Chemistry & Chemical Reactivity

John C Kotz, Paul M. Treichel; John Townsend, David Treichel

Chapter 12

The Solid State - all with Video Answers

Educators

Chapter Questions

Problem 1

Outline a two-dimensional unit cell for the pattern shown here. If the black squares are labeled A and the white squares are $B$, what is the simplest formula for a "compound" based on this pattern?
FIGURE CAN'T COPY.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 2

Outline a two-dimensional unit cell for the pattern shown here. If the black squares are labeled A and the white squares are B, what is the simplest formula for a "compound" based on this pattern?
FIGURE CAN'T COPY.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 3

A portion of the crystalline lattice for potassium is illustrated below.
(a) In what type of unit cell are the K atoms arranged?
FIGURE CAN'T COPY.
(b) If one edge of the potassium unit cell is 533 pm , what is the density of potassium?

G Macdonald

Numerade Educator

Problem 4

The unit cell of silicon carbide, SiC , is illustrated below.
(a) In what type of unit cell are the (dark gray) C atoms arranged?
(b) If one edge of the silicon carbide unit cell is 436.0 pm , what is the calculated density of this compound?

G Macdonald

Numerade Educator

Problem 5

One way of viewing the unit cell of perovskite was illustrated in Example 12.2. Another way is shown here. Prove that this view also leads to a formula of $\mathrm{CaTiO}_3$.

Catherine Lemar

Catherine Lemar

Numerade Educator

Problem 6

Rutile, $\mathrm{TiO}_2$, crystallizes in a structure characteristic of many other ionic compounds. How many formula units of $\mathrm{TiO}_2$ are in the unit cell illustrated here? (The oxide ions marked by an $x$ are wholly within the cell; the others are in the cell faces.)

G Macdonald

Numerade Educator

Problem 7

Cuprite is a semiconductor. Oxide ions are at the cube corners and in the cube center. Copper ions are wholly within the unit cell.
(a) What is the formula of cuprite?
(b) What is the oxidation number of copper?

G Macdonald

Numerade Educator

Problem 8

The mineral fluorite, which is composed of calcium ions and fluoride ions, has the unit cell shown here.
(a) What type of unit cell is described by the $\mathrm{Ca}^{2+}$ ions?
(b) Where are the $\mathrm{F}^{-}$ions located, in octahedral holes or tetrahedral holes?
(c) Based on this unit cell, what is the formula of fluorite?

G Macdonald

Numerade Educator

Problem 9

Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is $1.54 \mathrm{~g} / \mathrm{cm}^3$. What is the radius of a calcium atom?

G Macdonald

Numerade Educator

Problem 10

The density of copper metal is $8.95 \mathrm{~g} / \mathrm{cm}^3$. If the radius of a copper atom is 127.8 pm , is the copper unit cell primitive, body-centered cubic, or facecentered cubic?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 11

Potassium iodide has a face-centered cubic unit cell of iodide ions with potassium ions in octahedral holes. The density of KI is $3.12 \mathrm{~g} / \mathrm{cm}^3$. What is the length of one side of the unit cell? (Ion sizes are found in Figure 7.11.)

Eileen Sullivan

Eileen Sullivan

Numerade Educator

Problem 12

A A unit cell of cesium chloride is illustrated in Figure 12.8. The density of the solid is $3.99 \mathrm{~g} / \mathrm{cm}^3$, and the radius of the $\mathrm{Cl}^{-}$ion is 181 pm . Calculate the radius of the $\mathrm{Cs}^{+}$ion in the center of the cell. (Assume that the $\mathrm{Cs}^{+}$ion touches all of the corner $\mathrm{Cl}^{-}$ions.)

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 13

Predict the trend in lattice energy, from least negative to most negative, for the following compounds based on the ion charges and ionic radii: Lil, LiF, $\mathrm{CaO}, \mathrm{RbI}$.

G Macdonald

Numerade Educator

Problem 14

Examine the trends in lattice energy in Table 12.1. The value of the lattice energy becomes somewhat more negative on going from NaI to NaBr to NaCl , and all are in the range from -700 to $-800 \mathrm{~kJ} / \mathrm{mol}$. Suggest a reason for the observation that the lattice energy of NaF ( $\left.\Delta_{\text {Iatrice }} U=-926 \mathrm{~kJ} / \mathrm{mol}\right)$ is much more negative than those of the other sodium halides.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 15

To melt an ionic solid, energy must be supplied to disrupt the forces between ions so the regular array of ions collapses. Predict (and explain) how the melting point is expected to vary as a function of the distance between cation and anion.

