Gas and Liquids

7/29/2019 Gas and Liquids

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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

Gas and Liquids

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