Intermolecular Forces: Liquids, Solids, and Phase Changes

One of the most important enzymes in the world— nitrogenase, the plant protein that catalyzes nitrogen fixation— contains active clusters of iron, sulfur, and molybdenum atoms. Crystalline molybdenum (Mo) has a body-centered cubic unit cell (d of Mo is $\mathbf{10}\mathbf{.}\mathbf{28}\mathbf{ }\mathbf{g}\mathbf{/}{\mathbf{cm}}^{\mathbf{3}}$).

(a) Determine the edge length of the unit cell.

(b) Calculate the atomic radius of Mo.

When tin is added to copper, the resulting alloy (bronze) is much harder than copper. Explain.

In the process of doping a semiconductor, certain impurities are added to increase its electrical conductivity. Explain this process for an n-type and a p-type semiconductor.

State two molecular characteristics of substances that typically form liquid crystals. How is each related to function?

Distinguish between isotropic and anisotropic substances. To which category do liquid crystals belong?

How are the properties of high-tech ceramics the same as those of traditional clay ceramics, and how are they different? Refer to specific substances in your answer.

Why is the average molar mass of a polymer sample different from the molar mass of an individual chain?

How does the random coil shape relate to the radius of gyration of a polymer chain?

What factor(s) influence the viscosity of a polymer solution? What factor(s) influence the viscosity of a molten polymer? What is a polymer glass?

Use an example to show how branching and crosslinking can affect the physical behaviour of a polymer.

The repeat unit in a polystyrene coffee cup has the formula ${\mathbf{C}}_6{\mathbf{H}}_5{\mathbf{CHCH}}_2$. If the molar mass of the polymer is $\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^5\mathbf{g}\mathbf{/}\mathbf{mole}$  g/mole, what is the degree of polymerization?

The monomer of poly (vinyl chloride) has the formula ${\mathbf{C}}_2{\mathbf{H}}_3\mathbf{Cl}$ . If there are 1565 repeat units in a single chain of the polymer, what is the molecular mass (in amu) of that chain?

The polypropylene ${\mathbf{CH}}_3{\mathbf{CHCH}}_2$  (repeat unit) in a plastic toy has a molar mass of  $\mathbf{2}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^5$ g/mole and a repeat unit length of 0.252 pm. calculate the radius of gyration.

The polymer that is used to make 2-L soda bottles [poly (ethylene terephthalate)] has a repeat unit with molecular formula  ${\mathbf{C}}_{10}{\mathbf{H}}_8{\mathbf{O}}_4$ and length 1.075 nm. Calculate the radius of gyration of a chain with molar mass of  $\mathbf{2}\mathbf{.}\mathbf{30}\mathbf{\times }{\mathbf{10}}^4$ g/mol.

In an experiment, 5.00 L of  ${\mathbf{N}}_2$  is saturated with water vapour at  $\mathbf{22}\mathbf{°}\mathbf{C}$  and then compressed to half its volume at constant T. 

(a) What is the partial pressure of  ${\mathbf{H}}_2\mathbf{O}$ in the compressed gas mixture? 

(b) What mass of water vapor condenses to liquid?

Barium is the largest nonradioactive alkaline earth metal. It has a body-centred cubic unit cell and a density of  $\mathbf{3}\mathbf{.}\mathbf{62}\mathbf{g}/{\mathbf{cm}}^3$ . What is the atomic radius of barium? (Volume of a sphere: $\mathbf{V}\mathbf{=}\frac{\mathbf{4}}{\mathbf{3}}{\mathbf{\pi r}}^3$ .)

Tantalum (Ta;d=$\mathbf{16}\mathbf{.}\mathbf{634}\mathbf{ }\mathbf{g}\mathbf{/}{\mathbf{cm}}^{\mathbf{3}}$ and $\mathbf{M}\mathbf{=}\mathbf{180}\mathbf{.}\mathbf{9479}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{mol}$) has a body-cantered cubic structure with a unit-cell edge length of 3.3058 Å. Use these data to calculate Avogadro’s number.

