Adsorción de fenobarbital en carbones activados comerciales. Equilibrio cinético e isotermo de adsorción

Size: px
Start display at page:

Download "Adsorción de fenobarbital en carbones activados comerciales. Equilibrio cinético e isotermo de adsorción"

Transcription

1 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Adsorción d fnobarbial n carbons acivados comrcials. Euilibrio cinéico isormo d adsorción Carlos Albro Ry-Mafull, Julio Csar-Llopiz, Albro Iglsias-Crvo, Dachamir Hoza, Raul Garcia-Gallardo* Insiuo d Cincia y Tcnología d Marials d La Univrsidad d la Habana (Cuba) * Faculad d Física d La Univrsidad d la Habana (Cuba) ** Univrsidad Fdral d Sana Caarina, Florianópolis, (Brasil) *** Laboraorio Rinaldo Guiérrz (Cuba) Rcibido: 8 d marzo d 014. Acpado: 13 d novimbr d 014. Palabras clav: carbón acivado, adsorción, fnobarbial, cinéica, isormas. Kywords: acivad carbon, phnobarbial, adsorpion, kinic, isohrms. RESUMEN. La adsorcion in viro d fnobarbial n fluido gásrico simulado (FGS), ph 1, y 310 K, fu sudiada a parir d rs carbons acivados comrcials: Nori USP XX, Ch3J (ambos usados como anídoos) y M1. Las isormas d adsorción corrspondins furon analizadas por cuaro modlos: Langmuir (Tipo I y II), D-R, Frundlich y Tmkin; la cinéica d adsorción por si modlos: Elovich, psudo-primr ordn, psudo-sgundo ordn, ordn cro, primr ordn, sgundo ordn inraparícula. Los mjors ajuss n ambos casos furon obnidos por l modlo d monocapa d Langmuir y psudo-sgundo ordn rspcivamn. Es modlo cinéico propon u la vlocidad d adsorción sá conrolada por mcanismos d uimisorción nr l adsorbao y l adsorbn. El coficin d corrlación (R ) obnido por Langmuir n odos los casos, fu suprior a El sudio cinéico mosró u la adsorción d fnobarbial n los rs adsorbns alcanzó sus mjors rsulados con l modlo d psudo-scond ordr TI (R > 0.98) y TII (R 0.9). La variación d la nrgía libr d Gibbs (ΔG < 0) xplica l carácr sponáno dl procso d adsorción. Todos los marials sudiados musran poncials capacidads para la adsorción d fnobarbial. ABSTRACT. Th in viro adsorpion of phnobarbial by diffrn adsorbns in simulad gasric fluid (SGF) a ph 1. and 310 K, was drmind on hr yps of commrcial sampls of acivad carbon (AC): Nori USP XX, Ch3J (boh usd as anidos) and M1. Th uilibrium isohrms for h adsorpion of phnobarbial wr analyzd by four modls: Langmuir (Typ I and II), D-R, Frundlich and Tmkin isohrms uaions and h kinic curvs obaind wr fid using svn uaions (Elovich, psudo-firs ordr, psudo-scond ordr, zro ordr, firs ordr, scond ordr and h inraparicl modl) o drmin kinic paramrs of adsorpion. Th psudo-scond ordr and h Langmuir modl rspcivly showd h bs fiings. Th psudo-scond ordr suggrd ha h ovrall ra of h adsorpion was conrolld by chmisorpion which involvd valncy forcs hrough sharing or xchang of lcrons bwn h sorbn and adsorba Th corrlaion cofficins (R ) obaind from Langmuir modl for h linar rgrssion in all cass wr highr han Kinic sudis showd ha h adsorpion of phnobarbial on h hr adsorbns obaind h bs rsuls wih h psudo-scond ordr modl TI (R > 0.98) and TII (R 0.9) rspcivly. Th variaion of h fr Gibbs nrgy (ΔG < 0), in all cass, xplaind h sponanous characr of h adsorpion procss. Dspi h diffrn bhaviors all marials sd hav ponial for raing phnobarbial inoxicaions. INTRODUCTION Whil hisory provids ha h firs sudis on acivad carbon, from h rsarch poin of viw bgan in 1800, i was no unil 1980 ha sablishd sysmaic sudis of h applicaion of his marial in h ara of oxicological rsarch. 1 Th us of acivad carbon o adsorb drugs akn in ovrdos by humans is known only in h broads sns. By dialysis can prvn gasroinsinal absorpion of oxic nrohpaic circulaion and subsun passag 17

2 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. ino h bloodsram. Th xprincs in h clinical sudy (in vivo) of h applicaion of acivad carbon o pains in hospials and poison cnrs suppor hir us bu dos no dlv ino h xplanaion of why and how h procss of adsorpion. This mans ha ar unknown inracions in siu bwn his marial and drugs, so ha hy ar no wll lucidad y. Th in viro or prclinical sudy, which is par of his work, allowd undr crain condiions, sablish a baslin bhavior of h drug (phnobarbial) and is rlaionship wih crain adsorbn (acivad carbon) sag projcing is acion hrough h us of simulad gasric fluids [SGF]. 1-3 Th sarch for an anido o poison h slciv adsorpion is no inndd, bu h vrsail abiliy of adsorpion of hs adsorbns (univrsal characr). Tha is, h sam marial is abl o rain h gras numbr and variy of mdicins or drugs in a complx nvironmn. All of his imposs hr facors which ar dcisiv for h us of hs adsorbns: high chmical puriy, fas adsorpion kinics and high adsorpion capaciy. Ths facors was analyzd in his sudy mploying diffrn uaions known as: Langmuir (TI and TII), Dubinin-Radushkvich, Frundlich and Tmkin, bu is horical foundaions ar diffrn, as o how o addrss h phnomnon of adsorpion, which is gnrally vry conradicory and complx. Kinic sudis ar also addrssd in ordr o clarify which is or may b h mchanisms involvd during h adsorpion of h molcul on acivad carbons phnobarbial. Wll-known modls wr mployd, including: fracional powr, zro ordr, firs ordr, scond ordr, psudo scond ordr (TI, TII, TIII and TIV), Elovich and inraparicl diffusion. 4-7 Phnobarbial was slcd in his sudy du o i is a wll sudid molcul by and hr is updad informaion from in viro sudis, also bcaus i has a long prolongd half lif of 110 h for disposal, which drmind ha popl who ings i in ovrdos may b subjcd o a prolongd coma. Th minimum plasma drug concnraion ha has bn associad wih faal ovrdos was 60 mg/l. In associaion wih alcohol and ohr dprssans Cnral Nrvous Sysm (CNC) is causd dah a doss blow hos ha produc slp MATERIALS AND METHODS Acivad carbon Th acivad carbon mployd hr was h indusrial grad o applicaion in mdical and pharmacuical fild. Nori USP XX (Holland) and Ch3J (Chinss) akn as rfrncs. Th acivad carbon M1 was supplid by h Baracoa Acivad Carbon Plan from Cuban and purifid by acid/basic ramn. 11, 1 All sampls m h sandards s by USP Phnobarbial Phnobarbial [> 99 %] has bn purchasd from Sigma-Aldrich. I is a wak acid pk a = 7.4. Th solubiliy incrass wih incrasing ph. Form sodium sals (sodium phnobarbial), C 1 H 11 N NaO 3 = 54.. Nonionizd drugs adsorb rapidly in h somach by diffusion. Th Food and Drug Adminisraion (FDA) provids spcrophoomry UV in auous acid λ max. = 54 nm, as rfrnc mhod for is uanificaion. Th phnyl group a posiion 5 of phnobarbial givs h spcific anipilpic aciviy. 1,,8,9 Simulad gasric fluid (SGF) Th simulad gasric fluid was prpard according o h USP 30-NF 5, 13 was prpard wih h aciv ingrdin of phnobarbial as dscribd: g of NaCl wr dissolvd in 7 ml of concnrad HCl, nrazing o 1 L wih disilld war fr of CO by adjusing h ph of h soluion o 1.. Phnobarbial concnraion usd was 1000 mg/l. Th calibraion curv of phnobarbial in SGF was prformd using a spcrophoomr UV/VIS [Ulrospc 100 pro from Amrsham Bioscincs]. Th opical dnsiy of all sampls was drmind wih maximum absorbanc a λ max. = 54 nm in h zon of Lambr Br ransmianc. Th calibraion curv was adjusd using h linar rgrssion analysis or las suars uadraic. Each xprimn was prformd by riplica. Bach uilibrium adsorpion xprimns and analyical mhod Sock soluion of phnobarbial a h concnraion of 1000 mg/l was prpard by dissolving phnobarbial in 1 L of SGF radjusd o ph 1.. Th sampls of ACs wr analyzd granulomrically w disribuion, 100 % < 50 mµ. During adsorpion procss h amoun of carbon usd varid in h rang of 0.00 o 0.3 g and was addd o small vials prviously prpard wih phnobarbial dissolvd in SFG would b kp undr consan sirring of 150 r/min for 4 h a room mpraur [37 C ± 0.1 C]. Onc his im nding h sampls wr filrd o spara h solid phas and h liuid xrac 5 ml soluion for rading in h UV/VIS [Ulrospc pro from Amrsham Bioscincs]. Sampling was filrad by rmoving 5 ml aliuos nding h xprimnal. Exprimnal soluions a dsird concnraions wr obaind by diluion of h sock soluion wih SGF pradjusd o ph 1.. Prviously sablishd linar Br- Lambr rlaionships wr usd in h concnraion analysis. For h soluions wih highr concnraions, diluion was ruird o opra h analysis in h Br-Lambr rgion. Absorbanc % radings ar akn from h calibraion curv which drmins h uilibrium concnraion corrsponding o ach of h poins of h isohrm. Th amoun of adsorpion a uilibrium, [mg/g], was calculad by E

