Post on 14-Apr-2018
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Gas and Liquids
All matter exists in one of three aggregation: solid, liquid,or gaseous.
A Solid
a body possesing both definite volume and definiteshape at given temperature and pressure
the body must be crystalline
the body must be arranged in a definite configurationcharacteristic of the substance
Fluids : Liquids and Gases
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A Liquid
A definite volume but
no definite shape
Fills the container
adopt the shape of
container but retain its
definite volume
A Gas
Neither definite shape
nor volume
Fill completely the
container
The distinction among the three states of matter arenot always clear cut.
The particular state of aggregation of a substance is
determined by the temperature and pressure underwhich it exists.
Within certain limits of temperature and pressure asubstance may exist in more than one state at thesame time.
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Ideal Gas
the volume occupied by
the moleculesthemselves is negligible
compared with the total
volume at all pressure
and temperatures the intermolecular
attraction is extremely
smalI under all
conditions
Low pressure and high
temperature
Real Gas
these factors are
appreciable,
the magnitude of each
depending on the
nature, the
temperature and thepressure of gas
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Ideal Gas law:
(a) Boyles law.
(b) Charless or Gay-Lussacs law,
(c) Daltons law of partial pressures,
(d) Grahams law of diffusion
(e) Kinetic Theory
Boyles law :PV = K (T constant)
the volume of a gas at constant temperature
decreased with increasing pressure, within the limits of his experimental accuracy, the
volume or any definite quantity of gas at constanttemperature varied inversely as the pressure onthe gas
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Charless or Gay-Lussacs law :
V = KT (P constant)
the volume of a definite quantity of gas at constantpressure is directly proportional to the absolutetemperature.
Combined gas law:PV = KT
Totally independent of the nature of the gas
For any given pressure and temperature an increase inthe quantity of gas increases the volume, and therebyalso correspondingly the magnitude of K.
K is directly proportional to the number of moles of
gas involved
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Daltons law of partial pressures :
Ptotal= P1 + P2 + P3+
At constant temperature the total pressure
exerted by a mixture of gases in a definite
volume is equal to the sum of the individualpressures which each gas would exert if it
occupied the same total volume alone
Ideal gas law :
PV = nRT
R universal constant for all gases
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Grahams law of diffusion :
At constant temperature and pressure the rates ofdiffusion of various gases vary inversely as thesquare roots of their densities or molecular weights.
Amagats law of partial volume :
Vtotal= V1 + V2 + V3+
In any gas mixture the total volume may be consideredto be the sum of the partial volumes of theconstituents of the mixture if each constituent presentsalone at the given temperature and total pressure of
the mixture.
1
2
1
2
2
1
M
M
V
V
u
u
m
m
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Applicability of the ideal gas laws z = 1 at all temperatures and pressures
Compressibility factor:
nRT
PVz
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Boyle temperature
or Boyle point
The temperature at
which a real gas obeys
the ideal gas law over
an appreciablepressure range
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Equation of States (EOS) in physics and thermodynamics, an
equation of state is a relation betweenstate variables.
more specifically, an equation of state is athermodynamic equation describing thestate of matter under a given set of physical
conditions. an equation of state is a constitutive
equation which provides a mathematicalrelationship between two or more state
functions associated with the matter, such asits temperature, pressure, volume, orinternal energy.
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The van der Waals EOS
one of the first to perform markedly better
than the ideal gas law makes allowances both for the volume
occupied by the molecules themselves and the
attractive forces between them
nRTnbVPP '
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nRTnbVPP '
Pi
Attractive force
Observed/measured
pressure
Ideal pressure
PPi
P
Wa
ll
Wall
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nRTnbVPP 'the effective volume of the
molecules in one mole of gas
the total volume of n moles of
gas
the volume available for
compression or free
space
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Other EOS
Theoretical considerations
Empirical Kamerlingh Onnes Equation
Berthelot Equation
How to choose the appropriate EOS?
