9A. The Liquid Phase
Liquids and solids (condensed phases) are formed by
many atoms, ions, or molecules held closely together.
In liquids the particles (atoms, ions, or molecules) can
move freely but remain adjacent to the other particles.
In solids not only are the particles adjacent, but the
motion of the particles is limited.
In gases the particles move freely and independently; that
is, without attaching to other particles.
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Comparison of the phases
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9.1. Intermolecular forces
The atoms, ions, or molecules are held together by intermolecular forces.
All these forces are based on the attraction of a positive charge to a negative charge.
The magnitude of the lattice energy (U) is expressed by Coulomb's law
U = k (Q1Q2 / d)
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[J]
Q is the charge of ions,
d is the distance between the nuclei,
k is a proportionality constant.
The liquid phase
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The strongest intermolecular force is ion-ion attraction. This is the intermolecular
force in ionic compounds (salts). The force is stronger for ions with higher charges
(greater Q) or with smaller distances (d) between ions. d depends on the size
of the ions and the arrangement of ions, known as the lattice structure.
Substances with ionic forces of attraction exist in the solid state at room temperature.
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Polar molecules have partial charges and are held to each other by dipole-dipole forces.
Because these are only partial charges, unlike the full charges of ions, these forces are much
weaker. Thus substances with dipole-dipole forces of attraction tend to be gases (occasionally
liquids) at room temperature.
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When ionic compounds are mixed with polar compounds, they may dissolve.
The many small dipoles of the solvent may be more attractive than the other ions of the salt,
creating ion-dipole forces.
Dissolution will only occur if the ion-ion attraction is sufficiently weak and the ion-dipole
forces are sufficiently strong. Because there is both a full and a partial charge in ion-dipole forces,
these forces are stronger than dipole-dipole forces, but not as strong as ion-ion forces.
Another special case of dipole-dipole forces is hydrogen bonding. Hydrogen bonds occur
between molecules that have a hydrogen covalently bonded with an oxygen, nitrogen, or
fluorine atom. O, N, and F are the most electronegative atoms, which therefore attract most
of the electrons of the covalent bond. When the other end of that covalent bond is a hydrogen,
the electronegative atom is pulling all electrons associated with H away from it and H acts almost
as a positive charge. This high charge makes hydrogen bonds a very strong type of dipole-dipole
force. Substances which hydrogen bond are typically liquids at room temperature.
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Nonpolar molecules are attracted to each other by temporary dipoles, which are called
London or dispersion forces. Deforming the electron clouds surrounding the molecules
creates temporary dipoles. With more electrons the electron cloud is more easily and more
greatly deformed; thus the dipoles are larger and the attraction greater. Molecules with easily
deformed electron clouds are called polarizable.
Molecules with London forces are normally gases at room temperature.
sn a p sh o ts
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9.2. Solubility and miscibility
Forces of attraction determine the solubility of substances. The forces between the solute and
solvent must be stronger than the solute-solute and the solvent-solvent interactions for a
substance to be soluble. Polar substances dissolve in polar solvents and nonpolar substances
dissolve in nonpolar solvents.
In the case of ionic compounds, the solute-solvent forces can overcome the ion-ion forces since
there are usually many more solvent molecules than solute molecules (the weaker ion-dipole
forces can sometimes overcome the ion-ion forces). When water is the solvent, six waters
typically surround each ion (sphere of hydration).
When two liquids dissolve in each other in all proportions, they are called miscible.
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9.3. Vapor pressure, freezing and boiling
Forces of attraction can be overcome by increasing temperature and thus the kinetic energy
(movement) of the particles. When the temperature is sufficient to overcome some of the
attraction, solids will melt. That temperature is called the melting point. (= freezing point)
The stronger the force of attraction, the higher the melting point.
Kinetic energy allows particles on the surface of a liquid to escape the attractive forces and
become a vapor. When the number of particles escaping the liquid and the number of particles
being captured by the liquid are the same, the system is in equilibrium. The pressure of the
gaseous particles in such a system is called the vapor pressure.The vapor pressure depends
on the attractive forces and temperature. Substances with stronger attractive forces have
lower vapor pressures. An increase in temperature increases the vapor pressure. When the
vapor pressure reaches the atmospheric pressure, any molecule can escape the liquid and the
liquid boils. This temperature is called the boiling point.
Vapor pressure of solutions: is always smaller than that of the pure solvent.
For ideal solutions of substances of negligible vapor pressure
Raoult’s law:
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9.4. Colligative properties:
Solution properties that are affected by the amount (number
of moles) of solute and not the identity of the solute.
Osmotic pressure
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Boiling point elevation
For non-ionizing solutes (like
alcohols, sugars, etc)
T b= Kb m
For ionizing solutes (salts):
T b= i Kb m
m : molality (mol solute per kg solvent)
i : van’t Hoff factor
(mol ions from 1 mole solute)
Kb: ebullioscopic constant,
characteristic of the solvent
Freezing point depression
For non-ionizing solutes (like
alcohols, sugars, etc)
T f = Kf m
For ionizing solutes (salts):
T f = i Kf m
A d d salt
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m : molality (mol solute per kg solvent)
i : van’t Hoff factor
(mol ions from 1 mole solute)
Kb: cryoscopic constant,
characteristic of the solvent
The liquid phase
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The van’t Hoff factor:
Because ions often associate with each other in solution, forming ion pairs, the true van't
Hoff factor is often less than its theoretical value. True van't Hoff factors can be calculated
from any of the colligative properties, by adding the van't Hoff factor i to the equation.