3 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. = ( C C ) 0 M V (1) whr: C 0 [mg/ml] iniial concnraion a [ = 0]. C [mg/ml] uilibrium [=4 h]. V [L] volum of h soluion and M [g] is h wigh of carbon. Kinics uilibrium adsorpion During adsorpion procss h amoun of acivad carbon usd was fixd 0.5 g and was addd o 50 ml glass bakr prviously prpard wih phnobarbial dissolvd in SFG (ph = 1.) would b kp undr consan sirring of 150 r/min a room mpraur [37 C ± 0.1 C]. Sampls aliuos wr collcd a diffrn ims and wr filrd wih 0. µm syring filrs. Th rmoval fficincy (RE) was calculad by E. : RE = ( C0 C ) x 100 C 0 whr: C (mg/ml) concnraion of adsorba a im (s). C 0 [mg/ml] iniial concnraion a [ = 0]. () Adsorpion isohrms modls An uilibrium isohrm xprsss h rlaion bwn h amouns of adsorba rmovd from soluion a uilibrium by uni of mass of adsorbn a consan mpraur. In his sudy, uilibrium daa of h phnobarbial adsorpion wr procssing by fiv wo-paramr isohrms including: Langmuir Typ I and II, Frundlich, Dubinin Radushkvich and Tmkin, Linar xprssion of hs isohrm uaions and h way o obain h isohrm paramrs ar givn in Tabl 1. Th daa valus wr plod according o h ruirmns of hs modls. Th linar rgrssion mhod of las suars is usd for drawing h rnd lins. Th characrisic paramrs wr drmind from h linar form corrsponding o ach Tabl 1. Isohrms and hirs linarizd xprssions. Isohrms Exprssions Linar xprssions Plos Langmuir = m K LC 1 K LC + ΔG = RTln Frundlich 1/n = K FC Dubinin- Radushkvich = max (D-R) Tmkin xp Dε [ ] K L TI TII ln ln 1 C C = + K LI m m = + K LII m C 1 = lnk F + n lnc = ln Dε max 1 ε = RTln 1 + C E = [ D] 0.5 RT = BlnKTK + BlnC = ln[ K TKC ] b RT B = b 1 m C vsc 1 1 vs C ln vslnc ln vsε vslnc 174

4 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Kinic modls sudis Th sudis of adsorpion uilibrium ar imporan in drmining h ffcivs of adsorpion; howvr, i is also ncssary o idnify h yps of adsorpion mchanism in givn sysm. In his sudy i was usd diffrns modls, 14-6 o prdic h adsorpion kinic of phnobarbial, (Tabl ) Zro ordr, firs ordr and scond ordr ar h simpls modls and from h plos bwn, vs., ln vs. ln and -1 vs. was obaind h rlaiv kinics paramrs, whr K 0 [mg g -1 s -1 ], [mg g -1 ] ; K 1 [s -1 ], [mg g -1 ] and K [mg -1 s -1 ], [mg g -1 ] rspcivly. Tabl. Kinics modls and hir linarizd xprssions. Kinic modls Exprssions Linar xprssions Plo Zro ordr = K o = K o Firs ordr (K1) = xp Scond ordr Fracional powr = ( 1+ K ) ν FP =K = βln αβ vs ln ln = K1 vs 1 1 = K 1 vs + ln = lnk FP + νln Elovich ( ) 1 1 = ln( αβ) + ln Psudo scond ordr = K p ( 1+ K ) Inraparicl 0.5 =Kp TI TII 1 TIII TIV β 1 = K p p + β 1 1 = + K 1 = K p = K p K =K p 0.5 p 1 ln vsln vsln vs 1 1 vs vs vs 0.5 vs Th fracional powr or modifid Frundlich uaion, whr [mg g -1 ] is h amoun sorbd, K FP [mg g -1 s -ν ] and ν [g mg -1 ] ar consans and ν is posiiv and smallr han on, and [s] is im. This xprssion is gnrally mpirical, xcp for h cas in which ν = 0.5, whr i bcoms indisinguishabl from h parabolic-diffusion uaion. 7 Elovich uaion is on of h mos usful modls for dscribing chmisorpions. I has rcnly bn usd o modl h adsorpion of polluans from auous soluion, whr α [mg g -1 s -1 ] is h iniial sorpion ra and β [g/mg] is rlad o h xn of surfac covrag and acivaion nrgy for chmisorpion. Th paramrs α and β can b obaind from h slop and inrcp of h linar plo of vrsus ln. Psudo scond ordr modl assums ha h sorpion ra is conrolld by chmical sorpion and h sorpion capaciy is proporional o h numbr of sis on h sorbn. This modl has bn succssfully usd in many adsorpion procsss h whol im rang. Whr K p [g mg -1 s -1 ] is h ra consan of scond ordr adsorpion. Th linar plo of / vrsus gav 1/ as h slop and 1/K p as inrcp. This procdur is mor likly o prdic h bhavior ovr h whol rang of adsorpion. Th inraparicl diffusion modl, is basd on h hory proposd by Wbr and Morris 8 was mployd o idnify h diffusion This hory assums an mpirically basd funcional rlaionship, common o mos adsorpion procsss, whr upak varis almos proporionally o ½ han o h conac im. I s was usd o drmina h ra conrolling sp of h adsorpion kinic. Plos of vrsus 0.5 may prsn muli-linariy corrspond o succssiv sps in h adsorpion phnomnon. 9 Th kinic paramrs ar K p [g mg -1 s 0.5 ] and [mg g -1 ] 175