A 0.75-L bottle is cleaned, dried, and closed in a room where the air is${\mathbf{22}}^o\mathbf{C}$   and 44% relative humidity (that is, the water vapor in the air is 0.44 of the equilibrium vapor pressure at data-custom-editor="chemistry" ${\mathbf{22}}^o\mathbf{C}$ ). The bottle is brought outside and stored at. data-custom-editor="chemistry" $\mathbf{0}\mathbf{.}{\mathbf{0}}^o\mathbf{C}$

(a) What mass of liquid water condenses inside the bottle?

(b) Would liquid water condense at?data-custom-editor="chemistry" ${\mathbf{10}}^o\mathbf{C}$ (See Table 5.3, p. 207.)

Two important characteristics used to evaluate risks of fire or explosion are a compound’s lower flammable limit (LFL) and flash point. The LFL is the minimum percentage by volume in air that is ignitable. Below that, the mixture is too “lean” to burn. The flash point is the temperature at which the air over a confined liquid becomes ignitable. n-Hexane boils at  $\mathbf{68}\mathbf{.}{\mathbf{7}}^o\mathbf{C}$  at 1 atm. At  ${\mathbf{20}}^o\mathbf{C}$ , its vapour pressure is 121 mmHg. The LFL of n-hexane is 1.1%. Calculate the flash point of n-hexane.

Bismuth is used to calibrate instruments employed in high-pressure studies because it has several well-characterized crystalline phases. Its phase diagram (right) shows the liquid phase and five solid phases that are stable above 1 katm (1000 atm) and up to  $\mathbf{\text{300°C}}$ .

(a) Which solid phases are stable at  $\mathbf{\text{25°C}}$?

(b) Which phase is stable at 50 katm and $\mathbf{\text{175°C}}$ ?

(c) As the pressure is reduced from 100 to 1 katm at  $\mathbf{\text{200°C}}$, what phase transitions does bismuth undergo?

(d) What phases are present at each of the triple points?

In the photoelectric effect, the work function (Φ) is the minimum energy a photon must have to remove an electron from a metal surface (see Problem 7.70). For a given metal, Φ depends on how and where the photon strikes the crystal. Copper adopts the face-centered cubic structure. If the photon strikes perpendicular to the unit cell’s face, Φ is 4.59 eV; if perpendicular to a plane tangent to an edge, Φ is 4.48 eV; and if perpendicular to a plane tangent to a corner, Φ is 4.94 eV (1 eV =  $\mathbf{1}\mathbf{.}\mathbf{602}\mathbf{\times }{\mathbf{10}}^{-19}\mathbf{J}$). Find the wavelength (in nm) of the lowest energy photon that can remove an electron from copper, and state how it strikes the unit cell.

In making computer chips, a 4.00-kg cylindrical ingot of ultrapure n-type doped silicon that is 5.20 inches in diameter is sliced into wafers $\mathbf{1}\mathbf{.}\mathbf{12}\mathbf{\times }{\mathbf{10}}^{-4}$ m thick. 

(a) Assuming no waste, how many wafers can be made? 

(b) What is the mass of a wafer (d of Si = $\mathbf{2}\mathbf{.}\mathbf{34}\mathbf{g}\mathbf{/}{\mathbf{cm}}^3$ ; V of a cylinder = ${\mathbf{\pi r}}^2\mathbf{h}$ )?

(c) A key step in making p-n junctions for the chip is the chemical removal of the oxide layer on the wafer through treatment with gaseous HF. Write a balanced equation for this reaction. 

(d) If 0.750% of the Si atoms are removed during the treatment in part (c), how many moles of HF is required per wafer, assuming 100% reaction yield?

Methyl salicylate, ${\mathbf{C}}_8{\mathbf{H}}_8{\mathbf{O}}_3$, the odorous constituent of oil of wintergreen, has a vapor pressure of 1.00 torr at  $\mathbf{54}\mathbf{.}{\mathbf{3}}^o\mathbf{C}$  and 10.0 torr at  $\mathbf{95}\mathbf{.}{\mathbf{3}}^o\mathbf{C}$ . 

