Gas Properties and Kinetics Gas and Vapor Gas

Gas Properties and Kinetics

Gas and Vapor • Gas and vapors have some properties in common. – Both are composed of widely separated freely moving molecules. – Both will expand to fill a larger differently sahped container. – Both exert pressure in all directions. The major difference lies in the internal eneryg of the molecules.

Gas and Vapor • Gas if it is far removed from the liquid state. (Usually it means that the temperature of the substance is above its critical point) • Vapor a substance in the gaseous state that is not far from being a liquid. Therefore a vapor can usally be adsorbed onto surfaces or condensed into a liquid relatively easily.

Vapor Pressure • The pressure exerted by a pure component vapor in equilibrium with a flat surface of its pure component liquid at a certain temperature • is a measure of the escaping tendency or volatility of the liquid (liquid’s vapor pressure)

Vapor Pressure • Vapor pressure increases rapidly with an increase in the temperature • The pressure/temperature relatin can be given by Antoine equation: Pv in mm. Hg and T in o. C (if Table 9. 2 is used)

Equilibrium • When a pure liquid is placed in contact with air in a closed space, some of the liquid will volatilize until vapor-liquid equilibrium is established Pi partial pressure of component i, atm yi mole fraction of component i in the gas P= total pressure, atm

Example 10. 1 • An airstream is presently at 1 atm and 160 F. , and contains 40, 000 ppm toluene. To what temperature must the air be cooled to remove two-thirds of the toluene vapor?

Solution • 40, 000 ppm = 4% = 0. 04 mole fraction At equilibrium: 160 F 40 ppm y=0. 04 Pi=0. 04 atm Sıcaklık 0. 013 atm = 0. 196 psi 13. 33 ppm y=0. 013 Pi =0. 013 atm T=?

Solution, contd. 40 F

Solution, contd. Pv in mm. Hg and T in o. C (if Table 9. 2 is used) • Pvi =0. 013 atm = 10. 13 mm. Hg T = 6. 5 C

Comments on the Example • In the design of a heat exchanger to cool the air in the previous example, provide enough surface area to not only cool the air (remove sensible heat) bu also to condense the vapors (remove latent heat) • Usually chilled water or a refigerant might be sufficiently cool to remove enough vapor from the air to meet the pollution control objective • Even cooled to 6. 5 C, the air stream still contains 13. 333 ppm toluene.

Diffusivities • The matter will diffuse spontenously from a region of high concentration to one of low concentration • Fick’s first law describes diffusivity: the proportionality constant between the rate of flux of matter and the concentration gradient M=mass transfer rate, mol/s A= area normal to the direction of diffusion, cm 2 D=diffusivity, cm 2/s d. C/dx=concentration gradient, mol/cm 4 Since the concentration decreases in the direction of diffusion a minus sign is put

Diffusivities • The diffusivity of a particular substance depends on the substance itself and the medium through which it is moving • In all the gas and vapor control processes in which the gas flows past (and contacts) a solid or liquid, a laminar film layer is formed where the pollutant passes from one phase to the other is via molecular diffusion • Diffusion is ofther the rate-limitin step in control processes • More detailed discussion on diffusion will be seen in absorption process

Gas Liquid and Gas-Solid Equilibria • In absorption process, once a gas molecule has diffused thorughthe stagnnt gas film it must be absorbed into the liqud. • Once absorbed, the pollutant then diffuse through a stagnant ilquid film into the bulk liquid • Even thoud the rate of absoprtion is very fast and thus not a limitation, the extent of absorption (solubility) is crucial to the overall objective of mass transfer

Gas Liquid and Gas-Solid Equilibria • Most air pollution control equipment works at a or near atmospheric pressure and with relatively dilute solutions • For dilute solutions, the concentrations of the pollutant in the gas and the liquid are often linearly related (Henry’s Law) Henry’s Law constant = (M/atm) • Ci: concentration of pollutant i in the aqeuous phase • http: //www. mpch-mainz. mpg. de/~sander/res/henry. html

Henry’s Law Constants • Hi has units depending on the Ci and Pi unit. • The equation eventually becomes nonlinear at high Ci value and no longer valid. • Hi vary with T

Henry’s Law Constants Tür HA (298 K), mol/Latm -∆H/R, K SO 2 1. 23 3120 H 2 O 2 7. 45 E 4 6620 HNO 3 2. 1 E 5 HNO 2 49 4780 O 3 1. 13 E-2 2300 O 2 1. 3 E-3 NO 2 1. 0 E-2 2500 NO 1. 9 E-3 1480 CO 2 3. 4 E-2 2420 NH 3 75 3400 CH 3 C(O)O 2 NO 2 2. 9 5910 HCl 727 2020 HCHO 6. 3 E 3 6460 NO 3 2. 1 E 5 8700 OH. 25 5280 HO 2. 0 E 3 6640