Kathleen Pankow

Kathleen Pankow

Numerade Educator

Problem 16

Which compound in each of the following pairs should have the higher melting point? Explain briefly.
(a) NaCl or RbCl
(b) BaO or MgO
(c) NaCl or MgS

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 17

Calculate the molar enthalpy of formation, $\Delta_f H^{\circ}$, of solid lithium fluoride from the lattice energy (Table 12.1) and other thermochemical data. The enthalpy of formation of $\mathrm{Li}(\mathrm{g}), \Delta_f H^{\circ}[\mathrm{Li}(\mathrm{g})]=$ $159.37 \mathrm{~kJ} / \mathrm{mol}$. Other required data can be found in Appendices F and L.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 18

Calculate the lattice enthalpy for RbCl . In addition to data in Appendices F and L, you will need the following information:

$$
\begin{gathered}
\Delta_\mu H^{\circ}[\mathrm{Rb}(\mathrm{~g})]=80.9 \mathrm{~kJ} / \mathrm{mol} \\
\Delta_\mu H^{\circ}[\mathrm{RbCl}(\mathrm{~s})]=-435.4 \mathrm{~kJ} / \mathrm{mol}
\end{gathered}
$$

Ayushi Sambyal

Numerade Educator

Problem 19

Considering only the molecular orbitals formed by combinations of the $2 s$ atomic orbitals, how many molecular orbitals can be formed by 1000 Li atoms? In the lowest energy state, how many of these orbitals will be populated by pairs of electrons and how many will be empty?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 20

How many molecular orbitals will be formed by combination of the 3 s and $3 p$ atomic orbitals in 1.0 mol of Mg atoms? At 0 K , what fraction of these orbitals will be occupied by electron pairs?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 21

Conduction of an electric current is a general property associated with metals. How does the band theory for metallic bonding explain conductivity?

Jorge Villanueva

Jorge Villanueva

Numerade Educator

Problem 22

Most metals are shiny, that is, they reflect light. How does the band theory for metals explain this characteristic?

Averell Hause

Carnegie Mellon University

Problem 23

Elemental silicon and carbon (in the diamond allotropic form) have the same solid-state structure. However, diamond is an insulator and silicon is a semiconductor. Explain why there is a difference.

Narayan Hari

Numerade Educator

Problem 24

List the Group 4A elements in order of the size of the band gap.

Wilson Ma

The University of Alabama

Problem 25

Define the terms intrinsic semiconductor and extrinsic semiconductor. Give an example of each.

Ameer Said

Numerade Educator

Problem 26

Is aluminum-doped silicon a $p$-type or an $n$-type semiconductor? Explain how conductivity occurs in this semiconductor.

Ronald Prasad

Numerade Educator

Problem 27

Which of the following allotropes of carbon is not a network solid?
(a) graphite
(c) buckyballs ( $\mathrm{C}_{60}$ )
(b) diamond
(d) graphene

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 28

A soft, white waxy solid melts over a temperature range from $120{ }^{\circ} \mathrm{C}$ to $130^{\circ} \mathrm{C}$. It doesn't dissolve in water and it doesn't conduct electricity. These properties are consistent with its identity as
(a) a network solid
(c) an amorphous solid
(b) an ionic solid
(d) a metallic solid

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 29

A diamond unit cell is shown here.
(a) How many carbon atoms are in one unit cell?
(b) The unit cell can be considered as a cubic unit cell of C atoms with other C atoms in holes in the lattice. What type of unit cell is this ( $p c$, $\mathrm{bcc}, \mathrm{fcc}$ )? In what holes are other C atoms located, octahedral or tetrahedral holes?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 30

The structure of graphite is given in Figure 12.19.
(a) What type of intermolecular forces exist between the layers of six-member carbon rings?
(b) Account for the lubricating ability of graphite. That is, why does graphite feel slippery? Why does pencil lead (which is really graphite in clay) leave black marks on paper?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 31

We have identified six types of solids (metallic, ionic, molecular, network, amorphous, alloys). What particles make up each of these solids and what are the forces of attraction between these particles?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 32

List the general properties of each type of solid.