(a) What is its vapor pressure at ${\mathbf{25}}^o\mathbf{C}$ ? 

(b) What is the minimum number of liters of air that must pass over a sample of the compound at ${\mathbf{25}}^o\mathbf{C}$ to vaporize 1.0 mg of it?

Mercury (Hg) vapor is toxic and readily absorbed from the lungs. At  $\mathbf{20}\mathbf{°}\mathbf{C}$, mercury ( $\mathbf{\Delta Hvap}$ = 59.1 kJ/mol) has a vapor pressure of  $\mathbf{1}\mathbf{.}\mathbf{20}\mathbf{\times }{\mathbf{10}}^{-3}\mathbf{torr}$, which is high enough to be hazardous. To reduce the danger to workers in processing plants, Hg is cooled to lower its vapor pressure. At what temperature would the vapor pressure of Hg be at the safer level of  $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{-5}\mathbf{torr}$?

Polytetrafluoroethylene (Teflon) has a repeat unit with the formula ${\mathbf{F}}_2\mathbf{C}\mathbf{—}{\mathbf{CF}}_2$ . A sample of the polymer consists of fractions with the following distribution of chains:

(a) Determine the molar mass of each fraction. 

(b) Determine the number-average molar mass of the sample. 

(c) Another type of average molar mass of a polymer sample is called the weight-average molar mass: 

 ${\mathbf{\chi }}_w\mathbf{=}\frac{\mathbf{\pi }\mathbf{ }\mathbf{(}\mathbf{\chi }\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{fraction}\mathbf{ }\mathbf{\times }\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{fraction}\mathbf{)}}{\mathrm{total} \mathrm{mass} \mathrm{of} \mathrm{all} \mathrm{fractions}}$

Calculate the weight-average molar mass of the above sample.

A greenhouse contains  $\mathbf{256}{\mathbf{m}}^3$ of air at a temperature of  $\mathbf{26}\mathbf{°}\mathbf{C}$, and a humidifier in it vaporizes 4.20 L of water. 

(a) What is the pressure of water vapor in the greenhouse, assuming that none escapes and that the air was originally completely dry (d of  ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$ = 1.00 g/mL)? 

(b) What total volume of liquid water would have to be vaporized to saturate the air (i.e., achieve $\mathbf{100}\mathbf{\%}$   relative humidity)? (See Table 5.4, p. 221.)

Like most transition metals, tantalum (Ta) exhibits several oxidation states. Give the formula of each tantalum compound whose unit cell is depicted below:

a.

b.

Iron crystallizes in a body-centered cubic structure. The volume of one Fe atom is $\mathbf{8}\mathbf{.}\mathbf{38}\mathbf{\times }{\mathbf{10}}^{-24}{\mathbf{cm}}^3$, and the density of Fe is  $\mathbf{7}\mathbf{.}\mathbf{874}{\mathbf{gcm}}^{-3}$ . Find an approximate value for Avogadro’s number.

Corn is a valuable source of industrial chemicals. For example, furfural is prepared from corncobs. It is an important solvent in synthetic rubber manufacturing, and it is reduced to furfuryl alcohol, which is used to make polymer resins. Furfural can also be oxidized to 2-furoic acid. furfuryl alcohol furfural 2-furoic acid.

a) Which of these compounds can form H bonds? Draw structures in each case.

b) The molecules of some substances can form an “internal” H bond, that is, an H bond within a molecule. This takes the form of a polygon with atoms as corners and bonds as sides and an H bond as one of the sides. Which of these molecules is (are) likely to form a stable internal H bond? Draw the structure.(Hint: Structures with 5 or 6 atoms as corners are most stable.)

