\( \require{cancel} \) \( \newcommand{\xrightleftharpoons}[2]{\overset{#1}{\underset{#2}{\rightleftharpoons}}} \) \( \newcommand{\conc}[1]{\left[\mathrm{#1}\right]} \) \( \newcommand{\chem}[1]{\mathrm{#1}} \) \( \definecolor{green}{RGB}{0,128,0} \) \( \definecolor{blue}{RGB}{0,0,255} \)

Chapter 10

Liquids and Solids

Shaun Williams, PhD

Intermolecular Bonding

Intramolecular Bonding

Intermolecular Forces

Hydrogen Bonding in Water

A set of water molecules who are pointing their partially positive hydrogen atoms are pointing at partially negative oxygen atoms on neighboring molecules.

Phases Changes

Schematic Representation of the Three States of Matter

In a gas, the molecular are far apart and moving very fast. In a liquid, the molecules are close together, randomly arranged, and still moving. In a solid, the molecules are close together, ordered, and not moving relative to each other.

Phases Changes at the Molecular Level

Densities of the Three States of Water

State Density (\( \bfrac{\text{g}}{\text{cm}^3} \))
Solid (\(0^\circ\,\text{C}, 1\,\text{atm}\)) \( 0.9168 \)
Liquid (\(25^\circ\,\text{C}, 1\,\text{atm}\)) \( 0.9971 \)
Gas (\(400^\circ\,\text{C}, 1\,\text{atm}\)) \( 3.26 \times 10^{-4} \)

Dipole-Dipole Forces

Hydrogen Bonding

London Dispersion Forces

Melting and Boiling Points

A graph of the boiling points of the hydrides of families 15, 16, 17, 18. In each family, the boiling points fall in a nice straight line except for H2O, HF, and NH3. This is an indication of the hydrogren bond.

Concept Check 1

Which gas would behave more ideally at the same conditions of P and T?

$$ \chem{CO}\;\;\;\; \text{ or }\;\;\;\; \chem{N_2} $$

Why?

Concept Check 1 - Answer

Which gas would behave more ideally at the same conditions of P and T?

$$ \chem{CO}\;\;\;\; \text{ or }\;\;\;\; \color{green} \chem{N_2} $$

Why?

\(\chem{N_2}\) would behave more ideally because it is nonpolar and only exhibits London dispersion forces, therefore the intermolecular forces between \(\chem{N_2}\) molecules are weak (and thus the collisions will be more "elastic"). \(\chem{CO}\) also exhibits dipole-dipole interactions.

The Liquid State

Liquids

Convex Meniscus Formed by Nonpolar Liquid Mercury

The wall of a glass tube are polar since the molecules in glass are polar. In mercury, the atoms are nonpolar.

$$ \color{blue}\text{cohesive forces} $$

Concave Meniscus Formed by Polar Water

The wall of a glass tube are polar since the molecules in glass are polar. In water, the molecular are also polar.

$$ \color{blue}\text{adhesive forces} $$

Liquids

An Introduction to Structures and Types of Solids

Solids

Three Cubic Unit Cells and the Corresponding Lattices

Graphical representation of the three principle cubic unit cells.

Bragg Equation

Graphical representation of x-rays reflecting off the leading atoms in a crystal and the atoms in the second row of atoms in the crystal.

Types of Crystalline Solids

Examples of Three Types of Crystalline Solids

A representation of the atoms in diamond, salt, and water ice.

Classification of Solids

Atomic Solids
Metallic Network Group 18 Molecular Solids Ionic Solids
Components That Occupy
the Lattice Points		 Metal atoms Nonmetal atoms Group 18 atoms Discrete molecules Ions
Bonding Delocalized covalent Directional covalent (leading to giant molecules) London dispersion forces Dipole-dipole and/or London dispersion forces Ionic

Structure and Bonding in Metals

Closest Packing Model

The Closest Packing Arrangement of Uniform Spheres

A comparison of the first, second, and third layers in abab packing as described in the text on this slide.