Tianyu Li

Numerade Educator

Problem 33

Classify each of the following materials as falling into one of the categories listed in Table 12.2. What particles make up these solids and what are the forces of attraction between particles? Give one physical property of each.
(a) gallium arsenide
(b) polystyrene
(c) silicon carbide
(d) perovskite, $\mathrm{CaTiO}_3$

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 34

Classify each of the following materials as falling into one of the categories listed in Table 12.2. What particles make up these solids, and what are the forces of attraction between particles? Give one physical property of each.
(a) Si doped with P
(b) graphite
(c) benzoic acid, $\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}_2 \mathrm{H}$
(d) $\mathrm{Na}_2 \mathrm{SO}_4$

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 35

Benzene, $\mathrm{C}_6 \mathrm{H}_6$, is an organic liquid that freezes at $5.5^{\circ} \mathrm{C}$ (Figure 11.1) to form beautiful, feather-like crystals. How much energy is evolved as heat when 15.5 g of benzene freezes at $5.5^{\circ} \mathrm{C}$ ? (The enthalpy of fusion of benzene is $9.95 \mathrm{~kJ} / \mathrm{mol}$.) If the $15.5-\mathrm{g}$ sample is remelted, again at $5.5^{\circ} \mathrm{C}$, what quantity of energy is required to convert it to a liquid?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 36

The specific heat capacity of silver is $0.235 \mathrm{~J} / \mathrm{g} \cdot \mathrm{K}$. Its melting point is $962^{\circ} \mathrm{C}$, and its enthalpy of fusion is $11.3 \mathrm{~kJ} / \mathrm{mol}$. What quantity of energy, in joules, is required to change 5.00 g of silver from a solid at $25^{\circ} \mathrm{C}$ to a liquid at $962^{\circ} \mathrm{C}$ ?

Nicholas Mogoi

Numerade Educator

Problem 37

Consider the phase diagram of $\mathrm{CO}_2$ in Figure 12.28.
(a) Is the density of liquid $\mathrm{CO}_2$ greater or less than that of solid $\mathrm{CO}_2$ ?
(b) In what phase do you find $\mathrm{CO}_2$ at 5 atm and $0^{\circ} \mathrm{C}$ ?
(c) Can $\mathrm{CO}_2$ be liquefied at $45^{\circ} \mathrm{C}$ ?

Catherine Lemar

Catherine Lemar

Numerade Educator

Problem 38

Use the phase diagram given here to answer the following questions:
(a) In what phase is the substance found at room temperature and 1.0 atm pressure?
(b) If the pressure exerted on a sample is 0.75 atm and the temperature is $-114^{\circ} \mathrm{C}$, in what phase does the substance exist?
(c) If you measure the vapor pressure of a liquid sample and find it to be 380 mm Hg , what is the temperature of the liquid phase?
(d) What is the vapor pressure of the solid at $-122{ }^{\circ} \mathrm{C}$ ?
(e) Which is the denser phase-solid or liquid? Explain briefly.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 39

Liquid ammonia, $\mathrm{NH}_3(\ell)$, was once used in home refrigerators as the heat transfer fluid. The specific heat capacity of the liquid is $4.7 \mathrm{I} / \mathrm{g} \cdot \mathrm{K}$ and that of the vapor is $2.2 \mathrm{I} / \mathrm{g} \cdot \mathrm{K}$. The enthalpy of vaporization is $23.33 \mathrm{~kJ} / \mathrm{mol}$ at the boiling point. If you heat 12 kg of liquid ammonia from $-50.0^{\circ} \mathrm{C}$ to its boiling point of $=33.3^{\circ} \mathrm{C}$, allow it to evaporate, and then continue warming to $0.0^{\circ} \mathrm{C}$, how much energy must you supply?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 40

