Introduction: Introduction. material is transferred from one phase (gas, liquid, or solid) into another.

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Lee Rafe Little
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Introduction: Virtually all commercial chemical processes involve operations

(Scrubbing) Phase diagrams. Estimation of Pressure.

Percentage Saturation Percentage Humidity Multicomponent Gas-liquid Systems.

on a single species, such as freezing, melting, evaporation, and

designed to separate components of mixtures from one Most separations are

under conditions such that most of the remains in its original phase and most

1 Introduction: Virtually all commercial chemical processes involve operations in which material is transferred from one phase (gas, liquid, or solid) into another. rewing a cup of Coffee (Leaching) Removal of sulfur dioxide from a gas stream (Scrubbing) Phase diagrams. Estimation of Pressure. Clausius-Clapeyron Equation. ntoine Equation. pplication of Gibbs Phase rule. Gas Systems: One Condensable component. Raoult s Law, Single Condensable Species Saturation and humidity. Relative saturation(humidity). Molal Saturation Molal Humidity, bsolute Saturation bsolute Humidity, Percentage Saturation Percentage Humidity Multicomponent Gas-liquid Systems. Raoult s Law and Henry s Law. Introduction Virtually all commercial chemical processes involve operations in which material is transferred from one phase (gas, liquid, or solid) into another. Distillation These multiphase operations include all phase-change operations on a single species, such as freezing, melting, evaporation, and condensation, and most separation and purification processes, which are designed to separate components of mixtures from one another. Most separations are accomplished by feeding a mixture of species and into a two-phase system under conditions such that most of the remains in its original phase and most of the transfers into a second phase. The two phases then either separate themselves under the influence of gravity as when gases and liquids or two immiscible liquids separate -or are separated with the aid of a device such as a filter or a skimmer.

exists as a solid, a liquid, and a gas. The most common of these diagram plots pressure on the vertical axis versus temperature on the horizontal axis.

a Phase Diagrams Several familiar terms may be defined with reference to the phase diagram of a substance: 28. 3 VLE curve 6.a Phase Diagrams. If T and P correspond to a point -5 0 00 374.

or boiling point temperature) of the substance at pressure P. Check the Steam Table 2.

If (T, P) falls on the SLE curve, then T is called?? T is the melting point or freezing point at pressure P. 4.

3-5 SLE curve VLE curve 0 SVE 00 374.3 curve 5.

The VLE curve terminates at the critical temperature and critical pressure (T c & P c ).

2 6.a Phase Diagrams 6.a Phase Diagrams phase diagram of a pure substance is a plot of one system variable against another that shows the conditions at which the substance exists as a solid, a liquid, and a gas. The most common of these diagram plots pressure on the vertical axis versus temperature on the horizontal axis. The boundaries between the single-phase regions represent the pressures and temperatures at which two phases may coexist. 6.a Phase Diagrams Several familiar terms may be defined with reference to the phase diagram of a substance: VLE curve 6.a Phase Diagrams. If T and P correspond to a point on the VLE curve, P is the saturation pressure (vapor pressure) of the substance at temperature T, and T is the saturation temperature (boiling point or boiling point temperature) of the substance at pressure P. Check the Steam Table 2. The boiling point of a substance at P = atm is the normal boiling point of that substance. 6.a Phase Diagrams 3. If (T, P) falls on the SLE curve, then T is called?? T is the melting point or freezing point at pressure P. 4. If (T, P) falls on the SVE curve, then P is the vapor pressure of the solid at temperature T, and T is the sublimation point at pressure P SLE curve VLE curve 0 SVE curve 5. The point (T, P) at which solid, liquid, and vapor phases can all coexist is called the triple point of the substance. 6. The VLE curve terminates at the critical temperature and critical pressure (T c & P c ). bove and to the right of the critical point, two separate phases never coexist. 6.b Estimation of Pressure Which compound is more volatile, water or acetone? Volatility: is the degree to which the species tends to transfer from the liquid or solid phase to the vapor phase. The vapor pressure of a species is a measure of its Volatility. The higher the vapor pressure at a given temperature, the greater the volatility of that species at that temperature. The vapor pressure of water can be estimated by:. Thermodynamic Property Tables: a) The vapor pressure of water table. Table.3 page 638 b) Steam table Table.5 page 642 2

6.b Estimation of Pressure 6.b Estimation of Pressure Thermodynamic Property Tables a)the vapor pressure of water table. b)steam table Estimation of Pressure Equations a)clausius-clapeyron Equation.