5 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. RESULTS AND DISCUSSION Adsorpion isohrms of phnobarbial. Adsorpion isohrms dscrib h uilibrium rlaionships adsorbn-adsorba and ach poin on i rprsns a condiion of hrmodynamic uilibrium. Hnc, xprssing a spcific bhavior for ach adsorbn, (Figurs 1 o 5). All h isohrms wr concav owards h axis of h adsorpion capaciy [mg/g]. Th isohrms obaind ar yp I according IUPAC classificaion for microporous marials wih rlaivly small xrnal surfac. 30 Phnobarbial can inrac wih h basal carbon plan (non spcific inracion) and wih a paricular polar funcional group on h surfac (spcific inracion). Th surfac OH - groups ar h spcific sis for phnobarbial adsorpion. 8,31 Also, h phnobarbial is a mulifuncional molcul and his maks i asir bing abl o bind o diffrn pars of is srucur, (Figur 1). Mainly by amino groups R-NH and carbonyl -C = O radical pron o h formaion of hydrogn links. As soon raisd suggss ha his yp of link is h mos likly o occur bwn h drug and h surfac of h coals. Th ionizd sa of phnobarbial dcrass hir abiliy o bond wih h hydroxyl groups C-OH o los h amino group hydrogn o form C = N bing h N ngaivly chargd. This condiion may also drmin ha h adsorpion of h molcul of phnobarbial in is favor bu no ionizd a acid ph han a ph basic, bu also incras h solubiliy of inonizado sa, du o h incrasd ph, dcrasd adsorpion capaciy of acivad carbon.,31 Fig 1. Exprimnal daa of adsorpion of Phnobarbial ono Nori USP XX [ ] Ch3J [ ] M1[ ]. Th Langmuir adsorpion modl, dscribs monolayr adsorpion of adsorba ono a homognous adsorbn surfac. Morovr, hr is ngligibl inracion bwn h adsorbd molculs and adsorpion sis having uniform nrgis. Th Langmuir isohrm, [Figur. (a,b)], accouns for surfac-covrag by balancing h rlaiv ras of upak and rlas, h formr bing proporional o h fracion of h surfac is opn, whil h lar is proporional o h fracion ha is covrd. Th uilibrium consan for hos ras is K L [L/mg] which also corrsponds o h Hnry s law cofficin. Whn h fluid concnraion is vry high, a monolayr forms on h adsorbn surfac, having a loading of max [mg/g], (Tabl 3). Th ssnial characrisics of Langmuir uaion can L ( 1+ K C ) b xprssd in rms of dimnsionlss sparaion facor, L 0 R Th rm R L indicas h shap of h isohrm as follows: whn h paramrs, R L > 1 (unfavourabl isohrm), R L = 1 [linar isohrm], 0 < R L < 1 [favourabl isohrm]. In all cass 0 < R L < 1, and valus wr calculad as 7, [NXX], 7, 10-4 [Ch3J] and 7, [M1] rspcivly, which xprsss h isohrm has a favorabl bhavior. 3,33 Th Dubinin-Radushkvich uaion assums ha h amoun adsorbd corrsponding o any adsorba concnraion is a Gaussian funcion of h Polanyi ponial. Th dvlopmn of his hory is basd on h concp of h characrisic curv and Polanyi adsorpion ponial [ E/ T= 0] is applid o dscrib h adsorpion in micropors. 34,35 A linar plo of ln vs. ε [KJ/mol], Figur. c, from h inrcp and slop would giv h valu of max.. [mg/g] and D [mol/kj] Tabl 3. Th calculad valu of E [KJ/mol] is showd in h Tabl 4. 36,37 Characrisic curv, (Figur d), shows ha h valus nrgy bhav in h nvironmn prviously prdicd. To h xn ha h dgr of covrag dcrass o valus of 0.3 h valus of h nrgis can b found bwn 11 o 1 KJ/mol. =

6 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Achiving nrgy valus according o Tabl 6 for dgrs of covrag of 50 %. Th Tmkin modl considrd h ffcs of som indirc adsorbn/adsorba inracions on adsorpion isohrms, (Fig. ) As a rsul of adsorbn/adsorba inracions, h ha of adsorpion of all h molculs in h layr would dcras linarly wih covrag is h corrcion of Langmuir uaion, which is basd on Langmuir uaion and inroducs h influnc of mpraur on h adsorpion, whr B is h Tmkim consan rlad o ha of sorpion and K TK is h uilibrium binding consan ha corrsponds o h maximum binding nrgy [ml/g], (Tabl 3). Th mpirical Frundlich modl: is basd upon h assumpion of mulilayr formaion of adsorba on h hrognous solid surfac of h adsorbn and assums ha h srongr binding sis ar occupid firs and ha h binding srngh dcrass wih h incrasing dgr of si occupaion. Th valus K F (mg/g) (L/g) 1/n and n ar Frundlich consans rlad o adsorpion capaciy and innsiy of adsorpion, rspcivly, (Figur. f) Th lowr fracional valu of 1/n [0 < (1/n) < 1] indicas ha wak adsorpiv forcs ar ffciv on h surfac of acivad carbon. Valu of n > 1 rprsns a favourabl adsorpion condiion. I is considrd suiabl for highly hrognous surfacs. In his sudy, h valus found for n wr > 1, which prov ha h adsorpion is favourabl and procss could b physical in naur, howvr h valu of rgrssion cofficin is no good, (Tabl 3). 38,39 Fig. Adsorpion isohrms from Nori USP XX [ ] Ch3J [ ] M1[ ] fid by: a) Langmuir TII b) Langmuir TII c) D-R d) Characrisic curvs ) Tmkin f) Frundlich. From h Langmuir, Tmkin and D-R uaions, sponaniy of h sysms and h nrgy involvd during h adsorpion procss wr simad. (Tabl 4) 40 Gnrally, h ΔG is in h rang of 0 o 0 KJ/mol and 80 o 400 KJ/mol for physical and chmical adsorpion Th valus of ΔG calculad ar in h rang of physical adsorpion, (Tabl 4). Th valus simad of h molcular cross scional ara of phnobarbial by Langmuir, D-R and Frundlich uaions had bn rpord (Tabl 5) To calculad h molcular cross scional ara of phnobarbial h follow uaion was mployd. AspMW A = 1,,8 0 N K 0, Whr: A sp [m /g] spcific surfac ara of h acivad carbon. MW molcular wigh of phnobarbial. K numbr of mols of phnobarbial adsorbd pr gram of adsorbn a maximum surfac covrag (m.s.c). N 0 Avogadro s numbr. 177