(e.g., T = iKm). If the van't Hoff factor is used in the equation, the concentration refers to
the moles of overall solute rather than to moles of particles.
D
Dps, DTb and DTf are related to the
molecular mass of the dissolved material
D
p
1+/2-
Tb
Tf
ps = ps* xs = ps* (1-x)
x = n / (n+ns)  n / ns = (m/M) / (ms/Ms)
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Where s subscript denotes solvent
no subscript denotes solute
* superscript denotes pure solvent
m: mass
n: mol number
M: molar mass
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9.5. Surface phenomena:
Surface tension
The steel needle is floating on the surface of water
Temperature dependence
of surface tension the Eötvös rule:
Surface tension:
=F/4Rp
 [N/m] or [J/m2]
Vm2/3 = k (Tcr – 6 – T)
when T = Tcr - 6 ,  = 0
Vm :
molar volume
Vm2/3 : molar surface
 Vm2/3: energy of molar surface
k [J K-1 mol 2/3]
Tcr . Critical temperature
k=2.0-2.2 x10-7
for several liquids
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Surface tension is the resistance of a liquid to increase its surface area. It is higher with stronger
attractive forces and weaker at higher temperatures.
The attraction of the substance to the wall of a container is called the adhesive force, and the
attraction of the substance to itself is called the cohesive force. When the adhesive forces are
stronger than the cohesive forces, the substance creeps up the sides of the container, forming
a curved surface called a meniscus. In capillaries, there is sufficient wall that the substance
actually climbs the walls of the capillary until gravity overcomes the adhesive forces. The rising
of a liquid up a capillary tube is called capillary action.
Meniscus risen to height h is
in equilibrium with the original
liquid if its vapor pressure (ph) is:
ph = p0 exp [ rgh Vm / RT] =
= p0 exp [ 2LV cosa Vm / r RT]
h
From the force equilibrium for
perfectly wetting liquid:
2r p LV = r2p rgh
.
h>0
h<0
h = 2 LV / rg r
r : radius of capillary
Vm: molar volume of the liquid
r : density of liquid
r : radius of meniscus curvature 
• radius of capillary for convex menisci
• -1 times radius of capillary for concave
menisci
LV : surface (interfacial) tension of liquid
a : contact angle of the liquid wit the
capillary wall
Extra vapor pressure above curved surfaces relative to flat ones:
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capillary pressure = Dp = 2 cos a/r , where 1/r is the curvature
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Wetting
SV = SL + LV (cos a)
Young’s equation:
where
Vapor
SV
a
a is the contact angle
LV
SL
Adhesion:
When surfaces of condensed phases (SV, SL)
get into contact the energy of the new surface (SL)
is always lower than the sum of those of the
disappearing surfaces.
The energy liberated:
Wa = - SV - LV + SL <= 0
Solid
[J m-2]
Immersion wetting:
Spreading coefficient:
S = SV - SL - LV
Condition of complete wetting:
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When a powder is mixed with a wetting (a<90o)
liquid the heat of wetting (Qw) is lower than Wa as the
voids (LV surfaces) for the solid needs to be created:
S >= 0
SV
The liquid phase
LV
SL
Qw = Wa + LV = - SV + SL
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Adsorption
Concentration of some species in the interfacial layer changes
relative to the bulk phase
Gibbs equation:
G = - (c / RT) d / dc
G: surface excess concentration of a species
in the surface layer relative to the same
surface are chosen in the bulk liquid [mol/m2]
c : volume concentration of the species in question
d / dc: rate of change of surface tension with
concentration of the dissolved material
Those materials accumulate in the liquid/vapor interface that
decrease surface tension of the liquid (positive adsorption, ie. solvent
d / dc < 0). These are called surface (capillary) active.
The ones that increase surface tension suffer negative
adsorption (surface concentration is smaller than at the same
area taken at the bulk liquid).

c
Surfactants are the
most important capillary
active substances
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9.6. Viscosity:
The resistence of materials to flow (transport of momentum)
Newton’s law: t = h dV/dH = h d(D/H) / dt
t : shear stress = F/A [Pa]
dV/dH : shear rate = d(D/H) / dt = velocity gradient [s-1]
h: viscosity = constant [Pa.s]
D/H : shear (deformation)
Non-newtonian fluids: h is not constant constant and/or
there is a yield stress (ty)
a. power law (pseudoplastic) t = m (dV/dH)n
(n<=1)
b. plastic (Bingham)
t = ty + h (dV/dH)
c. combined (shear thinning) t = ty + m’ (dV/dH)n (n<=1)
d. dilatant – shear thickening
Shear
stress
Yield
stress
d
c
b
a
Shear
rate
Thixotropy: time dependent viscosity
at constant shear rate
h
Temperature dependence
h
t
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Liquids h = A exp [B/T] number and size of voids
increase with T
1/2
Gases: h = C T
number of collisions increases with T
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