Adsorption • Involves a gas-solid equilibrium that is quite similar in principle to the solubility equilibrium in liquid-gas systems • Amount adsorbed on the solid depends on – – – Type of vapor The partial pressure of the vapor The type of solid (adsorbent) The amount of sufrace area available for adsorption Temperature

A Typical Adsorption Isotherm

Adsorption Types • 1) PHYSICAL – Exothermic – Reversible (to separate VOCs from air) • 2) CHEMICAL – İnvolves the breaking and re-forming of bonds – Much more energetic than physical adsorption

Chemical Reactions • Once the pollutant is captured a chemical reaction takes place – In catalytic incineration of VOCs to from CO 2 and H 2 O – SO 2 scrubbing to form Ca. SO 4

Chemical Reactions-Kinetics • Reaction rate: the rate of “disapperance” of reactants or the rate of “apperance” of products. • Reaction rate =r. P =-r. R • r. P = rate of generation of product P • r. R = rate of generation of ractant R • Is the rate constant? • r is a function of » » Reactants concentration T Catalyst or inhibitor existence Light

Chemical Reactions-Kinetics • • Consider R + S P + Q r. P = k. Cx. RCy. S k = rate constant f(T) CR and CS= concentrations of reactants (mol/L) • x, y = exponents

Chemical Reactions-Kinetics • Consider R + S P + Q • r. P = k. Cx. RCy. S • k can be expressed by an Arrhenius equation such as: K=Ae-E/RT A: frequency factor E: activation energy R: universal gas constant, in energy units T: absolute temperature

Example 10. 3

Reactor Models • Two ideal reactor models are commonly used to descirbe real reactors where reactions take place • 1) CSTR (Continous stirred tank reactor • 2) Plug flow

CSTR • Continuous flow with inlet concentration (Cin) through a tank in which the contents are rapidly mixed • Homogenous distribution of the all species • Concentration in the tank equals outlet concentration (Cout) • At steady state: • d. C/dt = Qin. Cin-Qout. Cout+ri. V=0 V: tank volume (L) Q: volumetric flow rate (L/s)

Plug Flow Reactor • Can be described as one dimensional flow through a long tube. • Velocity is constant at all radial position in the tube • Axial dispersion is negligible • The stady-state material balance for component i: • d. C/dt = QVCi, V-QV+DVCi, V+DV+ri. V=0 If the flow rate is constant and ri in not a function of position then: d. Ci/ri=(1/Q)d. V

Example 10. 4 • The reaction R P in Example 10. 3 is to occur isothermally at 640 K in a) CSTR b)PFR. Calculate the required volume of each reactor to give 99% convesion of R to P when the volumetric flow rate is constant at 100 L/s.

Example 10. 4, Solution • From Example 10. 3 A=5. 28 E 7 s-1 , E=21. 53 cal/mol. k at 640 K: For a CSTR • d. C/dt = Qin. Cin-Qout. Cout+ri. V=0 then

Example 10. 4, Solution For a PFR if Q is constant: d. CR/r. R=d. CR/-k. CR=(1/Q)d. V

Thermodynamics • Reactions can be exothermic (release heat) and endothermic ( heat input) • These heat exchanges the temperature of the reacting mix and thus affects the reaction rates • T also affects the volumetric flow rates and concentrations in mol/L unit

Thermodynamics • • • Many chemical reactions do not go to 100% completion An equilibrium depending on the temperature is establisehde between reactants and products SO 2 + 1/2 O 2 SO 3 For this gas phase reaction equilibrium constant Kp = PSO 3/(PSO 2*(PO 2)1/2 Kp=1. 53 E-5 exp(11750/T) (T in Kelvin)

Thermodynamics • • As T increases Kp decreases rapidly at 298 Kp = 2(10)12 at 750 Kp = 97 Note that equilibrium concentrations are not often observed in industrial reactors. Generally the equilibrium constants for exothermic reactions decrease with increasing T while kinetic constants always increase with temperature Therefore it is possible for an optium T to exist for a given reaction. It should be low enough to allow the equilibrium to achieve the desired degree of conversion yet high enough to allow the reactions to proceed rapidly.

Gas Properties and Kinetics • Gas kinetics is a branch of statistical mechanics applied to gases • Applying statistical mechanics to gain a microscopic understanding of gas properties such as pressure, temperature, viscosity, and diffusivity. • Let’s examine gas transportation and interaction between gases and particulates

Ideal Gas Law • Ideal gas law is the result of two experiments and is stated as: • 1)For a given mass of gas held at a constant T, P is inversely proportional to the volume (Boyle’s law) • 2) For a given mass of gas held at a constant pressure, the V is directly proportional to the T (Law of Charles and Gay-Lussac) Given in an Equation: PV = n. RT (for a fixed mass of gas)

Ideal Gas Law PV = n. RT P in atm, V in L, T is in K, n is the number of moles of gas in the gas sample, and R is universal gas constant R = 0. 082 (Latm/mol. K)

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