6 C T 2 = 5.4 C P = 40 mm Hg P 2 = 60 mm Hg Calculate the latent heat of vaporization and the parameter in the the Clausius Clapeyron Equation and estimate P at 42.2 C using this equation. 6.b Estimation of Pressure The vapor pressure of pure substances can be estimated by:.

Δ H ln p = V + RT P vapor pressure. = HV = latent heat of vaporization. = energy required to vaporize one b) ntoine Equation. log P 0 = T + C mole of liquid.

3 6.b Estimation of Pressure 6.b Estimation of Pressure Thermodynamic Property Tables a)the vapor pressure of water table. b)steam table Estimation of Pressure Equations a)clausius-clapeyron Equation. b)ntoine Equation. Page:244 EXMPLE:6.- Pressure Estimation Using the Clausius Clapeyron Equation. The vapor pressure of benzene is measured at two temperatures with the following results: T = 7.6 C T 2 = 5.4 C P = 40 mm Hg P 2 = 60 mm Hg Calculate the latent heat of vaporization and the parameter in the the Clausius Clapeyron Equation and estimate P at 42.2 C using this equation. 6.b Estimation of Pressure The vapor pressure of pure substances can be estimated by:. Thermodynamic Property Tables (e.g.): a) The vapor pressure of water table. Table.3 page 638 b) Steam table Table.5 page Equations (e.g.): a) Clausius-Clapeyron Equation. Δ H ln p = V + RT P vapor pressure. = HV = latent heat of vaporization. = energy required to vaporize one b) ntoine Equation. log P 0 = T + C mole of liquid.,, and C are constants that vary from one substance to another. Intensive vs. Extensive Properties Properties of a system Intensive properties independent of the size of a system Extensive properties depend on the size of the system 5//204 7 Δ HV ln p = R Slope 6.b Estimation of Pressure plot of ln p versus gives a straight line. T 2.40 Δ H 2.20 V Slope = 2.00 R.80 Intercept = T + Intercept ln P ln P* T E E E-03 /T Intensive vs. Extensive Properties Properties are categorized as: Intensive properties: which are independent of the size of a system..,,,,, Extensive Properties whose values depend on the size of the system..,,, y y y y Lecture 3

When two phases are brought into contact with each other, a redistribution of the components of each phase normally takes place species evaporate, condense, dissolve, or precipitate until a state of

Suppose you have a closed vessel containing three components,, and C distributed between gas and liquid phases, and you wish to describe this system to someone else in sufficient detail for that

4 When two phases are brought into contact with each other, a redistribution of the components of each phase normally takes place species evaporate, condense, dissolve, or precipitate until a state of equilibrium is reached in which the temperatures and pressures of both phases are the same and the composition of each phase no longer changes with time. Suppose you have a closed vessel containing three components,, and C distributed between gas and liquid phases, and you wish to describe this system to someone else in sufficient detail for that person to duplicate it exactly. Specifying the system temperature and pressure, the masses of each phase, and two mass or mole fractions for each phase would certainly be sufficient; however, these variables are not all independent once some of them are specified, others are fixed by nature and, in some cases, may be calculated from physical properties of the system components. The variables that describe the condition of a process system fall into two categories: extensive variables, which depend on the size of the system, and intensive variables, which do not. Mass and volume are examples of extensive variables; intensive variables include temperature, pressure, density and specific volume, and mass and mole fractions of individual system components in each phase. The number of intensive variables that can be specified independently for a system at equilibrium is called degree of freedom of the system: DF = 2 + c Π ( non reactive systems ) 28.3 DF = Degrees of freedoom. c = number of chemical species Phase diagram of H 2 O (not drawn to scale) Π = number of phases in a system at equilibriu m. EXMPLE 6.2-: The Gibbs Phase Rule Determine the degrees of freedom for each of the following systems at equilibrium. Specify a feasible set of independent variables for each system.. Pure Water. 2. mixture of liquid, solid, and vapor. 3. vapor-liquid mixture of acetone and methyl ethyl ketone. t the beginning of contact, different T, P, and composition t equilibrium, T and P of both phases are the same and the composition of each phase no longer changes with time. DF = c Π + 2 When two phases are brought into contact with each other, a redistribution of the components of each phase normally takes place species evaporate, condense, dissolve, or precipitate until a state of equilibrium is reached in which the temperatures and pressures of both phases are the same and the composition of each phaseno longer changes with time. Systems containing several components of which only one is capable of existing as a liquid at the process conditions, are common in industrial processes. Separation processes that involve such systems include evaporation, drying, and humidification all of which involve transfer of liquid into the gas and condensation and dehumidification, which involve transfer of the condensable species from the gas to the liquid phase. 4