7 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Tabl 3. Consans and corrlaion cofficins of adsorpion isohrms for h adsorpion of phnobarbial ono acivad carbon commrcials. Langmuir Frundlich D-R Tmkin Adsorba TI TII Paramrs R Paramrs R Paramrs R Paramrs R Paramrs R max. = max. = K F = max. = b = Nori USP XX K LI = 1.7 K LII = 53 n = 4.93 D = K TK = 649 Ch3J M1 max. = 78 K LI = 1 max. = 370 K LI = max. = 33 K LII = max.. = 345 K LII = K F = 388 n = K F = 39 n = max. = 337 D = max. = 358 D= b = K TK = b = K TK = 310 Th ffcivnss of h dgr of compacion of h molcul of phnobarbial on h surfac of h acivad carbon is rlad o h opimal disribuion of h sis of adsorpion o h maximum xn of packaging of his molcul. Basd on h adsorpion sudis, h apparn aras occupid pr phnobarbial molcul on h surfacs of hydroxyl groups spacd mor closly han approximaly on pr Å will b inffciv a adsorbing addiional phnobarbial. If h surfac of an acivad carbon is complly and prfcly covrd wih phnobarbial, h ara occupid pr molcul is xpcd o b approximaly 110 o 10 Å. Tabl 4. Fr nrgy chang Gibss [ΔG] calculad by Langmuir and Tmkin uaions and characrisic nrgy [E 0 ] calculad by h Dubinin Radushkvich s uaion. Modls Paramrs Nori USP XX Ch3J M1 Langmuir TI ΔG [KJ/mol] Tmkin ΔG [KJ/mol] D-R E o [KJ/mol] Th drminaion of h ara of h molcul of phnobarbial, (Tabl 5) in hir non-ionizd sa in SGF, shows a br orinaion on h surfac of acivad carbon, in ordr of prioriy wih rgarding o h avrag rlaiv rror as follows: Nori USP XX [6.3 %] >Ch3J [14.5 %]> M1[10.7 %]. Th caus could b a br disribuion of h aciv sis of adsorpion, in boh xural and funcional plan rspcivly. Howvr, wih rlaion o h modls, h simad calculaion shows h following ordr: Frundlich [18.7 %] > Langmuir [16.8 %] > D-R [16 %]. Tabl 5. Esimaing h apparn aking as rfrnc h valu 110 Å ara of h phnobarbial molcul on h surfac of h acivad carbons. Langmuir D-R Frundlich Adsorbn m.c.s [Å ] rlaiv rror [%] m.c.s [Å ] rlaiv rror [%] m.c.s [Å ] rlaiv rror [%] Nori USP XX Ch3J M

8 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Kinics analyss Th adsorpion kinics was xprssd as C 0 -C/C 0 [%] vs. [s] (Figur. 3) Th adsorpion of phnobarbial is ui fas. Th fas adsorpion may b ascribd o h highr driving forc ha maks fas ransfr of phnobarbial o h surfac of adsorbn paricls along wih h availabiliy of h uncovrd ara, h aciv sis and hir disribuion on h adsorbn. Th adsorbns wih hs kinic propris ar vry usful in cass of poisoning sinc hy rain in h solid phas vry rapidly oxic nrohpaic sysm which prvns h sam happns wih a concnraion unfavorabl o h bloodsram. I can b sn walking round h lbow of h curv and immdialy bgins o pass his ara sabilizaion sysm which is characrisic of good affiniy and rapid kinics. Th plaau is rachd vry fas ha longr ims carry no ffciv adsorpion, bu o rach full sauraion in h sysm xcding 3 min. Similar sysms o his ar rpord and in all cass hr is a good fi wih h kinic psudo scond ordr modl Fig. 3 Exprimnal adsorpion daa ono Nori USP XX [ ] Ch3J [ ] M1[ ]a) Kinic xprimnal daa ph 1. and 310 K. b) Psudo scond ordr kinics modl for adsorpion of phnobarbial. c) Exprimnal xp. vs h calculad amoun calc.. Th kinic adsorpion daa wr procssd o sudy h dynamics of h adsorpion procss in rms of h ordr of ra consan, (Tabl 6 and figurs 3 o 5). Rgrssion lins buil o obain h kinic paramrs. Th uilibrium adsorpion capaciis do no agr wih xprimnal valus o h follows modls: Elovich, fracional powr, zro ordr, firs ordr, scond ordr and psudo scond ordr [TII, TIII and TIV] and inraparicl diffusion, du o low corrlaions cofficin [< 0.934]. This confirms ha do no giv a good rgrssion. Th corrlaion cofficin of linarizd form of psudo-scond ordr uaion wr > (Tabl 6). Furhrmor, h calculad calc. [mg/g] valu hrough his modl is clos o h xp. [mg/g] xprimnal wih R > 95. This dmonsrad ha h sorpion of phnobarbial ono acivad carbon is mos approprialy rprsnd by a psudo-scond ordr kinic modl, (Figur 4) This modl supposs ha wo racions ihr in sris or in paralll ar occurring, h firs on is fas and rachs uilibrium uickly and h scond is a slowr racion ha can coninu for a long priod of im. 48 Th produc K p is h iniial sorpion ra rprsnd as, h=k p [mg/g s], and was calculad for ach AC as follow: 0.44 [Nori USP XX], 0.59 [Ch3J] and 0.7 [M1] rspcivly. 179

9 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Fig. 4. Kinic xprimnal daa ( ) and prdicd daa (---) from psudo scond ordr modl TI a ph 1. and T = 37 C. Th produc K p is h iniial sorpion ra rprsnd as, h=k p [mg/g s], and was calculad for ach AC as follow: 0.44 [Nori USP XX], 0.59 [Ch3J] and 0.7 [M1] rspcivly. Th psudo-scond ordr TI modl was h mos suiabl uaion o dscrib h adsorpion of phnobarbial ono acivad carbon. This suggrd ha h ovrall ra of h adsorpion was conrolld by chmisorpion which involvd valncy forcs hrough sharing or xchang of lcrons bwn h sorbn and adsorba. Analyss of h inraparicl modl. Wbr Morris plos show ha h adsorpion procss of phnobarbial is a hr sp procss. Th firs sp, vry shor, corrsponds o a limiaion of adsorpion by xrnal diffusion, (Fig.5) Fig. 5 Wbr-Morris plos for phnobarbial adsorpion ono Nori USP XX [ ] Ch3J [ ] M1[ ]. 180

