Chapter 10. Liquids and Solids
Recommended Article : 【Chemistry】 Chemistry(https://jb243.github.io/pages/1362)
1. Definitions of Liquids and Solids
1. Definitions of Liquids and Solids
⑴ Definition of a Liquid is more ambiguous than that of a Gas or Solid
① Gas : Almost no intermolecular forces
② Solid : Particles are fixed in space
③ Liquid : Fluidic but can’t escape from each other, also used when defining the concept of meniscus
⑵ Definition based on Arrangement (Ordering)
① Gas : No ordering
② Solid : Long-range ordering
③ Liquid : Short-range ordering
⑶ Definition based on Vibrational Amplitude
① Gas
② Solid : When particles vibrate less than half the distance between them in a crystalline structure
③ Liquid : When particles vibrate more than half the distance between them in a crystalline structure
⑷ Liquid Crystal : A state where liquid maintains ordering like a solid
① Nematic Phase : Alignment in the same direction, not orderly
② Smectic Phase : Alignment in the same direction with regular spacing
③ Cholesteric Phase : When the next layer is tilted at a certain angle to the previous layer
2. Properties of Liquids
⑶ Vapor Pressure
① Vapor Pressure and Boiling Point
○ Vapor Pressure : Pressure exerted by vapor when evaporation and condensation of a liquid reach equilibrium
○ Boiling Point : Pressure at which vapor pressure of a liquid equals the external pressure
○ Normal Boiling Point (Tb) : Boiling point at 1 atmosphere pressure
② Vapor-Liquid Equilibrium (e.g., water)
③ Temperature and Raoult’s Law
○ Transition from vapor phase (steam) to gas phase (vapor) is an endothermic process, i.e., ΔH < 0
○ Increase in temperature ⇒ Equilibrium shift towards endothermic reaction according to Raoult’s Law ⇒ Increase in equilibrium constant (K) ⇒ Increase in vapor pressure
④ Clausius-Clapeyron Equation
○ Formulation : For absolute temperature (T)
○ Derivation
○ Vapor pressures at different temperatures
○ Calculation of enthalpy of vaporization and entropy of vaporization
○ Assumption : Enthalpy and entropy of vaporization do not change with temperature
○ Enthalpy of vaporization calculation : Calculate slope from ln P - 1/T curve and multiply by (-R)
Figure 1. Calculation of enthalpy of vaporization
○ Calculation of entropy of vaporization
⑤ Antoine Equation : Empirical equation to calculate vapor pressure
⑷ Freezing Phenomenon
① Definition : Phenomenon where a substance does not solidify even as the temperature goes below its freezing point, i.e., supercooling (e.g., water)
② Principle : Water takes a long time to form its hexagonal structure, preventing freezing below its freezing point
3. Properties of Solids
⑴ Types of Solids
① Classified into Crystalline Solids and Amorphous Solids
② Crystalline solids have ordered arrangements
③ Type 1: Metallic Crystals : Metallic bonding (electron sea). Conduct electricity (e.g., Na)
④ Type 2: Ionic Crystals : Ionic bonding. Conduct electricity only in liquid state (e.g., NaCl)
⑤ Type 3: Network Crystals : Covalent bonding. Do not conduct electricity
○ Means to define Avogadro’s number
○ Exception : Carbon crystal conducts electricity in the solid state
⑥ Type 4: Molecular Crystals : Intermolecular forces. Do not conduct electricity
⑵ Structure of Metallic Crystals
① Overview
○ Nearest neighbor : Atom or ion closest to a central atom or ion
○ Common coordination number : Number of nearest atoms to a specific atom
○ Coordination number of anion : Number of nearest cations to a specific anion
○ Coordination number of cation : Number of nearest anions to a specific cation
○ A total of 14 types of unit cells in metallic crystals
Figure 2. Key structures of metallic crystals
Figure 3. Hexagonal close-packed structure
② Simple Cubic Structure
○ Shape : Atoms at 8 corners of a cube
○ Number of particles per unit cell : Corner atoms are 1/8 of a sphere
○ Coordination number : 2 along each axis, total of 6
○ Radius relationship : Regarding the length of one side (a)
○ Space occupancy rate : Low, rarely found in nature
○ Density
○ Packing method : Simply stack in a straight line
③ Body-Centered Cubic Structure (BCC)
○ Cr, W, Mo, V, Li, Na, Ta, K, α-Fe, δ-Fe, etc.
