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Ch.21 - Transition Elements and Coordination Chemistry
All textbooksMcMurry 8th EditionCh.21 - Transition Elements and Coordination ChemistryProblem 42
Chapter 21, Problem 42

Briefly account for each of the following observations:
(a) Atomic radii decrease in the order Sc > Ti > V.
(b) Densities increase in the order Ti > V > Cr.

Verified step by step guidance
1
Understand the periodic trends and how they affect atomic radii and density. Atomic radii generally decrease across a period from left to right due to the increase in nuclear charge which pulls the electrons closer to the nucleus.
Examine the position of Scandium (Sc), Titanium (Ti), and Vanadium (V) in the periodic table. They are located in the same period with increasing atomic number. This increase in atomic number from Sc to V means an increase in the effective nuclear charge, explaining the decrease in atomic radii.
Consider the factors affecting density, which include atomic mass and volume. As atomic number increases, generally so does the mass. However, the volume can decrease if the atomic radius decreases.
Analyze the positions of Titanium (Ti), Vanadium (V), and Chromium (Cr) in the periodic table. They are consecutive elements in a period, and as you move from Ti to Cr, the atomic mass increases while the atomic radius decreases, leading to an increase in density.
Relate the increase in nuclear charge with the decrease in atomic radius and the increase in density. The stronger nuclear pull (higher nuclear charge) as you move from Sc to V and from Ti to Cr not only decreases the atomic radius but also increases the density due to a smaller volume occupied by the atoms.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Atomic Radius Trends

Atomic radius refers to the size of an atom, typically measured from the nucleus to the outermost electron shell. As you move across a period in the periodic table from left to right, atomic radii generally decrease due to increased nuclear charge, which pulls electrons closer to the nucleus. In the case of Sc, Ti, and V, the decrease in atomic radius can be attributed to the increasing positive charge in the nucleus as you move from Sc to V.
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Density and Atomic Mass

Density is defined as mass per unit volume and is influenced by both the mass of the atoms and how closely they are packed in a given volume. As you move from Ti to V to Cr, the densities increase due to the increase in atomic mass and the arrangement of atoms in the crystal lattice. The transition metals exhibit varying densities based on their atomic structure and bonding characteristics.
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Transition Metals and Electron Configuration

Transition metals, such as Sc, Ti, V, and Cr, have unique electron configurations that affect their physical properties, including atomic radius and density. The presence of d-electrons contributes to the complexity of their bonding and packing in solid form. Understanding how these electrons influence the size and mass of the atoms helps explain the observed trends in atomic radii and densities among these elements.
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Related Practice
Textbook Question

Use the periodic table to give the electron configuration for each of the following atoms and ions. 

(c) Co(V) in CoO43–

(d) Co(IV) in CoF62–

Textbook Question

Titanium, used to make jet aircraft engines, is much harder than potassium or calcium. Explain.

Textbook Question

Molybdenum (mp 2623 °C) has a higher melting point than yttrium (mp 1522 °C) or cadmium (mp 321 °C). Explain.

Textbook Question

Arrange the following atoms in order of decreasing atomic radius, and account for the trend.

(a) Cr

(b) Ti

(c) Mn

(d) V

Textbook Question

What is the lanthanide contraction, and why does it occur?

Textbook Question

The atomic radii of zirconium (160 pm) and hafnium (159 pm) are nearly identical. Explain.