If your air conditioner is more than several years old, it may use the chlorofluorocarbon $\mathrm{CCl}_2 \mathrm{~F}_2$ as the heat transfer fluid. The normal boiling point of $\mathrm{CCl}_2 \mathrm{~F}_2$ is $-29.8^{\circ} \mathrm{C}$, and the enthalpy of vaporization is $20.11 \mathrm{~kJ} / \mathrm{mol}$. The gas and the liquid have molar heat capacities of $117.2 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$ and $72.3 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$, respectively. How much energy is evolved as heat when 20.0 g of $\mathrm{CCl}_2 \mathrm{~F}_2$ is cooled from $+40^{\circ} \mathrm{C}$ to $-40^{\circ} \mathrm{C}$ ?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 41

Sketch a phase diagram for $\mathrm{O}_2$ from the following information: normal boiling point, 90.18 K ; normal melting point, 54.8 K ; and triple point, 54.34 K at a pressure of 2 mm Hg . Very roughly estimate the vapor pressure of liquid $\mathrm{O}_2$ at $-196^{\circ} \mathrm{C}$, the lowest temperature easily reached in the laboratory. Is the density of liquid $\mathrm{O}_2$ greater or less than that of solid $\mathrm{O}_2$ ?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 42

A Tungsten crystallizes in the unit cell shown here.
(a) What type of unit cell is this?
(b) How many tungsten atoms occur per unit cell?
(c) If the edge of the unit cell is 316.5 pm , what is the radius of a tungsten atom?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 43

Silver crystallizes in a face-centered cubic unit cell. Each side of the unit cell has a length of 409 pm . What is the radius of a silver atom?

Catherine Lemar

Catherine Lemar

Numerade Educator

Problem 44

The unit cell shown here is for calcium carbide. How many calcium atoms and how many carbon atoms are in each unit cell? What is the formula of calcium carbide? (Calcium ions are silver in color and carbon atoms are gray.)

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 45

The very dense metal inidium has a face-centered cubic unit cell and a density of $22.56 \mathrm{~g} / \mathrm{cm}^3$. Use this information to calculate the radius of an atom of the element.

Kevin Zaborsky

Numerade Educator

Problem 46

Vanadium metal has a density of $6.11 \mathrm{~g} / \mathrm{cm}^3$. Assuming the vanadium atomic radius is 132 pm , is the vanadium unit cell primitive cubic, bodycentered cubic, or face-centered cubic?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 47

Calcium fluoride is the well-known mineral fluorite. Each unit cell contains four $\mathrm{Ca}^{2+}$ ions and eight $\mathrm{F}^{-}$ions. The $\mathrm{F}^{-}$ions fill all the tetrahedral holes in a face-centered cubic lattice of $\mathrm{Ca}^{2+}$ ions. The edge of the $\mathrm{CaF}_2$ unit cell is $5.46295 \times 10^{-8} \mathrm{~cm}$ in length. The density of the solid is $3.1805 \mathrm{~g} / \mathrm{cm}^3$. Use this information to calculate Avogadro's number.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 48

Iron has a body-centered cubic unit cell with a cell dimension of 286.65 pm . The density of iron is $7.874 \mathrm{~g} / \mathrm{cm}^3$. Use this information to calculate Avogadro's number.

Nicholas Mogoi

Numerade Educator

Problem 49

You can get some idea of how efficiently spherical atoms or ions are packed in a three-dimensional solid by seeing how well circular atoms pack in two dimensions. Using the drawings shown here, prove that B is a more efficient way to pack circular atoms than A . The unit cell of A contains portions of four circles and one hole. In B, packing coverage can be calculated by looking at a triangle that contains portions of three circles and one hole. Show that A fills about $80 \%$ of the available space, whereas B fills closer to $90 \%$ of the available space.

Nicole Smina

Numerade Educator

Problem 50

Consider the three types of cubic units cells.
(a) Assuming that the spherical atoms or ions in a primitive cubic unit cell just touch along the cube's edges, calculate the percentage of occupied space within the unit cell. (Recall that the volume of a sphere is $(4 / 3) \pi r^3$, where $r$ is the radius of the sphere.)
(b) Compare the percentage of occupied space in the primitive cell (pc) with the bcc and fcc unit cells. Based on this, will a metal in these three forms have the same or different densities? If different, in which is it most dense? In which is it least dense?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 51

The solid-state structure of silicon is shown below.
(a) Describe this crystal as pc , bcc, or foc.
(b) What type of holes are occupied in the lattice?
(c) How many Si atoms are there per unit cell?
(d) Calculate the density of silicon in $\mathrm{g} / \mathrm{cm}^3$ (given that the cube edge has a length of 543.1 pm ).
(e) $\Delta$ Estimate the radius of the silicon atom. (Note: The Si atoms on the edges do not touch one another.)