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Molecular weights of gases
Chemical analysis:
the elements entering into the composition ofmolecule and their proportions (empirical formula)
not tell us how many atoms of each substance
involved
Example : CH3 compare to C2H6, C3H9 Avogadro hypothesis : under the same
condition of temperature and pressure, equal
volume of all ideal gases contain the same
number of molecules. Regnaoults method, Dumas method
Berthelots method
Limiting Densities method
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Molecular weights of gases
Abnormally high vapor densities: more than a
single structural unitExample : Fe2Cl6
Abnormally low vapor densities: break down
or dissociate
Example : NH4Cl = NH3 + HCl
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Kinetic Theory of Ideal Gases
1. Gases are considered to be composed of minute discrete particlescalled molecules. For any one gas, all molecules are thought to be ofthe same mass and size but to differ in these from gas to gas.
2. The molecules within a container are believed to be in ceaselesschaotic motion during which they collide with each other and withthe walls of the container.
3. The bombardment of the container walls by the molecules gives riseto the phenomenon we call pressure; i.e., the force exerted on thewalls per unit area is the average force per unit area which themolecules exert in their collisions with the walls.
4. Inasmuch as the pressure of a gas within a container does not varywith time at any given pressure and temperature, the molecularcollisions must involve no energy loss due to friction. In other words,all molecular collisions are elastic.
5. The absolute temperature is a quantity proportional to the averagekinetic energy of all the molecules in a system.
6. At relatively low pressure the average distances between moleculesare large compared with molecular diameters and hence theattractive force between molecules, which depend on the distance ofmolecular separation, may be considered negligible.
7. Finally, since the molecules are small compared with the distancebetween them, their volume may be considered to be negligiblecompared with the total volume of the gas,
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Rights yz planeLefts yz plane
Momentum of one molecule/wall : Before = After
mux = m.-uxChange of momentum/one molecule/wall =
BeforeAfter = mux
- m.-ux
= 2mux
Number of collision/second = ux/2l
Change of momentum/second/one molecule/wall =
(2mux). (ux/2l) = mux2/l
Change of momentum/second/one molecule in x direction =
2mux2/l
l
m.ux m.-ux
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Total change ofmomentum/second = 2nmu2/l
The rate change of momentum is the acting force, f.
2
2
3
22
'3
1
3
'
6
'2'2
umnPV
Vumn
lumn
lAumn
AfP
Deductions from the kinetic theory
Velocity of gas molecules
Kinetic theory of translation
Distribution of molecular velocities
Frequency of collisions and mean free path
Heat capacity of gases
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RCRCC VVP23;
Heat capacity of gases Heat capacity at constant volume : increase the
internal energy
Heat capacity at constant pressure : increase theinternal energy and expansion against theconfining pressure
Ideal gas containing only translational energy(monatomic gas) :
Crtitical phenomenon in liquid
No liquid can exist as such at temperature abovecritical temperature under any applied pressure.
At this temperature, the physical properties of liquidand vapor become identical, and no distinction can beobserved between the two.
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Tc
> Tc
< Tc
P
V
Isothermals
gas
liquid
gas-liquid
mixture
Vc
Pc
E
b
a
Pk
>Tc
Pq>Tc
k
d
q
Pressure
if
g
PE
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Tc
> Tc
< Tc
P
V
Isothermals
gas
liquid
gas-liquid
mixture
Vc
Pcb
a
Pa
Tc
PETc
k
b
q
Pb
Tc
distinctioncan be
observed
between
the liquid-
vapor
Pressure
EPE
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Tc
< Tc
P
V
Isothermals
gas
liquid
gas-liquid
mixture
Vc
Pcb
a
Pd
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Tc
> Tc
< Tc
P
V
gas
liquid
gas-liquid
mixture
Vc
Pc
M
b
a
d
Pressure
if
g
PE E
D
B
A
PE
Tc
PM
TM
PA
TA
TA
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Tc
> Tc
< Tc
P
V
Linde Process
gas
liquid
gas-liquid
mixture
Vc
Pc
gas
liquified gas
Adiabatic expansion
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Van der Waals equation Reduced equation of state
No constants
characterizing the
individuality of various
substances and be
generally applicable to
all liquids and gases