Chapter 7

Consider the stable elements through lead (Z = 82). In how many instances are the atomic weights of the elements out of order relative to the atomic numbers of the elements?

(a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the 3$s$ and 3p valence electrons in P? (b) Repeat these calculations using Slater's rules. (c) Detailed calculations indicate that the effective nuclear charge is $5.6+$ for the 3$s$ electrons and $4.9+$ for the 3$p$ electrons. Why are the values for the 3$s$ and 3$p$ electrons different? (d) If you remove a single electron from a Patom,which orbital will it come from?

As we move across a period of the periodic table, why do the sizes of the transition elements change more gradually than those of the representative elements?

In Table 7.8 , the bonding atomic radius of neon is listed as 0.58 A, whereas that for xenon is listed as 1.40 A. A classmate of yours states that the value for Xe is more realistic than the one for Ne. Is she correct? If so, what is the basis for her statement?

The As$-$As bond length in elemental arsenic is 2.48 A. The $\mathrm{Cl}-\mathrm{Cl}$ bond length in ${\mathrm{Cl}}_2$ is 1.99 A. (a) Based on these data, what is the predicted $\mathrm{As}-\mathrm{Cl}$ bond length in arsenic trichloride, $AsC{l}_3,$ in which each of the three Cl atoms is bonded to the As atom? (b) What bond length is predicted for $AsC{l}_3,$ , using the atomic radii in Figure 7.7?

The following observations are made about two hypothetical elements $A$ and $B:$ The $A-A$ and $B-B$ bond lengths in the elemental forms of $A$ and $B$ are 2.36 and $1.94\hat{A},$ respectively. A and $\mathrm{B}$ react to form the binary compound ${\mathrm{AB}}_2,$ which has a linear structure (that is $\mathrm{\angle }\mathrm{B}-\mathrm{A}-\mathrm{B}={180}^{\circ }).$ Based on these statements, predict the separation between the two B nuclei in a molecule of ${\mathrm{AB}}_2$ .

Elements in group 7A in the periodic table are called the halogens; elements in group 6A are called the chalcogens. (a) What is the most common oxidation state of the chalcogens compared to the halogens? (b) For each of the following periodic properties, state whether the halogens or the chalcogens have larger values: atomic radii, ionic radii of the most common oxidation state, first ionization energy, second ionization energy.

Note from the following table that there is a significant increase in atomic radius upon moving from Y to La, whereas the radii of $Zr$ to Hf are the same. Suggest an explanation for this effect.

(a) Which ion is smaller, ${\mathrm{Co}}^{3+}$ or ${\mathrm{Co}}^{4+}?(\mathbf{b})$ In a lithium-ion battery that is discharging to power a device, for every ${\mathrm{Li}}^{+}$ that inserts into the lithium cobalt oxide electrode, a ${\mathrm{Co}}^{4+}$ ion must be reduced to a ${\mathrm{Co}}^{3+}$ ion to balance charge. Using the CRC Handbook of Chemistry and Physics or other standard reference, find the ionic radii of ${\mathrm{Li}}^{+},{\mathrm{Co}}^{3+},$ and ${\mathrm{Co}}^{4+}.$ Order these ions from smallest to largest. (c) Will the lithium cobalt oxide cathode expand or contract as lithium ions are inserted? (d) Lithium is not nearly as abundant as sodium. If sodium ion batteries were developed that function in the same manner as lithium ion batteries, do you think "sodium cobalt oxide" would still work as the electrode material? Explain. (e) If you don’t think cobalt would work as the redox-active partner ion in the sodium version of the electrode, suggest an alternative metal ion and explain your reasoning.

In the chemical process called electron transfer, an electron is transferred from one atom or molecule to another. (We will talk about electron transfer extensively in Chapter 20.) A simple electron transfer reaction is $$\mathrm{A}(g)+\mathrm{A}(g)⟶{\mathrm{A}}^{+}(g)+{\mathrm{A}}^{-}(g)$$ In terms of the ionization energy and electron afnity of atom A, what is the energy change for this reaction? For a representative nonmetal such as chlorine, is this process exothermic? For a representative metal such as sodium, is this process exothermic?