vapor pressure equilibrium

8/11/2019 Vapor Pressure Equilibrium

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Free Energy, Vapor Pressure

and the Equilibrium Between aVapor and Condensed Phase

References:

Thermodynamics, G. N. Lewis and M. Randall,rev. K. Pitzer and L. Brewer, McGraw Hill, NewYork (1961).

Chemical Thermodynamics, I. Klotz, Benjamin,New York (1964).


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The Gibbs Free Energy is generallyagreed to be the weapon of choice fordescribing (a) chemical reactions and (b)equilibria between phases. It is definedas:

G = HTS = E + PVTS (1)

Where H = Enthalpy E = Total internal energy

T = [Absolute] Temperature

S = Entropy

Obviously dG = dE + PdV +VdPTdSSdT


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Aside

Remember that thermodynamic variablescome in pairs

One is intrinsic (does not depend onsystem size)

One is extrinsic (depends on systemsize)

Examples: P and V, T and S

Also G and N, the number of moles of stuffin the system.

Hence G is the appropriate variable when

material is moving between phases


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From the

First Law of Thermodynamics

dE = TdSPdV since dS = Q/T andthe mechanical work done ona system

when it expands isPdV.

Substituting into

dG = dE + PdV +VdPTdSSdT

Leaves: dG = -SdT + VdP


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Apply equation to a closed system

Closed system contains pure substance

vapor

condensed phase

Phases co-exist in equilibrium.

Objective will be to see how the pressureof the vapor depends on the temperature

of the system.


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Write the Free Energy Equation twice

Once for each phase

dGc= -ScdT + VcdP c refers to thecondensed phase

dGv= -SvdT + VvdP v refers to the

vapor phase


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Objective of the Exercise

Change system temperature

See how the pressure of the vaporchanges

Note:

Both the vapor and condensed phase are inthermal equilibrium

Both are at the same temperature

System remains in thermal equilibrium if themolar free energy of the system, also known

as the chemical potential, remains constant.


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Definition of chemical equilibrium

between two phases

Free energy is the same in both phases

Gc= Gv

Changes in free energy when someindependent variable is changed must bethe same if they are to remain in

equilibrium


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dP/dT = (SvSc)/(VvVc) = Hv/(TV)

This is the Clapeyron equation (E.Clapeyron, J. cole polytech. (Paris)

14(23), 153 (1834). It relates the changein pressure of a vapor to the temperature

in a closed, mono-component system to

the heat of vaporization, systemtemperature and molar volume change of

the material on vaporization.


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Creating of an Ideal Gas

For lack of a better model, we treat mostvapors as ideal gases, whose molar

volume is given by:

V/n = RT/P

Alternatively, equation of state is needed

Molar volume of gas is typically factor of500 larger than condensed phase

Hence Vcis negligible in comparison


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Substituting and Integrating

dP = (Hv/Vv)dT/T = (PHv/RT)dT/T

dP/P =Hv/R)dT/T2

ln(P(T)/ P0) = -(Hv/R)(1/T1/T0)

P(T) = P0exp(-Hv/R(1/T1/T0))


13/23

The vapor pressure in equilibrium with acondensed phase increases exponentially

(sort of: exp(-1/T) isnt exactly anexponential!) with temperature from zero

up to the critical temperature.

Borne out in the vapor pressure charts andgenerating functions for them.

Deviations from linearity on the log-log plot

Temperature dependence of the heat ofvaporization

exp (-1/T) isnt really linear in the exponent.


14/23

Heat of Vaporization from CRC Data

Log10p(Torr) = -0.2185*A/T + BVapor Pressure of Water

Temperature (C)

-20 0 20 40 60 80 100 120

Vapo

rPressure(T

orr)

0.1

1

10

100

1000

10000

"Normal boiling point"


15/23

Generating Function s Imperfect

Normal boiling point of water on the plot isabout 108.2 C.

I cheated; I looked at the data!

What does Normal boiling point mean??

What does boiling mean???


16/23

Kubaschewski, Evans and Alcock, Metallurgical

Thermochemistry, Pergammon, Oxford (1967)

Log10p(Torr) = A/T + BlogT + CT + D

Vapor Pressure of Water

Temperature (C)

-20 0 20 40 60 80 100 120

VaporP

ressure(Torr)

0.1

1

10

100

1000

10000

"Normal boiling point"

Kubaschewski et al.


17/23

From Kubaschewskis Data

Vapor pressure at 100 C is 758 Torr

Much better approximation!

Caveat emptor! Life is like a sewer: the quality of the fit

depends on the number of terms in the

generating function!


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RCA Charts

Great resource tool: the RCA Charts,which live in 327 JFB. Treat them with

great respect: they are much older than

you are and irreplaceable.

Often imitated

Never duplicated


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Other Sources of Data

Vapor Pressures of Pure Substances,Daniel R. Stull, Industrial and Engineering

Chemistry, April 1947, pp. 517550.

(Tables give data on temperature requiredto generate a specific vapor pressure.)

Vapour Pressure of the Elements, An. N.

Nesmeyanov, Academic Press, NY, NY(1963).


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Gibbs Phase Rule

F = CP + 2

F = number of degrees of freedom

C = number of components P = number of phases

What is a phase?

What is a component? What is a degree of freedom?


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vapor pressure equilibrium

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