10 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. Th scond sp corrspond o a gradual adsorpion sag during h inraparicl diffusion is h ra limiing facor. Th hird sp is h final uilibrium in which adsorba concnraion in auous soluion bcoms vry wak, hus slowing down h inraparicl diffusion phnomnon. Th valu of h inrcp indicas whhr xrnal diffusion limis h adsorpion phnomnon: if h sraigh lin passs hrough h origin, inraparicl diffusion is h ra limiing facor; ohrwis xrnal diffusion opras simulanously o conrol h ra of adsorpion. I was obsrvd ha any h linar lins did no pass hrough h origin, which rvald ha h inraparicl diffusion was par h adsorpion bu was no h only ra conrolling sp. Som ohr mchanisms as complxs may also involvd in h ra of adsorpion. Tabl 6. Kinic modls paramrs by linar rgrssion mhod for h sorpion of phnobarbial by acivad carbon. Kinic modls Paramrs Adsorbn Nori USP XX Ch3J M1 Elovich Fracional Powr Zro ordr Firs ordr Scond ordr Psudo scond ordr TI TII TIII TIV Inraparicl α β R K FP ν R K 0 R K 1 R K R K P R K P R K P R K P R x K p 1.76 R x CONCLUSIONS Th Langmuir isohrm modl fid h uilibrium daa br han D-R isohrm modl, rvaling ha h adsorpion of phnobarbial ono h acivad carbon was monolayr adsorpion. Th hrmodynamic paramrs ΔG and E 0 calculad from h xprimnal daa show ha acivad carbons hav inracions boh spcific and non spcific vry similar. This shows ha hs marials bhav agains phnobarbial adsorpion similarly and procss sponanous (ΔG<0). Th adsorpion kinic rsuls dmonsra ha h adsorpion procss of phnobarbial ono acivad carbon follows closly h psudo-scond ordr kinic modl. Wbr Morris plos show ha h adsorpion procss of phnobarbial is a hr sp procss. Also hs plos indica ha h inraparicl diffusion is no h ralimiing sp for h whol racion. ACKNOWLEDGEMENTS Th auhors hank o Programa d Esudans-Convênio d Pós-Graduação (PEC/PG), Coordnação d Aprfiçoamno d Pssoal d Nívl Suprior (Caps), Brazil. 181

11 Rvisa CENIC Cincias Químicas, Vol. 45, pp , 014. REFERENCE BIBLIOGRAPHIC 1. Nuvonn P. and Olkkola K. Oral Acivad Charcoal in h Tramn of inoxicaions. Rol of singl and rpad doss, Mdical Toxicol. 1988:(3): Wurs D, Burk G, Brg M, Vng P, and Scholiuas D. Phnobarbial Adsorpion from Simulad Insinal Fluid, USP., and Simulad Gasric Fluid, USP., by Two Acivad Charcoals. Pharm Rs. 1988:(5): Hogbrg LC, Chrisophrsn AB, Chrisnsn HR, Anglo HR., Comparison of h adsorpion capaciis of an acivad-charcoal yogur mixur vrsus acivad-charcoal war slurry in vivo and in viro, Clin. Toxicol. 005:43: Srividya K,, Kausubha M. Influnc of Tmpraur on Euilibrium, Kinic and Thrmodynamic Paramrs of Biosorpion of Cr(VI) ono Fish Scals as Suiabl Biosorbn, J War Rsourc and Procion. 011: 3: Thio C., Mirna M., Sudaryano Y. and Ismadji S. Adsorpion of basic dy ono acivad carbon prpard from durian shll: Sudis of adsorpion uilibrium and kinics, Chm Eng J. 007:17: Yanhui Li. Prparaion of acivad carbon from Enromorpha prolifra and is us on Caionic rd X-GRL rmoval, Applid Surfac Sci. 011: 57: Qing-Song Liu. Adsorpion isohrm, kinic and mchanism sudis of som subsiud phnols on acivad carbon fibrs, Chm Eng J. 010:157: Aburub A. and Wurs D., Phnobarbial inracions wih drivaizd acivad carbon surfacs. J. Colloid. Inrf. Sci. 006:96: Burk, G., Wurs, D., Brg, M., Vng, P. and Scholiuas D. Surfac Characrizaion of Acivad Charcoal by X-Ray Phoolcron Spcroscopy (XPS): Corrlaion wih Phnobarbial Adsorpion Daa. Pharm Rs. 199:9: Burk, G., Wurs, D., Brg M., Vng P. and Scholiuas, D., Modl slcion for h Adsorpion of Phnobarbial by Acivad Charcoal, Pharm Rs. 1991:8: Carlos RM, Csar JLL, Iglsias A. Esudio comparaivo dl carbón acivado M1 d producción nacional para su uso como anídoo, Rvisa CENIC Cincias Químicas. 007:38: Carlos RM, Iglsias A, García RG, Muñiz RA. Procdimino cnológico para la obnción d carbón acivado calidad USP 30 para uso médico farmacéuico, Rvisa CENIC Cincias Químicas. 010:41: Unid Sad Pharmacopia, USP, USP30-NF5, p. 1701, Acivad Charcoal 14. Ali, B. and Mohammad M., Euilibrium and kinic sudis on fr cyanid adsorpion from auous soluion by acivad carbon, J Hazardous Marials. 009:170: Isaribl, Q. Comparaiv adsorpion of lvodopa from auous soluion on diffrn acivad carbons, Chm Eng J. 009:15: Dominiu, R. al, Adsorpion of complx phnolics compounds on acivad charcoal: Adsorpion capaciy and isohrms, Chm Eng J. 009:148: Mohd, A. and Nazira, K., Euilibrium, kinics and hrmodynamic of Rmazol Brillan Orang 3R dy adsorpion on coff husk-basd acivad carbon. Chm Eng J. 011:170: Xiaodong, X. Adsorpion of bnzoic acid from auous soluion by hr kinds of modifid bnonis, J. Colloid Inrf. Sci. 011:359: I.A.W.Tan, A.L.Ahmad and B.H. Hamd, Adsorpion isohrms, kinics, hrmodynamics and dsorpion sudis of,4,6-richlorophnol on oil palm mpy frui bunch-basd acivad carbon, J Hazardous Marials Hamdi M.H and Ashraf A. El-Sayd, Acivad carbon from agriculural by-producs for h rmoval of Rhodamin-B from auous soluion, J Hazardous Marials. 009:168: Chaim, A. Kinics of Soil Chmical Racions: Rlaionships bwn Empirical Euaions and Diffusion Modls. Soil Sci Soc Am J. 1991:55: Lunhong, A. Rmoval of mhyln blu from auous soluion wih magni loadd muli-wallcarbon nanoub: Kinic, isohrm and mchanism analysis, J Hazardous Marials. 011:198: M.N. Sahmoun, K. Louhab and A. Boukhiar, Kinic and uilibrium modls for h biosorpion of Cr (III) on Srpomycs riosas, Rs J Applid Sci. 008:3: Ho, Y.S., McKay, G., Th kinics of sorpion of divaln mal ions ono sphagnum moss pa, War Rs. 000:34: Ho, Y.S., McKay, G., Psudo-scond ordr modl for sorpion, Proc Biochm. 1999:34: Chiou, M.S., Li, H.Y.Adsorpion bhavior of raciv dy in auous soluion on chmical cross-linkd chiosan bads, Chmosphr. 003:50: Wu, F.C., Tsng, R.L. and Juang, R.S., Kinic modling of liuid phas adsorpion of raciv dys and mal ions on chiosan. War Rs. 001:35:

