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:

TC

BAP

i

iivi log Pv in mmHg and T in oC (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

ivii PPyP

Pi partial pressure of component i, atm

yi mole fraction of component i in the gasP= 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

40 ppmy=0.04

Pi=0.04 atm

13.33 ppmy=0.013

Pi =0.013 atm

Sıcaklık

160 F

T = ?

ivii PPyP At equilibrium:

0.013 atm = 0.196 psi

Solution, contd.

40 F

Solution, contd.

• Pvi =0.013 atm = 10.13 mmHgTC

BAP

i

iivi log Pv in mmHg and T in oC (if Table 9.2 is used)

377.219)13.10log(95334.6

943.343,1

log

i

vii

i CPA

BT

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

dx

dCD

A

M

M=mass transfer rate, mol/s

A= area normal to the direction of diffusion, cm2

D=diffusivity, cm2/s

dC/dx=concentration gradient, mol/cm4

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)

• Ci: concentration of pollutant i in the aqeuous phase• http://www.mpch-mainz.mpg.de/~sander/res/henry.html

i

ii p

CH

][Henry’s Law constant =

(M/atm)

Henry’s Law Constants

• Hi vary with T

• Hi has units depending on the Ci and Pi unit.

• The equation eventually becomes nonlinear at high Ci value and no longer valid.

Henry’s Law ConstantsTür HA (298K),mol/Latm -∆H/R, K

SO2 1.23 3120

H2O2 7.45E4 6620

HNO3 2.1E5

HNO2 49 4780

O3 1.13E-2 2300

O2 1.3E-3

NO2 1.0E-2 2500

NO 1.9E-3 1480

CO2 3.4E-2 2420

NH3 75 3400

CH3C(O)O2NO2 2.9 5910

HCl 727 2020

HCHO 6.3E3 6460

NO3 2.1E5 8700

OH. 25 5280

HO2. 2.0E3 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 CO2

and H2O

– SO2 scrubbing to form CaSO4

Chemical Reactions-Kinetics

• Reaction rate: the rate of “disapperance” of reactants or the rate of “apperance” of products.

• Reaction rate =rP =-rR

• rP = rate of generation of product P• rR = 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• rP = kCx

RCyS

• k = rate constant f(T)• CR and CS= concentrations of reactants

(mol/L)• x,y = exponents

Chemical Reactions-Kinetics

• Consider R + S P + Q• rP = kCx

RCyS

• k can be expressed by an Arrhenius equation such as:

K=Ae-E/RT

A: frequency factorE: activation energyR: universal gas constant, in energy unitsT: 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: • dC/dt = QinCin-QoutCout+riV=0V: 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:

• dC/dt = QVCi,V-QV+VCi,V+V+riV=0

If the flow rate is constant and ri in not a function of position then:

dCi/ri=(1/Q)dV

Example 10.4

• The reaction RP 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=5.28E7 s-1 , E=21.53 cal/mol. k at 640 K:

For a CSTR

• dC/dt = QinCin-QoutCout+riV=0 then

LC

CV

kC

CCQCV

r

CCQV

inR

inR

outR

inRoutRinR

R

outRinR

4230)01.0(34.2

)01.01(100

)/1(

)(

,

,

,

,,,

,,

34.2)640*987.1/(53.217)10(28.5 ek

Example 10.4, Solution

For a PFR if Q is constant:

dCR/rR=dCR/-kCR=(1/Q)dV

LV

V

k

Q

V

C

C

k

dVQkC

dC

inR

outR

VC

CR

RoutR

inR

197)01.0ln(34.2

100100

)01.0ln(1

ln1

1

,

,

0

,

,

Thermodynamics

• Reactions can be exothermic (release heat) and endothermic ( heat input)

• These heat exchange changes 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

• SO2 + 1/2O2SO3

• For this gas phase reaction equilibrium constant Kp = PSO3/(PSO2*(PO2)1/2

• Kp=1.53E-5exp(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 = nRT (for a fixed mass of gas)

Ideal Gas Law

PV = nRT

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/molK)

Useful Links

• http://www.aim.env.uea.ac.uk/aim/aim.php