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Chapter 23: Problem 12

Sketch a plot of atomic radius versus number of valence \(d\) electrons for the period 5 transition metals, and explain the trend.

Short Answer

Expert verified
The atomic radius of period 5 transition metals generally decreases with the increase in the number of valence d electrons, due to the increasing effective nuclear charge. This trend can be seen in a plot of atomic radius versus the number of valence d electrons for these elements: Yttrium (Y) with 1 d electron and 180 pm atomic radius, through Zirconium (Zr), Niobium (Nb), Molybdenum (Mo), Technetium (Tc), Ruthenium (Ru), and Rhodium (Rh) with 7 d electrons and 134 pm atomic radius. The slight increase in atomic radius for Palladium (Pd), Silver (Ag), and Cadmium (Cd) can be attributed to the increased shielding effect, resulting in a weaker attraction between the nucleus and the valence electrons and a larger atomic radius.

Step by step solution

01

Understanding atomic radius

Atomic radius refers to the size of an atom and can be measured as the distance from the nucleus to the outermost electron shell. Atomic radius generally decreases across a period and increases down a group in the periodic table due to the increase in the number of electron shells.
02

Identifying period 5 transition metals

Period 5 transition metals are the elements found in the 5th period and the d-block of the periodic table. These elements have a general electronic configuration of [Kr] 4d^n 5s^m, where n ranges from 1 to 10, and m ranges from 0 to 2. The period 5 transition metals are: - Yttrium (Y, atomic number 39) - Zirconium (Zr, atomic number 40) - Niobium (Nb, atomic number 41) - Molybdenum (Mo, atomic number 42) - Technetium (Tc, atomic number 43) - Ruthenium (Ru, atomic number 44) - Rhodium (Rh, atomic number 45) - Palladium (Pd, atomic number 46) - Silver (Ag, atomic number 47) - Cadmium (Cd, atomic number 48)
03

Determining the number of valence d electrons

For each period 5 transition metal, determine the number of valence d electrons (based on their electronic configuration): - Yttrium (Y): 1 d electron - Zirconium (Zr): 2 d electrons - Niobium (Nb): 3 d electrons - Molybdenum (Mo): 4 d electrons - Technetium (Tc): 5 d electrons - Ruthenium (Ru): 6 d electrons - Rhodium (Rh): 7 d electrons - Palladium (Pd): 8 d electrons - Silver (Ag): 9 d electrons - Cadmium (Cd): 10 d electrons
04

Finding atomic radii of period 5 transition metals

Look up the atomic radii of period 5 transition metals from a reference source, such as a textbook or online database. Here are approximate atomic radii values for these elements: - Yttrium (Y): 180 pm - Zirconium (Zr): 160 pm - Niobium (Nb): 145 pm - Molybdenum (Mo): 139 pm - Technetium (Tc): 136 pm - Ruthenium (Ru): 134 pm - Rhodium (Rh): 134 pm - Palladium (Pd): 137 pm - Silver (Ag): 144 pm - Cadmium (Cd): 151 pm
05

Sketching the plot

Using the data collected in steps 3 and 4, sketch a plot of atomic radius (y-axis) versus the number of valence d electrons (x-axis) for the period 5 transition metals. You should notice that the atomic radius generally decreases with the increase in the number of valence d electrons up to Rh, with a slight increase from Pd to Cd.
06

Explaining the trend

The trend in atomic radii can be explained by the increasing effective nuclear charge, which is the net positive charge experienced by the valence electrons due to the increased number of protons in the nucleus and the shielding effect of inner electron shells. As the number of valence d electrons increases, the effective nuclear charge also increases, causing a stronger attraction between the nucleus and the valence electrons, and thus a smaller atomic radius. The slight increase in atomic radius for Pd, Ag, and Cd can be attributed to the increased shielding effect, due to the filled or almost filled d orbitals, which results in a weaker attraction between the nucleus and the valence electrons and a larger atomic radius.