12 Rvisa CENIC Cincias Químicas, Vol. 45, pp , Chaim, A. Kinics of Soil Chmical Racions: Rlaionships bwn Empirical Euaions and Diffusion Modls. Soil Sci Soc Am J. 1991:55: Y. Onal, Kinics of adsorpion of dys from auous soluion using acivad carbon prpard from was aprico, J Hazardous Marials. 006:137: Wu, F.C., R Tsng, L. and Juang, R.S., Comparisons of porous and adsorpion propris carbons acivad by sam and KOH. J Colloid Inrf Sci. 005:: IUPAC Manual of Symbols and Trminology, Appndix, Par. 1, Colloid and Surfac Chmisry Pur and App. Chm. 3. Dal, E. W., Akham, A., Th Effcs of Surfac Lacon Hydrolysis and Tmpraur on h Spcific and Nonspcific Inracions Bwn Phnobarbial and Acivad Carbon Surfacs. J Pharm Sci. 95 (006). 33. Ali, B. and Mohammad M., Euilibrium and kinic sudis on fr cyanid adsorpion from auous soluion by acivad carbon. J Hazardous Marials. 009:170: Isaribl, Q. al., Comparaiv adsorpion of lvodopa from auous soluion on diffrn acivad carbons, Chm Eng J. 009:15: Sockli, F. al., Por siz disribuions of aciv carbons assssd by diffrn chnius. Carbon. 000:38: McEnany, B., Esimaion of h dimnsions of micropors in acivad carbons using h Dubinin- Radushkvich uaion. Carbon. 1987:5: I.A.W.Tan, A.L.Ahmad and B.H. Hamd, Adsorpion isohrms, kinics, hrmodynamics and dsorpion sudis of,4,6-richlorophnol on oil palm mpy frui bunch-basd acivad carbon. J Hazardous Marials. 009:164: Hong, Z. Sorpion isohrm and kinic modling of anilin on Cr-brnyoni. J Hazardous Marials. 009:167: Mohd, A. and Nazira, K., Euilibrium, kinics and hrmodynamic of Rmazol Brillan Orang 3R dy adsorpion on coff husk-basd acivad carbon. Chm Eng J. 011:170: Lunhong, A., al, Rmoval of mhyln blu from auous soluion wih magni loadd muliwallcarbon nanoub: Kinic, isohrm and mchanism analysis. J Hazardous Marials. 011:198: Indra, D., Vimal, C., Niin Kumar, A. and, Indra M., Rmoval of congo rd from auous soluion by bagass fly ash and acivad carbon: Kinic sudy and uilibrium isohrm analyss, Chmosphr. 005:61: Y. Liu, Is h fr nrgy chang of adsorpion corrcly calculad?. J Chm Eng Daa. 009:54: Li, Y.H. al., Adsorpion hrmodynamic, kinic and dsorpion sudis of Pb + on carbon nanoubs. War Rs. 005:39: Qing-Song, L., al., Adsorpion isohrm, kinic and mchanism sudis of som subsiud phnols on acivad carbon fibrs. Chm Eng J. 010:157: Alxandro M.M. Vargas, André L. Caza, Marcos H. Kunia, Taís L. Silva, Vior C. Almida. Adsorpion of mhyln blu on acivad carbon producd from flamboyan pods (Dlonix rgia): Sudy of adsorpion isohrms and kinic modls. Chm Eng J. 011:168: Li, W., al., Adsorpion of Pb(II) on acivad carbon prpard from Polygonum orinal Linn.: Kinics, isohrms, ph, and ionic srngh sudis. Biorsourc Tch. 010:101: Gomz, M.S. and Larrchi, M.P., Kinic and adsorpion sudy of acid dy rmoval using acivad carbon. Chmosphr. 007:69: Niyaz Mohammad Mahmoodi, Raziyh Salhi and Mokhar Arami, Binary sysm dy rmoval from colord xil waswar using acivad carbon: Kinic and isohrm sudis, Dsalinaion. 011:7: Khambhay, Y., Mody, K., Basha, and Jha, S. B., Kinics uilibrium and hrmodynamic sudis on biosorpion of hxavaln chromium by dad fungal biomass of marin Asprgillus nigr. Chm Eng J. 009:145: Mohd Azmir Ahmad, Rasyidah Alrozi, Rmoval of malachi grn dy from auous soluion using rambuan pl-basd acivad carbon: Euilibrium, kinic and hrmodynamic sudis. Chm Eng J. 011:171:

Journal of Chemical and Pharmaceutical Research, 2014, 6(6): Research Article

Journal of Chemical and Pharmaceutical Research, 2014, 6(6): Research Article Availabl onlin www.jocpr.com Journal of hmical and Pharmacuical Rsarch, 214, 6(6):154-159 Rsarch Aricl ISSN : 975-7384 ODEN(USA) : JPR5 Th adsorpion of nickl ions in auous soluion by chiosan gl bads Muing

More information

Pelagia Research Library

Pelagia Research Library Availabl onlin a www.plagiarsarchlibrary.com Plagia Rsarch Library Dr Chmica Sinica, 04, 5(): 8-3 ISSN: 0976-8505 CODEN (USA) CSHIA5 Sorpion dynamics of acid and basic dys ono acivad carbon drivd from

More information

Department of Chemistry, Thiru Vi Ka Govt. Arts College, Thiruvarur , India. 3

Department of Chemistry, Thiru Vi Ka Govt. Arts College, Thiruvarur , India. 3 Scholars Journal of Enginring and Tchnology (SJET) Sch. J. Eng. Tch., 24; 2(2B):258-263 Scholars Acadmic and Scinific Publishr (An Inrnaional Publishr for Acadmic and Scinific Rsourcs) www.saspublishr.com

More information

Keywords: Adsorption modeling, Crystal violet, Isotherms, Kinetics, Natural adsorbent. 1. INTRODUCTION 2. MATERIALS AND METHODS

Keywords: Adsorption modeling, Crystal violet, Isotherms, Kinetics, Natural adsorbent. 1. INTRODUCTION 2. MATERIALS AND METHODS Inrnaional Journal of Enhancd Rsarch in Scinc Tchnology & Enginring, ISSN: 239-7463 Vol. 4 Issu 6, Jun-25, pp: (55-66), Impac Facor:.252, Availabl onlin a: www.rpublicaions.com Bach Adsorpion Sysm of Hazardous

More information

Equilibrium Kinetics and Isotherm Studies of Cu (II) Adsorption from Waste Water onto Alkali Activated Oil Palm Ash

Equilibrium Kinetics and Isotherm Studies of Cu (II) Adsorption from Waste Water onto Alkali Activated Oil Palm Ash Amrican Journal of Applid Scincs 8 (3): 230-237, 20 ISSN 546-9239 200 Scinc Publicaions Euilibrium Kinics and Isohrm Sudis of Cu (II) Adsorpion from Was War ono Alkali Acivad Oil Palm Ash Zaira Zaman Chowdhury,