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 52

The solid-state structure of silicon carbide is shown below.
(a) How many atoms of each type are contained within the unit cell? What is the formulas of silicon carbide?
(b) $\Delta$ Knowing that the $\mathrm{Si}-\mathrm{C}$ bond length is 188.8 pm (and the $\mathrm{Si}-\mathrm{C}-\mathrm{Si}$ bond angle is $109.5^{\circ}$ ), calculate the density of SiC.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 53

Spinels are solids with the general formula $\mathrm{AB}_2 \mathrm{O}_4$ (where $\mathrm{A}^{2+}$ and $\mathrm{B}^{3+}$ are metal cations of the same or different metals). The best-known example is common magnetite, $\mathrm{Fe}_3 \mathrm{O}_4$ [which you can formulate as $\left.\left(\mathrm{Fe}^{2+}\right)\left(\mathrm{Fe}^{3+}\right)_2 \mathrm{O}_4\right]$. Another example is the mineral often referred to as spinel, $\mathrm{MgAl}_2 \mathrm{O}_4$.
The oxide ions of spinels form a face-centered cubic lattice. In a normal spinel, cations occupy $1 / 8$ of the tetrahedral sites and $1 / 2$ of the octahedral sites.
(a) In $\mathrm{MgAl}_2 \mathrm{O}_4$, in what types of holes are the magnesium and aluminum ions found?
(b) The mineral chromite has the formula $\mathrm{FeCr}_2 \mathrm{O}_4$. What ions are involved, and in what types of holes are they found?

Ayushi Sambyal

Numerade Educator

Problem 54

Using the thermochemical data below and an estimated value of $-2481 \mathrm{~kJ} / \mathrm{mol}$ for the lattice energy for $\mathrm{Na}_2 \mathrm{O}$, calculate the value for the second electron affinity of oxygen $\left[\mathrm{O}^{-}(\mathrm{g})+\mathrm{e}^{-} \rightarrow \mathrm{O}^{2-}(\mathrm{g})\right]$.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 55

The band gap in gallium arsenide is $140 \mathrm{~kJ} / \mathrm{mol}$. What is the maximum wavelength of light needed to excite an electron to move from the valence band to the conduction band?

Chai Santi

Numerade Educator

Problem 56

The conductivity of an intrinsic semiconductor increases with increasing temperature. How can this be rationalized?

David Collins

Numerade Educator

Problem 57

Which will show the highest conductivity at 298 K , silicon or germanium?

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 58

Identify the following as either p-or $n$-type semiconductors.
(a) germanium doped with arsenic
(b) silicon doped with phosphorus
(c) germanium doped with indium
(d) germanium doped with antimony

Matthew Bamidele

Matthew Bamidele

Numerade Educator

Problem 59

Diamond-based semiconductors are currently of enormous interest in the research community. Although diamond itself is an insulator, the addition of a dopant will narrow the band gap. One semiconductor system has diamond with boron as a dopant. Is this a $p$ - or an $n$-type semiconductor?

David Collins

Numerade Educator

Problem 60

Molecular solids, network solids, and amorphous solids all contain atoms that are joined together by covalent bonds. However, these classes of compounds are very different in overall structure, and this leads to different physical properties associated with each group. Describe how the overall structures of these classes of solids differ from each other.

Matthew Hurlock

Matthew Hurlock

Numerade Educator

Problem 61

Like ZnS , lead(II) sulfide, PbS (commonly called galena), has a $1: 1$ empirical formula with a $2+$ cation combined with the sulfide anion.
Does PbS have the same solid structure as ZnS ? If different, how are they different? How is the unit cell of PbS related to its formula?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 62

$\mathrm{CaTiO}_3$, a perovskite, has the structure below.
(a) If the density of the solid is $4.10 \mathrm{~g} / \mathrm{cm}^3$, what is the length of a side of the unit cell?
(b) Calculate the radius of the $\mathrm{Ti}^{4+}$ ion in the center of the unit cell. How well does your calculation agree with a literature value of 75 pm ?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 63

Potassium bromide has the same lattice structure as NaCl . Given the ionic radii of $\mathrm{K}^{+}(133 \mathrm{pm})$ and $\mathrm{Br}^{-}(196 \mathrm{pm})$, calculate the density of KBr .

