chapter 19 equations of change for multicomponent systems

7/25/2019 Chapter 19 Equations of Change for Multicomponent Systems

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Chapter 19

Equation of Change for

Multicomponent Systems


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Summary of themulticomponent equations of

change

+

=

entityof

production

ofrate

entityof

additionof

ratenet

entity

ofincrease

ofrate

Entity stands for mass, momentum, or ene


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Summary of themulticomponent uxes

For multicomponent gas mixtures at moderatepressure, MaxwellStefan equations may !eused

"here are additional contri!utions dri#ing

forces other than concentration $Chapter %&'

onlybinaryj A AABDMass =


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Example 19(1) di*usion pro!lem that occurs in the +eld of

microelectronics is the oxidation of silicon

according to the reaction Si -%Si-%( .hen asla! of the material is exposed to gaseous oxygen$species )', the oxygen undergoes a +rstorderreaction with rate constant k1"to produce a layerof the oxide$species /'( "he tas0 is to predict thethic0ness dof the #ery slowlygrowing oxide layer

as a function of time tusing a steadystateapproach $which suggests that the rate of changeof the dissol#ed oxygen content in the layer issmall compared to the rate of reaction'( et theoxygen, whose dissol#ed concentration is cA2atthe free surface of the oxide layer at z3 2, di*use

through the layer as per Fic04s law to reach thereaction surface at z3 das in the +gure !elow(

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http://www.syvum.com/cgi/online/serve.cgi/eng/mass/mass1901.htmlhttp://www.syvum.com/cgi/online/serve.cgi/eng/mass/mass1901.html


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5/(11 "he Equation ofContinuity For Species ) $page

671'


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Example 19(%Consider a fat plate, o porous material, o

thickness and with the other twodimensions very large. Gas B is thepredominant gas in the slab, but gas A isgenerated throughout the slab at a constantrate, A!moles o A"t#hr$. %ne ace o the

slab is impermeable to the gas, while theconcentration o A at the other ace is CA&.

a' )ssuming 8)/is constant and that theconcentration of ) is small, o!tain the di*erentialequation for C)as a function of position(

!' .rite the two !oundary conditions(c'-!tain the expression for C)as a function ofposition(

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671'


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Example 19(

8e#elop expressions for the molefraction pro+le x)$y' and the

temperature pro+le "$y' for the

systems shown in Figure(

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5 9 h i f $


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5/(9 "he Equation of Energy $page672'


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Example 19(

) catalytic tu!ular reactor

5/ 11 "he Equation of


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5/(: "he Equation of Motion $page6&6'


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Example 19(& Catalyticoxidation of car!on monoxide

"he reaction is assumed to occur instantaneously andirre#ersi!ly at the catalytic surface( "he gas composition atthe outer edge of the +lm $at ;32' is presumed 0nown, andthe catalyst surface is at ;3


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Example 19(&


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Equations


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Equations


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Equations


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=esults


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8imensionless >um!ers

8i* i ith ? Ch i l


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8i*usion with ?omogeneous Chemical=eaction of a Solid Sphere in a iquid

) solid sphere $of radius Rand density r' made of

su!stance ) $of molecular weight M' issuspended in a liquid /( Solid ) undergoes a+rstorder homogeneous chemical reaction withrate constant k1444!eing slightly solu!le in liquid/( et cA

2!e the molar solu!ility of ) in /, and

DAB!e the di*usi#ity of ) in /(

a' Esta!lish the concentration pro+le for ) atsteady state $i(e(, when the mass di*usion is inexact !alance with the chemical reaction'(

!' @sing a quasisteadystate approach, deri#e anexpression for the time trequired for the sphereradius to decrease from an initial radius R2to R(


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5/ 11 "he Equation of


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Case StudyDetailed information is on Blackboard.

UND chemical engineering department plans to remodel the power plant for

campus heating. In the power plant pul!eri"ed coal particles are fluidi"ed

within a hot combustion chamber where o#ygen in the air reacts the coal to

produce carbon mono#ide and$or carbon dio#ide gas. %his process produces

energy by the heat of combustion. &h' ()* students ha!e proposed to build

a fluidi"ed coal reactor for a new power plant. If operated at **+,- theprocess will be limited by the diffusion of o#ygen countercurrent to the

carbon dio#ide &2 formed at the particle surface. Assume that the coal is

pure solid with a density of *.2/0*)(kg$m(and that the particle is spherical

with an initial diameter of *.,0*)1+ m *,)Am3. Air 2*4 2and 564 N

23

e#ists se!eral diameters away from sphere. Under the conditions ofcombustion process the diffusi!ity of o#ygen in the gas mi#ture at **+,- is

*.(0*)1+ m2$s.


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>ext "opic

Fluid Machinery

chapter 19 equations of change for multicomponent systems

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