$If a gas at temperature T and pressure P contains a saturated vapor whose mole fraction is y i (mol vapor/mol total gas), and if this vapor is the only species that would condense if the temperature$

5 TRNSFER OF SPECIES FROM LIQUID INTO THE GS Evaporation Drying Humidification TRNSFER OF THE CONDENSLE SPECIES FROM THE GS TO THE LIQUID PHSE. Condensation Dehumidification It follows that only two out of the three intensive variables T, P, and can be specified and that some relationship must exist that uniquely determines the value of the third variable once the first two have been specified. If a gas at temperature T and pressure P contains a saturated vapor whose mole fraction is y i (mol vapor/mol total gas), and if this vapor is the only species that would condense if the temperature were slightly lowered, then the partial pressure of the vapor in the gas equals the pure-component vapor pressure P i (T) at the system temperature. Water Dry ir T= 75 C P= 760 mm Hg t t=0 0 P = y P = P i ( T ) where: Pi = partial pressure of component i. yi = mole fraction of component i P = total pressure. P i i i 6.3- ( T ) = Pure component vapor pressure at system temperature. Example: 6.3- Composition of a Saturated Gas- System (page 250) ir and liquid water are contained at equilibrium in a closed chamber at 75 o C and 760 mm Hg (.03 bar). Calculate the molar composition of the gas phase. saturated vapor Several important points concerning the behavior of gas-liquid systems and several terms used to describe the state of such systems are summarized here. DF = c Π Dry ir T= 75 C P= 760 mm Hg t t=0 0 When water begins to evaporate, increases This continues until no more water vapor enters the vapor phase and the gas phase is then said to be saturated with water. (saturated vapor).. gas in equilibrium with a liquid must be saturated with the volatile components of that liquid. 2. The partial pressure of a vapor at equilibrium in a gas mixture containing a single condensable component cannot exceed the vapor pressure of the pure component at the system temperature. If, the vapor is saturated: any attempt to increase either by adding more vapor to the gas phase or by increasing the total pressure at constant temperature must instead lead to condensation. Saturated 3. vapor present in a gas in less than its saturation amount is referred to as a superheated vapor. For such a vapor, Superheated

Saturated Superheated Saturated Dew Point of The Gas The partial pressure of a vapor at equilibrium in a gas mixture containing a single condensable component cannot exceed the vapor pressure of the

6 Saturated Superheated Saturated Dew Point of The Gas The partial pressure of a vapor at equilibrium in a gas mixture containing a single condensable component cannot exceed the vapor pressure of the pure component at the system temperature. vapor present in a gas in less than its saturation amount is referred to as a superheated vapor. If a gas containing a single superheated vapor is cooled at constant pressure, the temperature at which the vapor becomes saturated is referred to as the dew point of the gas cooling Superheated Dew Point T of the gas. To achieve condensation in a system containing a superheated vapor To achieve condensation in a system containing a superheated vapor one or more of the variables of Equation must be changed so that the inequality becomes the equality of Raoult's law. This can be done in several ways, such as by increasing the pressure at constant temperature or by decreasing the temperature at constant pressure Increase the pressure at constant temperature Decrease the Temperature at constant pressure or 28.3 Increase P Decrease T Superheated vapor If a gas containing a single superheated vapor is cooled at constant pressure, the vapor becomes saturated. Dew Point: Is the temperature at which the vapor becomes saturated.. To achieve condensation in a system containing a superheated vapor one or more of the variables of Equation must be changed so that the inequality becomes the equality of Raoult's law. This can be done in several ways, such as by increasing the pressure at constant temperature or by decreasing the temperature at constant pressure. 4. If a gas containing a single superheated vapor is cooled at constant pressure, the temperature at which the vapor becomes saturated is referred to as the dew point of the gas Example Material alance round a Condenser stream of air at 00 o C and 5260 mm Hg contains 0.0% water by volume.. Calculate the dew point and degree of superheat of the air. 2. Calculate the percentage of the water vapor that condenses and the final composition of the gas phase if the air is cooled to 80 o C at constant pressure. 3. Calculate the percentage condensation and the final gas-phase composition if, instead of being cooled, the air is compressed isothermally to 8500 mmhg. The difference between the temperature and the dew point of a gas is called the degrees of superheat of the gas. If any two of the quantities,, (or, equivalently, the temperature of the gas and the degrees of superheat) are known, the third quantity may be determined from Equation and a table, graph, or equation relating p and T.. 6

Saturation and Humidity Several quantities besides those introduced in the previous section are commonly used to describe the state and composition of a gas containing a single condensable vapor.