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Most popular questions from this chapter

A classmate says, "A weak-field ligand usually means the complex is high spin." Is your classmate correct? Explain.

Sketch the structure of the complex in each of the following compounds and give the full compound name: (a) cis- \(\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\left(\mathrm{NO}_{3}\right)_{2}\) (b) \(\mathrm{Na}_{2}\left[\mathrm{Ru}\left(\mathrm{H}_{2} \mathrm{O}\right) \mathrm{Cl}_{5}\right]\) (c) trans- \(\mathrm{NH}_{4}\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right]\) (d) cis- \(\left[\mathrm{Ru}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]\)

When Alfred Werner was developing the field of coordination chemistry, it was argued by some that the optical activity he observed in the chiral complexes he had prepared was because of the presence of carbon atoms in the molecule. To disprove this argument, Werner synthesized a chiral complex of cobalt that had no carbon atoms in it, and he was able to resolve it into its enantiomers. Design a cobalt(III) complex that would be chiral if it could be synthesized and that contains no carbon atoms. (It may not be possible to synthesize the complex you design, but we won't worry about that for now.)

Indicate the coordination number of the metal and the oxidation number of the metal as well as the number and type of each donor atom of the ligands for each of the following complexes: (a) \(\mathrm{K}_{3}\left[\mathrm{Co}(\mathrm{CN})_{6}\right]\) (b) \(\mathrm{Na}_{2}\left[\mathrm{CdBr}_{4}\right]\) (c) \(\left[\mathrm{Pt}(\mathrm{en})_{3}\right]\left(\mathrm{ClO}_{4}\right)_{4}\) (d) \(\left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)\right]^{+}\) (e) \(\mathrm{NH}_{4}\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{2}(\mathrm{NCS})_{4}\right]\) (f) \(\left[\mathrm{Cu}(\text { bipy })_{2} \mathrm{I}\right] \mathrm{I}\)

The molecule methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) can act as a monodentate ligand. The following are equilibrium reactions and the thermochemical data at \(298 \mathrm{~K}\) for reactions of methylamine and en with \(\mathrm{Cd}^{2+}(a q):\) $$ \begin{array}{c} \mathrm{Cd}^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \rightleftharpoons\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) \\ \Delta H^{\circ}=-57.3 \mathrm{~kJ} ; \quad \Delta S^{\circ}=-67.3 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-37.2 \mathrm{~kJ} \\\ \mathrm{Cd}^{2+}(a q)+2 \mathrm{en}(a q) \rightleftharpoons\left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q) \\ \Delta H^{\circ}=-56.5 \mathrm{~kJ} ; \quad \Delta S^{\circ}=+14.1 \mathrm{~J} / \mathrm{K} ; \quad \Delta G^{\circ}=-60.7 \mathrm{~kJ} \end{array} $$ (a) Calculate \(\Delta G^{\circ}\) and the equilibrium constant \(K\) for the following ligand exchange reaction: \(\left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q)+2 \operatorname{en}(a q) \rightleftharpoons\) $$ \left[\mathrm{Cd}(\mathrm{en})_{2}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) $$ Based on the value of \(K\) in part (a), what would you conclude about this reaction? What concept is demonstrated? (b) Determine the magnitudes of the enthalpic \(\left(\Delta H^{\circ}\right)\) and the entropic \(\left(-T \Delta S^{\circ}\right)\) contributions to \(\Delta G^{\circ}\) for the ligand exchange reaction. Explain the relative magnitudes. (c) Based on information in this exercise and in the "A Closer Look" box on the chelate effect, predict the sign of \(\Delta H^{\circ}\) for the following hypothetical reaction: $$ \begin{aligned} \left[\mathrm{Cd}\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)_{4}\right]^{2+}(a q) &+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \\ \left[\mathrm{Cd}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(a q)+4 \mathrm{CH}_{3} \mathrm{NH}_{2}(a q) \end{aligned} $$
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