius increases going down the group, so the order is Bi > Sb > P.

Key Concepts

Understanding Periodic Table Trends

The periodic table is not just a tabulation of elements, it's a map that reveals the landscape of atomic characteristics. Atomic radius is one of the key features of this landscape, showcasing a clear pattern across the table.

As students progress through chemistry, understanding these trends is crucial. From left to right across a period, as the effective nuclear charge (the net charge an electron experiences from the nucleus) increases, the atomic radius decreases. This is because elements gain more protons, thus pulling electrons closer to the nucleus. Conversely, as you travel down a group, the atomic radius increases because each successive element has an additional electron shell, distancing the outer electrons from the nucleus.

Take silicon (Si), sulfur (S), and chlorine (Cl) in the periodic table's third period for example. They follow the trend with silicon having the largest atomic radius and chlorine the smallest. Noticing these patterns helps in solving problems involving atomic size, reactions, and other properties of molecules.

The Role of Effective Nuclear Charge

Diving deeper into why these trends exist, the concept of effective nuclear charge (ENC) is pivotal. ENC is essentially the force exerted by the positively charged nucleus on the valence electrons, and it determines how tightly the electrons are held.

ENC increases across a period because, although more electrons are being added, they are largely unable to shield the increased positive charge from the additional protons. This leads to a stronger attraction between the nucleus and electrons, resulting in a smaller atomic radius. For instance, chlorine's higher ENC than silicon pulls its electrons closer, decreasing its radius.

How to Use ENC in Atomic Radius Predictions

When ENC increases substantially, the electrons experience a greater pull towards the nucleus, effectively reducing the atomic radius. Thus, knowing the ENC can help predict and understand various properties of an element, such as ionization energy, electronegativity, and chemical reactivity.

Trends Involving Transition Elements

The transition elements, which include metals such as iron, copper, and titanium, have unique properties and trends as well. Located in the middle of the periodic table, these elements often have comparable atomic and ionic radii from one to the next.

The similarities stem from their electron configurations, where electrons are added to an inner d-subshell. This contributes to their unique chemistry and lesser extent of radius decrease across a period. For example, the atomic radii of cobalt (Co), titanium (Ti), and chromium (Cr) decrease across the period but by a smaller margin than the main group elements.

Characteristics of Transition Metals

Transition metals are known for their

• High melting and boiling points
• Formation of colorful compounds
• Ability to exist in various oxidation states

Understanding the nuances of transition elements is crucial for grasping the full scope of chemistry and the applications of these versatile materials.