7 Saturation and Humidity Several quantities besides those introduced in the previous section are commonly used to describe the state and composition of a gas containing a single condensable vapor. Saturation refers to any gas-vapor combination Humidity refers specifically to an air-water system. Suppose a gas at a temperature T and Pressure P contains a vapor whose partial pressure P i and whose vapor pressure P i (T). 6.4 MULTICOMPONENT GS-LIQUID -SYSTEMS Gas liquid processes that involve several components in each phase include many chemical reactions, distillation, and transfer of one or more species from a gas to a liquid (absorption or scrubbing) or vice versa (stripping). When multicomponent gas and liquid phases are in equilibrium, a limited number of intensive system variables may be specified arbitrarily (the number is given by the Gibbs phase rule), and the remaining variables can then be determined using equilibrium relationships for the distribution of components between the two phases. In this section we define several such relationships and illustrate how they are used in the solution of material balance problems. % 6.4 MULTICOMPONENT GS-LIQUID -SYSTEMS MULTICOMPONENT GS-LIQUID -SYSTEMS distillation chemical reactions absorption scrubbing stripping % % M i = molecular weight of the vapor. M dry = average molecular weight of the dry gas. When multicomponent gas and liquid phases are in equilibrium, a limited number of intensive system variables may be specified arbitrarily (the number is given by the Gibbs phase rule), and the remaining variables can then be determined using equilibrium relationships for the distribution of components between the two phases. In this section we define several such relationships and illustrate how they are used in the solution of material balance problems. Example: 6.3-3(page 254) Humid air at 75 C,. bar, and 30% relative humidity is fed into a process unit at a rate of 000 m 3 /h. Determine () the molar flow rate of water, dry air, and oxygen entering the process unit, (2) the molal humidity, absolute humidity, and percentage humidity of the air, and (3) the dew point. If you apply the Gibbs phase rule to a multicomponent gas liquid system at equilibrium, you will discover that the compositions of the two phases at a given temperature and pressure are not independent. Once the composition of one of the phases is specified (in terms of mole fractions, mass fractions, concentrations, or for the vapor phase, partial pressures), the composition of the other phase is fixed and, in principle, can be determined from physical properties of the system components. Relationships governing the distribution of a substance between gas and liquid phases are the subject matter of phase-equilibrium thermodynamics and, for the most part fall beyond the scope of this text. However, we will cover several simple approximate relationships that provide reasonably accurate results over a wide range of conditions. Such relationships form the bases of more precise methods that must be used when system conditions require them. 7

8 Suppose is a substance contained in a gas liquid system in equilibrium at temperature T and pressure P. Two simple expressions Raoult's law and Henry's law provide relationships between P, the partial pressure of in the gas phase and x, the mole fraction of in the liquid phase. P = partial pressure of in the gas phase. x = mole fraction of in the liquid phase. P = vapor pressure of pure liquid at temperature T. y = mole fraction of in the gas phase. H (T) = Henry's law constant for in a specific solvent Raoult s Law and Henry s Law Relate y to x x = mole fraction of in the liquid phase. y = mole fraction of in the gas phase. Raoult s Law mixture with high concentration of (x is high) y, y x, x Phase phase Henry s Law mixture with very low concentration of (dilute solution of : x close to 0) The vapor pressure of pure substances can be estimated by:. Thermodynamic Property Tables (e.g.): a) The vapor pressure of water table. b) Steam table 2. Equations (e.g.): a) Clausius-Clapeyron Equation. Δ H ln p = V + RT 6.b Estimation of Pressure H V= = latent heat of vaporization. energy required to vaporize one b) ntoine Equation. log P 0 = T + C mole of liquid. Raoult s Law and Henry s Law Relate y to x x = mole fraction of in the liquid phase. y = mole fraction of in the gas phase. Raoult s Law mixture with high concentration of (x is high) y, y x, x Phase phase Henry s Law mixture with very low concentration of (dilute solution of : x close to 0) Gas- Systems: Example :6.4-2 Raoult s Law and Henry s Law Use either Raoult s Law and Henry s Law to solve the following problems.. gas containing.00 mole % ethane is in contact with water at 20.0 o C and bar. Estimate the mole fraction of dissolved ethane. 2. n equimolar liquid mixture of benzene () and toluene (T) is in equilibrium with its vapor at 30 C. What is the system pressure and the composition of the vapor? Data: Ethane has low solubility in water. Henry s constant for ethane in water at 20 o C is atm

WEEK 6. Multiphase systems

WEEK 6. Multiphase systems WEEK 6 Multiphase systems Multiphase systems P 237. Processes usually deal with material being transferred from one phase (gas, liquid, or solid) to another. 6.1a Phase diagrams F = force on piston Water