Material Balances on Reactive Processes F&R

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Maximillian Robertson
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1 Material Balaces o Reactive Processes F&R What does a reactio do to the geeral balace equatio? Accumulatio = I Out + Geeratio Cosumptio For a reactive process at steady-state, the geeral balace equatio becomes: 0 = I Out + Geeratio Cosumptio Accouts for material produced or cosumed withi the system The stoichiometric equatio of the reactio imposes costraits o the relative amouts of reactats ad products i the iput ad output streams. CHEE 221 1

2 Material Balaces o Reactive Processes What quatities are coserved? Type of Balace Without Rx With Rx Total mass Total moles Mass of a chemical compoud Moles of a chemical compoud Mass of a atomic species Moles of a atomic species CHEE 221 2

3 Stoichiometry Basics Stoichiometry theory of the proportios i which chemical species combie with oe aother i a reactio 2 SO 2 + O 2 2 SO 3 Stoichiometric Equatio a equatio that relates the relative umber of molecules or moles of reactats ad products (but ot mass!) that participate i a chemical reactio. To be valid, the equatio must be balaced. For example, Are the followig stoichiometric equatios balaced? C 2 H 5 OH + O 2 CO 2 + H 2 O (NH 4 ) 2 Cr 2 O 7 Cr 2 O 3 + N 2 + H 2 O C 4 H /2 O 2 4CO H 2 O» Stoichiometric Coefficiets -1, -13/2, 4, 5» -ve for reactats» +ve for products CHEE 221 3

4 Stoichiometry Basics Stoichiometric Coefficiets ( i ) values precedig each molecular species (i) i a balaced stoichiometric equatio. Values are defied to be positive for products ad egative for reactats. For the reactio, 2 SO 2 + O 2 2 SO 3 2; 1 SO ; 2 O2 SO3 2 Stoichiometric Ratio ratio of stoichiometric coefficiets i a balaced stoichiometric equatio. For the above reactio for example, 2 mol SO 1mol O 2 geerated cosumed Two reactats, A ad B, are i stoichiometric proportio if the ratio (moles of A preset)/(moles of B preset) equals their stoichiometric ratio determied from the balaced stoichiometric equatio. 3 CHEE 221 4

5 Limitig ad Excess Reactats If the reactats are ot preset i stoichiometric proportios, the reactat that would be completely cosumed if a reactio wet to completio is kow as the limitig reactat (LR). The other reactat(s) are termed excess reactat(s). The fractioal excess of the reactat is the ratio of the excess to the stoichiometric requiremet: fractioal excess of A ( ) feed - ( A ) stoich ( A ) or ( A ) stoich ( A feed - ( A ) stoich A ) stoich where, ( A ) feed is the umber of moles of a excess reactat, A, preset i the feed to a reactor ad ( A ) stoich is the stoichiometric requiremet of A, or the amout eeded to react completely with the limitig reactat, eve if the reactio does ot go to completio. Percetage excess of A is 100 times the fractioal excess. CHEE 221 5

6 CHEE Idetifyig the Limitig Reactat 1. Balace the stoichiometric equatio 2. Compare the ratios,, stoich y x feed y x stoich y x feed y x stoich y x feed y x versus If, If, reactat x is the limitig reactat reactat x is ot the limitig reactat

7 Fractioal Coversio Chemical reactios do ot occur istataeously, but ofte proceed quite slowly. Therefore, it is ofte ot practical to desig a reactor for complete coversio of the limitig reactat. Istead, the reactat is separated from the reactor outlet stream ad recycled back to the reactor ilet. The fractioal coversio of a reactat is the ratio of the amout reacted to the amout fed: f A A reacted A fed or f A A reacted A fed If o reactat is specified, the fractioal coversio refers to the limitig reactat (LR). This is usually the case. Fractioal coversio is uitless. The percetage coversio is 100 x f A. The fractio ureacted (i.e., i exit stream) is 1 f A. CHEE 221 7

8 Extet of Reactio-How to Hadle Differet Stoichiometric Ratios The extet of reactio ( or ) is a quatity that characterizes the reactio ad ca sigificatly simplify calculatios. For a cotiuous process at steady-state: i i0 i where, ad are the molar flow rates of species i i the feed ad i0 i outlet streams, respectively (out = i +/- coversio). For a batch process: i i0 i where, i0 ad i are the iitial ad fial molar amouts of species i, respectively. The extet of reactio ( or ) has the same uits as (or ). Every reactio has a sigle, uique value of. CHEE 221 8

9 Example: The biological removal of itroge (i the form of itrate) from wastewater is accomplished by aaerobic bacteria i which methaol is added as a carbo (eergy) source for the cells accordig to the reactio show below: 6NO 3 + 5CH 3 OH 5CO 2 + 3N H 2 O + 6OH If 100 g methaol is added to a water source cotaiig 50 g of itrate, determie which is the limitig reactat ad the % excess of the olimitig reactat. For a fractioal coversio of 30% of the limitig reactat determie the compositio of the molecular species at the ed of the reactio. CHEE 221 9