The Closest Packing Arrangement of Uniform Spheres - cont.

A comparison of the first, second, and third layers in abca packing as described in the text on this slide.

Hexagonal Closest Packing

A comparison of the first, second, and third layers in abab packing as previously then sliced up showing a hexagonal unit cell.

Cubic Closest Packing

A comparison of the first, second, and third layers in abca packing as previously then sliced up showing a cubic unit cell.

The Indicated Sphere Has 12 Nearest Neighbors

Each atom in hexagonal closest packing (hcp) has six neightbors in its layer, three neighbords in the layer above, and three neighbords in the layer below. This gives us a total of 12 nearest neighbords in hcp.

The Net Number of Spheres in a Face-Centered Cubic Unit Cell

Half of each atom on the face of the unit cell is within the cell. Atoms at the corners are one-eigth inside the cell. This gives us a total of four atoms within the cell.

Bonding Models for Metals

The Electron Sea Model

A graphical representation of nuclei and core electrons of the metal atoms in an ordered patter. The valence electrons then form a large sea of electrons around the system.

Band or Molecular Orbital (MO) Model

A graphical of the valence energy levels of metals atoms and the number of atoms increases. As you get to a mole of atoms, the individual orbitals have merge to form a band.

The Band Model for Magnesium

A graphical of the valence energy levels of magnesium atoms. It shows the 1s, 2s, and 2p levels are localized to the area around each atom. The 3s and 3p (filled and unfilled) span the entire system.

Metal Alloys

Two Types of Alloys

In a substitutional allow, a second element has similar sizes atoms so they replace atoms in the original metal atom lattice. In a interstitial allow, elements with much smaller sized atoms are added and they fit in the gaps between the original atoms.

Carbon and Silicon: Network Atomic Solids

The Structures of Diamond and Graphite

In graphite, each carbon atom is covalently bound to four neighboring carbon atoms. In graphite, each carbon atom is covalently bound to three neighboring carbon atoms to found large 2D planes of graphite which then can stack one on top of another.

Partial Representation of the Molecular Orbital Energies in Diamond and a Typical Metal

In diamond, there is a large energy gap betwee the highest filled MO and the lowest unfilled MO. In a typical metal, there is no energy gap between the highest filled and lowest unfilled energy levels.

The p Orbitals and Pi-system in Graphite

In graphite, the large pi system, which is similar to what we learned in the previous chapter for benzene, spans the entire sheet of graphite.

Ceramics

Semiconductors

Energy Level Diagrams for an n-type Semiconductor and a p-type Semiconductor

In an n-type semiconductor, the donor add electrons at an energy that is close to that of the empty MO in the original, pure metal. In a p-type semiconductor, the donor removes electrons from the filled MO in the original metal.

Silicon Crystal Doped with Arsenic and Boron

Silicon doped with arsenic is an n-type semiconductor because the arsenic has extra, high energy electrons in its valence. Silicon doped with boron have less electrons so we end up with a p-type semiconductor.

Ionic Solids

Ionic Solids

Three Types of Holes in Closest Packed Structures

  1. Trigonal holes are formed by three spheres in the same layer. In a crystal there are small trigonal hole created between three adjacent atoms.
  2. Tetrahedral holes are formed when a sphere sits in the dimple of three spheres in an adjacent layer. In a crystal there are tetrahedral hole created between four adjacent atoms. Tetrahedral holes are larger than trigonal holes.

Three Types of Holes in Closest Packed Structures - cont.

  1. Octahedral holes are formed between two sets of three spheres in adjoining layers of the closest packed structures. In a crystal there are octahedral holes created between six adjacent atoms. These holes are larger than both trigonal and tetrahedral holes.

