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Phase Equilibrium When a gas in addition to a liquid phase which are not th
California Western School of Law, US has reference to this Academic Journal, Phase Equilibrium When a gas in addition to 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 so that 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 in addition to nuclear engineering. In this experiment, a method in consideration of determining diffusion coefficients of Carbon dioxide gas in Stoddard solvent at constant volume, pressure in addition to temperature is developed using Integral Phase Equilibria Unit. Determine diffusion coefficient, Solubility, Henrys Constant The enthalpy of solution of carbon dioxide in Stoddard solvent in the range of 18 – 35øC in addition to at 1.0 atmosphere pressure. Objective Introduction Diffusion Coefficient Measures the rate of diffusion Time-dependent Solubility Measures maximum amount of gas dissolved in liquid Time-independent Henry?s Law constant Dissolved gas in liquid is proportional so that partial pressure in vapor phase Heat of mixing Correlation between Henry?s Law constant in addition to T
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Determination of diffusion coefficient from experimental data C Gas phase Interface Z Z(t) Z=0 Cav A number of mathematical models have been proposed so that determine the diffusion coefficients from experimental volume?time profiles, however all these models are developed from the equation of continuity in consideration of the solute component: where r = Rate of reaction (kg/m3s) J = Mass transfer by the mechanism of molecular diffusion (kg/m2s) v = Molar volume (m3) Stoddard Solvent V=100 CC Referring so that Fig 1&2 in consideration of 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 in addition to 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 alongside respect so that the rate at which gaseous molecules can be added so that the interface. It is also assumed that the distance between the interface in addition to 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 so that the concentration at the interface. According so that the film theory the gas in addition to 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 in addition to pressure of the system are kept constant. Ci C(t,Z) Z(t) Z Gas V=104 CC Thus the unsteady-state differential equation representing concentration changes alongside time in addition to position is: Solution of Fick?s 2nd Law using the boundary conditions described is: Solve in consideration of the number of moles added up so that a time t: If one plots NT versus t1/2, the slope of this line is equal so that 2ACi (D12/?)1/2 where C = Concentration of dissolved CO2 in the liquid phase at Z in addition to t. Z = Distance in cm traveled from the liquid interface. t = time D12 =Diffusion coefficient of species 1 in 2. The boundary conditions are: Z = 0 C = Ci Z ? ?: C = 0 The initial condition is C = 0 at t = 0:
Solubility Henry?s Law constant The solubility of a gas in a liquid solvent may be represented so that 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 alongside the liquid phase of concentration X of dissolved gas. H is the Henry?s law constant, which is a function of temperature. Thus, by measuring the solubility one can obtain an estimate of the Henry’s law constant. n = gram moles of carbon dioxide absorbed in the liquid phase PT = corrected barometer reading = vapor pressure of Stoddard Solvent at cell temperature Tp = temperature at the pump Tc = temperature of the cell (bath temperature) = total gas volume delivered from the pump so that the cell Vcg = volume of the gas phase in the cell Zp = compressibility factor of CO2 at pump T in addition to PT Zc = compressibility factor of CO2 at cell T in addition to PT Vd = dead volume in the system (cc) The fugacity, f, can be determined from the Lewis in addition to Randall Rule, which gives f = fugacity of CO2 in the gas phase fo = fugacity of pure gaseous CO2 at PT in addition to cell T y = mole fraction of CO2 in gas phase Thus by definition: the fugacity coefficient in consideration of pure CO2 in the gas phase at cell T in addition to P T
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Heat of Mixing Use Henry?s Law coefficients at the three experimental temperatures so that obtain the heat of mixing: Plotting ln(H) vs. 1/T gives a line alongside a slope of ?Hmix/R. ?Hmix is expected so that be negative, which would indicate that CO2 in addition to Stoddard solvent are more energetically stable than apart (i.e., the interactions are favorable). Experimental: Cell Evacuation Experimental: Filling Syringe
Experimental: Reduce so that Atmospheric Pressure Experimental: Fill Cell ???????? between V4 in addition to the cell is 40.5 cm in addition to the pipe diameter is 0.15 cm? Penetration Model
References Koretsky, Milo D. Engineering in addition to Chemical Thermodynamics. John Wiley & Sons, Inc., 2004. Ophardt, Charles E. Virtual Chembook. Elmhurst College, 2003. [Online] Available at: elmhurst /~chm/vchembook/174temppres.html en.wikipedia /wiki/Lake_Nyos Cell information the dimension Diameter = 51.43 mm Height of the lid = 21.7 mm Diameter so that the lower section = 50.4 mm Depth of the lower section averaged = 70.5 mm Volume of the Stoddard liquid 100ml Volume of the space (Gas) 104 ml
Hill, Larry Host
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