○ Shape : Atoms at 8 corners of a cube, and an atom at the center of the cube
○ Physical properties : High melting point and high strength
○ Number of particles per unit cell : Corner atoms are 1/8 of a sphere, center atom is whole
○ Coordination number : Convenient when considering the center atom. 8
○ Radius relationship : Consider 3D diagonal for length (a)
○ Space occupancy rate
○ Density
○ Packing method : Each layer is stacked in a straight line, alternating between layers
④ Face-Centered Cubic Structure (FCC)
○ Al, Ag, Au, Cu, Ni, Pb, Ca, Co, γ-Fe, etc.
○ Shape : Atoms at 8 corners of a cube, atoms at the centers of 6 cube faces
○ Physical properties : High electrical conductivity, excellent ductility
○ Number of particles per unit cell : Corner atoms are 1/8 of a sphere, face atoms are 1/2 of a sphere
○ Coordination number : Consider face atoms. 4 on that face, 4 in front, 4 behind, total of 12
○ Radius relationship : Consider 2D diagonal for length (a)
○ Space occupancy rate : Most densely packed
○ Density
○ Packing method : Each row is stacked slightly off from the surrounding rows
⑤ Hexagonal Close-Packed Structure (HCP)
○ Mg, Zn, Cd, Ti, Be, Zr, Ce, etc.
○ Shape : 6-3-6 unit cells are packed like a beehive
○ Physical properties : Poor electrical conductivity, adhesiveness, and ductility
○ Number of particles per unit cell : Corner atoms are 1/6 of a sphere, hexagonal face atoms are 1/2 of a sphere, 3 internal atoms are singular
○ Coordination number : Easily understood with reference to Figure 2.
○ Radius relationship : Regarding the length of one side (a)
○ Space occupancy rate : Packed most densely like FCC
○ Density
⑥ Crystal Structure of Iron
Table 1. Structure of Iron
⑶ Structure of Ionic Crystals
① Examples of Ionic Crystals
Figure 4. Examples of Ionic Crystals
② Binding Energy of Ionic Bonds
○ Coulomb Potential of a Single Dipole
Figure 5. Coulomb Potential of a Single Dipole
○ Coulomb Potential of 1D Crystal : Multiply Coulomb potential of the central atom in an infinite 1D crystal by Avogadro’s number
○ Coulomb Potential of NaCl Crystal : Multiply Coulomb potential of the central atom in an infinite 3D crystal by Avogadro’s number
○ Coulomb Potential of CsCl Crystal : Multiply Coulomb potential of the central atom in an infinite 3D crystal by Avogadro’s number
○ Lattice Energy : Absolute value of Coulomb potential. Lower lattice energy leads to higher solubility
○ Binding Energy of Ionic Bonds = - Metal Ionization Energy + Non-metal Electron Affinity + Lattice Energy
○ Metal Ionization Energy : E(Na+(g)) - E(Na(g))
○ Non-metal Electron Affinity : E(Cl(g)) - E(Cl-(g))
○ Lattice Energy : E(Na+(g)) + E(Cl-(g)) - E(NaCl(s))
○ Binding Energy of Ionic Bonds : E(Na(g)) + E(Cl(g)) - E(NaCl(s))
③ Holes in FCC Structure
○ Two types of holes in FCC structure
○ Tetrahedral interstice : 8 tetrahedral interstices centered on each corner atom in FCC structure
○ Octahedral interstice : 4 octahedral interstices exist, as illustrated below
Figure 6. Illustration of Octahedral Interstice Tip
○ Tetrahedral interstices are smaller than octahedral interstices in FCC structure
⑷ Structure of Atomic Crystals
① Structure of Diamond
○ Overall structure of diamond
Figure 7. Overall structure of diamond
○ Unit cell structure of diamond : The unit cell contains 8 atoms
Figure 8. Unit cell structure of diamond
○ Space occupancy rate
Input: 2018.12.30 22:29