Phase Equilibrium

1
Phase Equilibrium

• When a gas and a liquid phase which are not
  thermodynamically in equilibrium are brought into
  close contact, transfer of one or more components
  may occur from the gas phase to the liquid or,
  vice versa, by the mechanism of molecular
  diffusion.
• Mass transfer by molecular diffusion is the basic
  physical mechanism underlying many important
  areas of soil science, petroleum engineering,
  chemical engineering, biotechnology and nuclear
  engineering.
• In this experiment, a method for determining
  diffusion coefficients of Carbon dioxide gas in
  Stoddard solvent at constant volume, pressure and
  temperature is developed using Integral Phase
  Equilibria Unit.

2
Objective

• Determine
• diffusion coefficient,
• Solubility,
• Henrys Constant
• The enthalpy of solution of carbon dioxide in
  Stoddard solvent in the range of 18 - 35C and at
  1.0 atmosphere pressure.

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Introduction

• Diffusion Coefficient
• Measures the rate of diffusion
• Time-dependent
• Solubility
• Measures maximum amount of gas dissolved in
  liquid
• Time-independent
• Henrys Law constant
• Dissolved gas in liquid is proportional to
  partial pressure in vapor phase
• Heat of mixing
• Correlation between Henrys Law constant and T

4
Determination of diffusion coefficient from
experimental data
A number of mathematical models have been
proposed to determine the diffusion coefficients
from experimental volumetime profiles, however
all these models are developed from the equation
of continuity for the solute component
Gas phase
Interface
Ci
C
Z Z(t) Z0
where r Rate of reaction (kg/m3s) J Mass
transfer by the mechanism of molecular diffusion
(kg/m2s) v Molar volume (m3)
5

• Referring to Fig 12
• for a one-dimensional diffusion cell
• absence of chemical reaction,
• movement of the interface in the boundary
  conditions of the system, in which a component in
  the gas phase is absorbed into a liquid phase
  starting at time zero and continuing at longer
  times.
• Based upon a model proposed by Higbie
  (penetration theory)
• the liquid interface is thus always at
  saturation, since the molecules can diffuse in
  the liquid phase away from the interface only at
  rates which are extremely low with respect to the
  rate at which gaseous molecules can be added to
  the interface.
• It is also assumed that the distance between the
  interface and the bottom of the cell is
  semi-infinite that is, diffusion is slow enough
  that the concentration at the bottom of the cell
  is negligible compared to the concentration at
  the interface.
• According to the film theory
• the gas and the liquid phases at the interface
  are thermodynamically in equilibrium, i.e. the
  interface concentration of the solute, Ci remains
  unchanged as long as temperature and pressure of
  the system are kept constant.

Gas V104 CC
Ci
Stoddard Solvent V100 CC
Z(t)
C(t,Z)
Z
6
where C Concentration of dissolved CO2 in the
liquid phase at Z and t. Z Distance in cm
traveled from the liquid interface. t time D12
Diffusion coefficient of species 1 in 2.

• Thus the unsteady-state differential equation
  representing concentration changes with time and
  position is
• Solution of Ficks 2nd Law using the boundary
  conditions described is
• Solve for the number of moles added up to a time
  t
• If one plots NT versus t1/2, the slope of this
  line is equal to

The boundary conditions are Z 0 C Ci
Z ? 8 C 0 The initial condition is C
0 at t 0
7
SolubilityHenrys Law constant

• The solubility of a gas in a liquid solvent may
  be represented to good accuracy at dilute
  concentrations of the dissolved gas by Henry's
  Law
• f H X
• where f is the fugacity of the gas in the gas
  phase in equilibrium with the liquid phase of
  concentration X of dissolved gas.
• H is the Henrys law constant, which is a
  function of temperature.
• Thus, by measuring the solubility one can obtain
  an estimate of the Henry's law constant.

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• N gram moles of carbon dioxide absorbed in
  the liquid phase
• PT corrected barometer reading
• Po vapor pressure of Stoddard Solvent at
  cell temperature
• Tp temperature at the pump
• Tc temperature of the cell (bath
  temperature)
• ?Vp total gas volume delivered from the pump
  to the cell
• Vcg volume of the gas phase in the cell
• Zp compressibility factor of CO2 at pump T
  and PT
• Zc compressibility factor of CO2 at cell T
  and PT
• Vd dead volume in the system (cc)

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• The fugacity, f, can be determined from the Lewis
  and Randall Rule, which gives
• f fugacity of CO2 in the gas phase
• fo fugacity of pure gaseous CO2 at PT and cell
  T
• y mole fraction of CO2 in gas phase
• Thus
• by definition
• the fugacity coefficient for pure CO2 in the gas
  phase at cell T and P T

10
Heat of Mixing

• Use Henrys Law coefficients at the three
  experimental temperatures to obtain the heat of
  mixing
• Plotting ln(H) vs. 1/T gives a line with a slope
  of ?Hmix/R.
• ?Hmix is expected to be negative, which would
  indicate that CO2 and Stoddard solvent are more
  energetically stable than apart (i.e., the
  interactions are favorable).

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Experimental Cell Evacuation
12
Experimental Filling Syringe
13
Experimental Reduce to Atmospheric Pressure
14
Experimental Fill Cell
???????? between V4 and the cell is 40.5 cm and
the pipe diameter is 0.15 cm?
15
Penetration Model Brownian motion

• Brontan motion

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References

• Koretsky, Milo D. Engineering and Chemical
  Thermodynamics. John Wiley Sons, Inc., 2004.
• Ophardt, Charles E. Virtual Chembook. Elmhurst
  College, 2003. Online Available at
  http//www.elmhurst.edu/chm/vchembook/174temppres
  .html
• http//en.wikipedia.org/wiki/Lake_Nyos

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Cell information

• Properties of Stoddard Solvent and Cell
  Dimensions
•  
• Molecular Weight of Stoddard Solvent 136 g/mole
• Density of Stoddard Solvent 0.76988 g/cc at
  21C
• (The isobaric expansion coefficient is
  0.00104/C.)
•  
• Weight of Stoddard Solvent in the cell 67.75 g
  at room temp
• Volume of the Cell 146 ml
• Volume of the magnetic stirrer 1.5 ml
• Length of the tube from the top of the cell to
  valve 4 43.815 cm
• Di of the tube 0.3175 cm
•  
• From these info please Calculate the Void volume
  (gas volume above the liquid phase)
• And the total volume of CO2 gas to full the space
  when you open valve 4.