Question: On a humid day in New Orleans, the temperature is  , and the partial pressure of water vapor in the air is 31.0 torr. The 9000-ton air-conditioning system in the Louisiana Superdome maintains an inside air temperature of  also, but a partial pressure of water vapor of 10.0 torr. The volume of air in the dome is  , and the total pressure inside and outside the dome are both 1.0 atm.

(Hint: How many moles of gas are in the dome? How many moles of water vapor? How many moles of dry air? How many moles of outside air must be added to the air in the dome to simulate the composition of outside air?)

Question: Diamond has a face-centered cubic unit cell, with four more C atoms in tetrahedral holes within the cell. Densities of diamonds vary from   to   because C atoms are missing from some holes.

1. Calculate the unit-cell edge length of the densest diamond.
2. Assuming the cell dimensions are fixed, how many C atoms are in the unit cell of the diamond with the lowest density?

Question: A 4.7-L sealed bottle containing 0.33 g of liquid ethanol, ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}\mathbf{O}$, is placed in a refrigerator and reaches equilibrium with its vapor at 11⁰C .

(a) What mass of ethanol is present in the vapor? 

(b) When the container is removed and warmed to room temperature, 20⁰C, will all the ethanol vaporize? 

(c) How much liquid ethanol would be present at -2.3⁰C? The vapor pressure of ethanol is 10. torr at  2.3⁰C and 40. torr at 19⁰C .

The boiling point of amphetamine, ${\mathbf{C}}_9{\mathbf{H}}_{13}\mathbf{N}$, is   ${\mathbf{201}}^o\mathbf{C}$at 760torr and ${\mathbf{83}}^o\mathbf{C}$   at 13torr. What is the concentration (in$\mathbf{g}\mathbf{/}{\mathbf{m}}^3$) of amphetamine when it is in contact with ${\mathbf{20}}^o\mathbf{C}$ air?

KF has the same type of crystal structure as NaCl. The unit cell of KF has an edge length of 5.39 $\stackrel{\mathbf{°}}{\mathbf{A}}$. Find the density of KF.

The crystal structure of sodium is based on the body-centered cubic unit cell. What is the mass of one unit cell of Na?

The ball-and-stick models below represent three compounds with the same molecular formula ${\mathbf{C}}_{\mathbf{4}}{\mathbf{H}}_{\mathbf{8}}{\mathbf{O}}_{\mathbf{2}}$:

(a) Which compound(s) can form intermolecular H-bonds? 

(b) Which has the highest viscosity?

An aerospace manufacturer is building a prototype experimental aircraft that cannot be detected by radar. Boron nitride is chosen for incorporation into the body parts, and the boric acid/ammonia method is used to prepare the ceramic material. Given 85.5% and 86.8% yields for the two reaction steps, how much boron nitride can be prepared from 1.00 metric ton of boric acid and $\mathbf{12}\mathbf{.}\mathbf{5}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}$ of ammonia at 275 K and $\mathbf{3}\mathbf{.}\mathbf{07}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{\text{ kPa}}$ ? Assume that ammonia does not behave ideally under these conditions and is recycled completely in the reaction process.

Question: Silicon and germanium are both semiconducting elements from group 4A (14) that can be doped to improve their conductivity. Would each of the following form an n- type or a p-type semiconductor:

a. Ge doped with As

b. Si doped with B

Question: Silicon and germanium are both semiconducting elements from group 4A (14) that can be doped to improve their conductivity. Would each of the following form an n- type or a p-type semiconductor: 

1. Ge doped with P
2. Si doped with ln? 

Question: One way to purify gaseous H₂ is to pass it under high pressure through the holes of a metal’s crystals structure. Palladium, which adopts a cubic closest packed structure, absorbs H₂ than any other element and is one of the metals currently used for this purpose. Although the metal-hydrogen interaction is unclear, it is estimated that the density of absorbed H₂approaches that of liquid hydrogen (70.8g/L). what volume (in L) of gaseous H₂ measured at STP, can be packed into the spaces of of palladium metal? 

Question: Is it possible for a salt of formula AB₃ to have a face-centered cubic unit cell of anions with cations in all the eight available holes? Explain