More information

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA MTHEMTICL MODEL FOR NTURL COOLING OF CUP OF TE 1 Mrs.D.Kalpana, 2 Mr.S.Dhvarajan 1 Snior Lcurr, Dparmn of Chmisry, PSB Polychnic Collg, Chnnai, India. 2 ssisan Profssor, Dparmn of Mahmaics, Dr.M.G.R Educaional

More information

Removal of Atrazine from Aqueous Solutions Using HNO 3 Treated Oil Palm Shell-Based Adsorbent

Removal of Atrazine from Aqueous Solutions Using HNO 3 Treated Oil Palm Shell-Based Adsorbent Rmoval of Arazin from Aquous Soluions Using HNO 3 Trad Oil Palm Shll-Basd Adsorbn I.A.W. Tan, L.L.P. Lim, and K.T. Lim Absrac Acivad carbon is a prominn marial for adsorpion of arazin, howvr is usag is

More information

Copper (II) Uptake by Adsorption Using Palmyra Palm Nut

Copper (II) Uptake by Adsorption Using Palmyra Palm Nut Availabl onlin a www.plagiarsarchlibrary.com Plagia Rsarch Library Advancs in Applid Scinc Rsarch, 0, (6):66-75 ISSN: 0976-860 CODEN (USA): AASRFC Coppr (II) Upak by Adsorpion Using Palmyra Palm Nu Josph

More information

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o

More information

COD removal from industrial wastewater using activated carbon prepared from animal horns

COD removal from industrial wastewater using activated carbon prepared from animal horns African Journal of Biochnology Vol. 7 (2), pp. 37-3, 5 Novmbr, 2008 Availabl onlin a hp://www.acadmicjournals.org/ajb ISSN 684 535 2008 Acadmic Journals Full Lngh Rsarch Papr COD rmoval from indusrial

More information

JMES, 2017 Volume 8, Issue 3, Page ICMES2016, 1-3 Dec. 2016, Oujda

JMES, 2017 Volume 8, Issue 3, Page ICMES2016, 1-3 Dec. 2016, Oujda Journal of Marials and Environmnal Scincs ISSN: 08-508 Copyrigh 07, Univrsiy of Mohammd Prmir Oujda Morocco JMES, 07 Volum 8, Issu 3, Pag 784-800 hp://www.jmarnvironsci.com/ ICMES06, -3 Dc. 06, Oujda Dcolourizaion

More information

Biosorption of acid dyes using spent brewery grains: Characterization and modeling

Biosorption of acid dyes using spent brewery grains: Characterization and modeling Inrnaional Journal of Applid Scinc and Enginring 2009. 7, 2: 115-125 Biosorpion of acid dys using spn brwry grains: Characrizaion and modling Dr.V.Jaikumar a, *, K.Sahish Kumar b, D.Gnana Prakash b a Dparmn

More information

Biosorption of Azure Dye with Sunflower Seed Hull: Estimation of Equilibrium, Thermodynamic and Kinetic Parameters

Biosorption of Azure Dye with Sunflower Seed Hull: Estimation of Equilibrium, Thermodynamic and Kinetic Parameters Inrnaional Journal of Enginring Rsarch and Dvlopmn -ISSN: 2278-67X, p-issn: 2278-8X, www.ijrd.com Volum, Issu 6 (Jun 24), PP.26-4 Biosorpion of Azur Dy wih Sunflowr Sd Hull: Esimaion of Equilibrium, Thrmodynamic

More information

UPTAKE OF METHYLENE BLUE DYE FROM AQUEOUS SOLUTIONS ONTO CHEMICAL ACTIVATED CARDOON (CYNARA CARDUNCULUS)

UPTAKE OF METHYLENE BLUE DYE FROM AQUEOUS SOLUTIONS ONTO CHEMICAL ACTIVATED CARDOON (CYNARA CARDUNCULUS) Procdings of h 14 h Inrnaional Confrnc on Environmnal Scinc and Tchnology Rhods, Grc, 3-5 Spmbr 2015 UPTAKE OF METHYLENE BLUE DYE FROM AQUEOUS SOLUTIONS ONTO CHEMICAL ACTIVATED CARDOON (CYNARA CARDUNCULUS)

More information

Lecture 2: Current in RC circuit D.K.Pandey

Lecture 2: Current in RC circuit D.K.Pandey Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging

More information

Zinc Chloride-activated Waste Carbon Powder for Decolourization of Methylene Blue

Zinc Chloride-activated Waste Carbon Powder for Decolourization of Methylene Blue Jurnal Tknologi Full papr Zinc Chlorid-acivad Was Carbon Powdr for Dcolourizaion of Mhyln Blu Muhammad Abbas Ahmad Zaini a*, Ting Chiw Ngiik a, Mohd. Johari Kamaruddin a, Sii Hamidah Mohd. Sapar a, Mohd.

More information

Chemically Modified Cornulaca monacantha Biomass for Bioadsorption of Hg (II) from Contaminated Water: Adsorption Mechanism

Chemically Modified Cornulaca monacantha Biomass for Bioadsorption of Hg (II) from Contaminated Water: Adsorption Mechanism Journal of Environmnal Procion, 3, 4, 8-89 hp://dx.doi.org/.436/jp.3.4333 Publishd Onlin March 3 (hp://www.scirp.org/journal/jp) Chmically Modifid Cornulaca monacanha Biomass for Bioadsorpion of Hg (II)

More information

N.A. Adesola Babarinde 1* ; Jonathan O. Babalola 2 ; John Adegoke 1 ; Esther O. George 1 ; Henrietta O. Okeke 1 ; and Ayoola T.

N.A. Adesola Babarinde 1* ; Jonathan O. Babalola 2 ; John Adegoke 1 ; Esther O. George 1 ; Henrietta O. Okeke 1 ; and Ayoola T. Kinic, Euilibrium, and Thrmodynamic Sudis of h Biosorpion of Cd(II),, and from Auous Soluions using Coconu (Cocos nucifra) Laf. N.A. Adsola Babarind * ; Jonahan O. Babalola 2 ; John Adgok ; Eshr O. Gorg

More information

Charging of capacitor through inductor and resistor

Charging of capacitor through inductor and resistor cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.