10 Example: Butae Combustio The complete combustio of butae ca be described as: C 4 H 10 + O 2 CO 2 + H 2 O (always make sure that the stoichiometric equatio is balaced!). For a cotiuous flow process at steady state with a feed of 100 moles of butae per secod, ad 1000 moles of oxyge per secod, determie the compositio of the outlet stream if the fractioal coversio of butae i the burer is 70%. Aalyze the problem usig compoet, extet of reactio, ad elemetal balace methods. CHEE

11 Example: F&R Acryloitrile Productio Acryloitrile is produced i the reactio of propylee, ammoia, ad oxyge: 3 C3H6 NH3 O2 C3H3N 3 H2O 2 The feed cotais 10.0 mole% propylee, 12.0 mole% ammoia, ad 78.0 mole% air. A fractioal coversio of 30.0% of the limitig reactat is achieved. Takig 100 mol of feed as a basis, determie which reactat is limitig, the percetage by which each of the other reactats is i excess, ad the molar amouts of all product gas costituets. CHEE

12 Multiple Reactios Geerally, the sythesis of chemical products do ot ivolve a sigle reactio but rather multiple reactios. The goal is to maximize the productio of the desirable product ad miimize the productio of uwated byproducts. For example, ethylee is produced by the dehydrogeatio of ethae: C 2 H 6 C 2 H 4 + H 2 C 2 H 6 + H 2 2CH 4 C 2 H 4 + C 2 H 6 C 3 H 6 + CH 4 udesirable side reactios This leads to the followig defiitios: mols of desired product formed Yield mols formed if there were o side rxs ad limitig reactat reacted completely Selectivity mols of desired product formed mols of udesired product formed CHEE

13 Multiple Reactios Extet of Reactio The extet of reactio method ca also be applied to multiple reactios, with each reactio havig its ow extet. If a set of reactios takes place i a batch or cotiuous steady-state reactor, we ca write: i i0 vij j where, ij is the stoichiometric coefficiet of substace i i reactio j j is the extet of reactio for reactio j. For a sigle reactio, the above equatio reduces to the equatio reported previously. j CHEE

14 Example: Ethylee Oxide The ethylee oxide reactat used i the productio of ethylee glycol is made by the partial oxidatio of ethylee with excess oxyge over a silver catalyst. The primary reactio is: C 2 H 4 + O 2 C 2 H 4 O Ufortuately some of the ethylee also udergoes complete oxidatio to CO 2 ad water accordig to: C 2 H 4 + O 2 CO 2 + H 2 O For a feed flow of 1000 moles/h cotaiig 10% (mole basis) ethylee, ad a ethylee coversio of 25%, a yield of 8% ethylee oxide is obtaied. Determie the flowrates of the species leavig the reactor. CHEE

15 Example: F&R The reactios C 2 H 6 C 2 H 4 + H 2 C 2 H 6 + H 2 CH 4 take place i a cotiuous reactor at steady-state. The feed cotais 85.0 mole% ethae (C 2 H 6 ) ad the balace ierts (I). The fractioal coversio of ethae is 0.501, ad the fractioal yield of ethylee is Calculate the molar compositio of the product gas ad the selectivity of ethylee to methae productio. CHEE

16 Balaces o Reactive Species Systems that ivolve chemical reactios ca be aalyzed usig oe of three possible methods: (a) Molecular species balaces the approach always used for oreactive systems, but approach is more cumbersome for reactive processes. Balaces must iclude geeratio ad cosumptio terms for each species. (b) Atomic species (C, H, O, etc.) balaces straightforward method. Balaces are of the form iput=output sice atomic species caot be created or destroyed. (c) Extets of reactio Each approach provides the same results, but oe method may be more coveiet tha the other for a give calculatio, so you should be comfortable with both methods. CHEE

17 DFA for Reactive Processes Molecular Species Balaces ad Extet of Reactio: df = ukows + idepedet chemical reactios idepedet molecular species balaces other equatios relatig variables Atomic Species Balaces: df = ukows idepedet atomic species balaces molecular balaces o idepedet oreactive species - other equatios relatig variables Note: F&R develops a separate DFA equatio for molecular species balaces ad extet of reactio techique, but they are the same. F&R gives several good examples of these methods i sectios 4.7 a-e; READ THESE SECTIONS CAREFULLY. CHEE

18 Idepedet Chemical Reactios Chemical reactios are idepedet if the stoichiometric equatio of ay oe of them caot be obtaied by addig ad subtractig multiples of the stoichiometric equatios of others. Cosider the followig equatios: A 2B (1) B C (2) A 2C (3) These three reactios are ot all idepedet, sice (3) = (1) + 2 x (2) CHEE

19 Idepedet Species Balaces Geerally, there are balaces for idepedet species. BUT! If 2 species are i the same ratio to each other wherever they appear i the process, balaces o these species will ot be idepedet equatios. Example: Air is 3.76 mol N 2 /mol O 2, but oly if either oe reacts (e.g. whe evaporatig a volatile compoud i Air). If oe of them does participate i a reactio (e.g. O 2 i a combustio reactio), the these compouds will ot be i the same proportio i differet streams. CHEE

CHEE 221: Chemical Processes and Systems

CHEE 221: Chemical Processes ad Systems Module 3. Material Balaces with Reactio Part a: Stoichiometry ad Methodologies (Felder & Rousseau Ch 4.6 4.8 ot 4.6c ) Material Balaces o Reactive Processes What