Types and Properties of Solids

Type of Solid Atomic Molecular Ionic
Network Metallic Group 18
Structural Unit Atom Atom Atom Molecule Ion
Type of Bonding Directional covalent bonds Nondirectional covalent bonds involving electrons that are delocalized throughout the crystal London dispersion forces Polar molecules: dipole-dipole interactions; Nonpolar molecules: London dispersion forces Ionic
Typical Properties Hard Wide range of hardness Soft Hard
High melting point Wide range of melting points Very low melting point Low melting point High melting point
Insulator Conductor Insulator Insulator
Examples Diamond Silver, Iron, Brass Argon(s) Ice (solid \(\chem{H_2O}\)), Dry ice (solid \(\chem{CO_2}\)) Sodium chloride, Calcium fluoride

Vapor Pressure and Changes of State

Behavior of a Liquid in a Closed Container

With just a liquid in a sealed container we only have evaporation. As the amount of vapor builds, condensation can also occur. At some point, the rate of evaporation and the rate of condensation are the same and the system is at equilibrium.

The Rates of Condensation and Evaporation

A graph of the system described on the last slide. There is a constant rate of evaporation. At first the rate of condensation is zero. As time goes on, the rate of condensation increases until the two rates are the same.

Vapor Pressure

Example 1

What is the vapor pressure of water at 100°C?

$$ \phantom{1\,\text{atm}} $$

How do you know?

Example 1 - Answer

What is the vapor pressure of water at 100°C?

$$ \color{green} 1\,\text{atm} $$

How do you know?

The vapor pressure of water at 100°C is 1 atm. You know this because atmospheric pressure is 1 atm and this is the temperature at which we observe water to boil.

Vapor Pressure - cont.

Measuring vapor press involves modifying a barometer so that instead of a vacuum above the mercury in the glass tube, you have the solution you are measure. You measure the difference between atmospheric pressure and that shown in these modified barometers.

Vapor Pressure vs. Temperature

For all compounds, as the temperature of the liquid increases, the vapor pressure increases. Each material crosses the 1 atm pressure at different temperatures.

Clausius-Clapeyron Equation

$$ \ln \left( \frac{P_{\text{vap},T_1}}{P_{\text{vap},T_2}} \right) = \frac{\Delta H_\text{vap}}{R} \left( \frac{1}{T_2} - \frac{1}{T_1} \right) $$

Example 2

The vapor pressure of water at 25°C is 23.8 torr, and the heat of vaporization of water at 25°C is 43.9 kJ/mol. Calculate the vapor pressure of water at 65°C.

Example 2 - Answer

The vapor pressure of water at 25°C is 23.8 torr, and the heat of vaporization of water at 25°C is 43.9 kJ/mol. Calculate the vapor pressure of water at 65°C.

$$ 194\,\text{torr} $$

Heating Curve for Water

As heat is added to ice at -20 degrees celsius the temperature rises. When the temperature reaches zero it flattens off as the ice is converted to liquid water as more heat is added. Once all the solid is converted to liquid, the temperature starts rising as more heat is added. When the temperature reached 100 degrees celsius it flatters off as the liquid is converted into gas as heat is added. Once all the liquid is converted to gas, the temperature increases as more heat is added.

Phase Diagrams

Phase Diagram for Carbon Dioxide

A pressure versus temperature graph. There are line seperating the three phases of matter. All three lines come together at the triple point. The liquid-gas line ends at the critical point. All the lines have a positive slope.

Phase Diagram for Water

A pressure versus temperature graph. There are line seperating the three phases of matter. All three lines come together at the triple point. The liquid-gas line ends at the critical point. The line separating solid and liquid has a negative slope (backwards from the triple point). This means that adding pressure to solid ice cause it to cross the phase boundary and convert into liquid. This is what allows for ice-skating.

Concept Check 2

As intermolecular forces increase, what happens to each of the following?

Concept Check 2 - Answer

As intermolecular forces increase, what happens to each of the following?

← →

/