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 64

Calculate the lattice energy of $\mathrm{CaCl}_2$ using a BornHaber cycle and data from Appendices F and L and Table 7.5.

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 65

A. Boron phosphide, BP , is a semiconductor and a hard, abrasion-resistant material. It is made by reacting boron tribromide and phosphorus tribromide in a hydrogen atmosphere at high temperature ( $>750{ }^{\circ} \mathrm{C}$ ).
(a) Write a balanced chemical equation for the synthesis of BP.
(b) Boron phosphide crystallizes in a zinc-blend structure, formed from boron atoms in a facecentered cubic lattice and phosphorus atoms in tetrahedral holes. How many tetrahedral holes are filled with P atoms in each unit cell?
(c) The length of a unit cell of BP is 478 pm . What is the density of the solid in $\mathrm{g} / \mathrm{cm}^3$ ?
(d) Calculate the closest distance between a B and a P atom in the unit cell. (Assume the B atoms do not touch along the cell edge. The B atoms in the faces touch the B atoms at the comers of the unit cell.)

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 66

Why is it not possible for a salt with the formula $\mathrm{M}_3 \mathrm{X}\left(\mathrm{Na}_3 \mathrm{PO}_4\right.$, for example) to have a facecentered cubic lattice of $X$ anions with $M$ cations in octahedral holes?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 67

A Two identical swimming pools are filled with uniform spheres of ice packed as closely as possible. The spheres in the first pool are the size of grains of sand; those in the second pool are the size of oranges. The ice in both pools melts. In which pool, if either, will the water level be higher? (Ignore any differences in filling space at the planes next to the walls and bottom.)

Kristela Garcia

Kristela Garcia

Numerade Educator

Problem 68

Spinels are described in Study Question 53. Consider two normal spinels, $\mathrm{CoAl}_2 \mathrm{O}_4$ and $\mathrm{SnCo}_2 \mathrm{O}_4$. What metal ions are involved in each? What are their electron configurations? Are the metal ions paramagnetic, and if so how many unpaired electrons are involved?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 69

Outline a procedure to calculate the percent of space occupied by the atoms in an foc arrangement.

Muhammad Bin

Numerade Educator

Problem 70

The sample of nephrite jade shown on page 545 has the formula $\left.\mathrm{Ca}_2\left(\mathrm{Mg}, \mathrm{Fe}_5\right)_{\left(\mathrm{Si}_4 \mathrm{O}_{11}\right.}\right)_2(\mathrm{OH})_2$ - (Iron in this formula is in the +2 oxidation state.)
(a) What is the charge on the $\left(\mathrm{Si}_4 \mathrm{O}_{11}\right)^{\mathrm{n}-}$ ion in this compound?
(b) What is the oxidation state of Si in this compound?
(c) What is the percent of iron in a sample of jade that has the formula $\mathrm{Ca}_2\left(\mathrm{Mg}_{0.35} \mathrm{Fe}_{0.65}\right)_5\left(\mathrm{Si}_4 \mathrm{O}_{11}\right)_2$ $(\mathrm{OH})_2$ ?
(d) The iron ions in the formula for nephrite have the same degree of paramagnetism as seen for $\mathrm{Fe}^{2+}(\mathrm{g})$. How many unpaired electrons per iron ion does this represent?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 71

Phase diagrams for materials that have allotropes can be more complicated than those shown in the chapter. Use the phase diagram for carbon given here to answer the following questions.
(a) How many triple points are present and what phases are in equilibrium for each?
(b) Is there a single point where all four phases are in equilibrium?
(c) Which is more stable at high pressures, diamond or graphite?
(d) Which is the stable phase of carbon at room temperature and 1 atmosphere pressure?

Carlene Jimenez

Carlene Jimenez

Numerade Educator

Problem 72

Prepare a graph of lattice enthalpy for lithium, sodium, and potassium halides (Table 12.1) vs. the sum of the ionic radii for the component ions (Figure 7.11). Evaluate the results and comment on the relationship between these quantities.

Carlene Jimenez

Carlene Jimenez

Numerade Educator