More information

AMMONIUM ADSORPTION ON NATURAL ZEOLITE (CLINOPTILOLITE): ADSORPTION ISOTHERMS AND KINETICS MODELING

AMMONIUM ADSORPTION ON NATURAL ZEOLITE (CLINOPTILOLITE): ADSORPTION ISOTHERMS AND KINETICS MODELING ISSN 1848-0071 UDC 549.67+544.723=111 Rcivd: 2012-06-15 Accpd: 2012-07-12 Original scinific papr AMMONIUM ADSORPTION ON NATURAL ZEOLITE (CLINOPTILOLITE): ADSORPTION ISOTHERMS AND KINETICS MODELING DAJANA

More information

Cd(II) ADSORPTION FROM AQUEOUS SOLUTION BY ACTIVATED CARBON FROM SUGAR BEET PULP IMPREGNATED WITH PHOSPHORIC ACID

Cd(II) ADSORPTION FROM AQUEOUS SOLUTION BY ACTIVATED CARBON FROM SUGAR BEET PULP IMPREGNATED WITH PHOSPHORIC ACID Volum No. 9 REPRINT pp. 5-58 Cd(II) ADSORPTION FROM AQUEOUS SOLUTION BY ACTIVATED CARBON FROM SUGAR BEET PULP IMPREGNATED WITH PHOSPHORIC ACID Ahm Özr - Fikr Tümn Angrsr. 855 Frising - Grmany Phon: ++9

More information

REMOVAL OF BASIC BLUE 3 AND REACTIVE ORANGE 16 BY ADSORPTION ONTO QUARTENIZED SUGAR CANE BAGASSE

REMOVAL OF BASIC BLUE 3 AND REACTIVE ORANGE 16 BY ADSORPTION ONTO QUARTENIZED SUGAR CANE BAGASSE Th Malaysian Journal of Analyical Scincs, Vol 13 No 2 (29): 185-193 REMOVAL OF BASIC BLUE 3 AND REACTIVE ORANGE 16 BY ADSORPTION ONTO QUARTENIZED SUGAR CANE BAGASSE (Pnyingkiran Basik Biru 3 Dan Rakif

More information

Comparison the New Kinetics Equation of Noncompetitive Sorption Cd(II) and Zn(II) onto Green Sorbent Horse Dung Humic Acid (HD-HA)

Comparison the New Kinetics Equation of Noncompetitive Sorption Cd(II) and Zn(II) onto Green Sorbent Horse Dung Humic Acid (HD-HA) Availabl onlin a BCREC Wbsi: hps://bcrc.undip.ac.id Bullin of Chmical Racion Enginring & Caalysis, 13 (3) 2018, 475-488 Rsarch Aricl Comparison h Nw Kinics Equaion of Noncompiiv Sorpion Cd(II) and Zn(II)

More information

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b 4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs

More information

Modelling the Effect of Dosage on the Biosorption of Ni 2+ Ions onto Luffa Cylindrica

Modelling the Effect of Dosage on the Biosorption of Ni 2+ Ions onto Luffa Cylindrica Journal of Marials Scincs and Applicaions 2018; 4(1): 1-9 hp://www.aasci.org/journal/jmsa ISSN: 2381-0998 (Prin); ISSN: 2381-1005 (Onlin) Modlling h Effc of Dosag on h Biosorpion of Ni 2+ Ions ono Luffa

More information

Investigation on Biosorption of Reactive Blue 140 by Dead Biomass of Aspergillus niger HM11: Kinetics and Isotherm Studies

Investigation on Biosorption of Reactive Blue 140 by Dead Biomass of Aspergillus niger HM11: Kinetics and Isotherm Studies Global Journal of Biochnology & Biochmisry 4 (): 169-178, 9 ISSN 78-466X IDOSI Publicaions, 9 Invsigaion on Biosorpion of Raciv Blu 14 by Dad Biomass of Asprgillus nigr HM11: Kinics and Isohrm Sudis 1

More information

+Modelling the Sorption of Zn 2+ Ions onto Luffa cylindrica

+Modelling the Sorption of Zn 2+ Ions onto Luffa cylindrica Amrican Journal of Scinc and Tchnology 218; 5(1): 1-13 hp://www.aasci.org/journal/ajs ISSN: 2375-3846 +Modlling h Sorpion of Zn 2+ Ions ono Luffa cylindrica Oboh Innocn O. 1, Aluyor Emmanul O. 2 1 Dparmn

More information

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35 MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h

More information

7.4 QUANTUM MECHANICAL TREATMENT OF FLUCTUATIONS *

7.4 QUANTUM MECHANICAL TREATMENT OF FLUCTUATIONS * Andri Tokmakoff, MIT Dparmn of Chmisry, 5/19/5 7-11 7.4 QUANTUM MECANICAL TREATMENT OF FLUCTUATIONS * Inroducion and Prviw Now h origin of frquncy flucuaions is inracions of our molcul (or mor approprialy

More information

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED 006-0 Asian Rsarch Publishing work (ARP). All righs rsrvd. USTEADY FLOW OF A FLUID PARTICLE SUSPESIO BETWEE TWO PARALLEL PLATES SUDDELY SET I MOTIO WITH SAME SPEED M. suniha, B. Shankr and G. Shanha 3

More information

Lecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey

Lecture 1: Growth and decay of current in RL circuit. Growth of current in LR Circuit. D.K.Pandey cur : Growh and dcay of currn in circui Growh of currn in Circui us considr an inducor of slf inducanc is conncd o a DC sourc of.m.f. E hrough a rsisr of rsisanc and a ky K in sris. Whn h ky K is swichd

More information

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an

More information

Batch Biosorption of Metanil Yellow from Aqueous Solution on Egg Membrane: Kinetics and Mechanism

Batch Biosorption of Metanil Yellow from Aqueous Solution on Egg Membrane: Kinetics and Mechanism Inrnaional Journal of Chmical, Marial and Environmnal Rsarch 018, 5 (): 155-164 Rsarch aricl INTERNATIONAL JOURNAL OF CHEMICAL, MATERIAL AND ENVIRONMENTAL RESEARCH An Inrnaional Opn Fr Accss, Pr Rviwd

More information

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT [Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI

More information

A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER

A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc

More information

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 ) AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc

More information

Microscopic Flow Characteristics Time Headway - Distribution

Microscopic Flow Characteristics Time Headway - Distribution CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,

More information

Comparative analysis of the efficiencies of two low cost adsorbents in the removal of Cr(VI) and Ni(II) from aqueous solution

Comparative analysis of the efficiencies of two low cost adsorbents in the removal of Cr(VI) and Ni(II) from aqueous solution African Journal of Environmnal Scinc and Tchnology Vol. 3 (11), pp. 360-369, Novmbr 2009 Availabl onlin a hp://www.acadmicjournals.org/ajs ISSN 1991-637X 2009 Acadmic Journals Full Lngh Rsarch Papr Comparaiv

More information

The Comparison of Red Mud Modification by Acid and Heat for Phosphate Removal from Aqueous Solution

The Comparison of Red Mud Modification by Acid and Heat for Phosphate Removal from Aqueous Solution Inrnaional Journal of Innovaiv Sudis in Scincs and Enginring Tchnology ISSN 2455-4863 (Onlin) www.ijiss.org Volum: 2 Issu: 12 Dcmbr 2016 Th Comparison of Rd Mud Modificaion by Acid and Ha for Phospha Rmoval

More information

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline. Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.

More information

Chemistry 988 Part 1

Chemistry 988 Part 1 Chmisry 988 Par 1 Radiaion Dcion & Masurmn Dp. of Chmisry --- Michigan Sa Univ. aional Suprconducing Cycloron Lab DJMorrissy Spring/2oo9 Cours informaion can b found on h wbsi: hp://www.chmisry.msu.du/courss/cm988uclar/indx.hml

More information

The influences on the Phosphate Removal from Aqueous Solution by using red mud

The influences on the Phosphate Removal from Aqueous Solution by using red mud Inrnaional Journal of Innovaiv Sudis in Scincs and Enginring Tchnology ISSN 2455-4863 (Onlin) www.ijiss.org Volum: 3 Issu: 6 Jun 2017 Th influncs on h Phospha Rmoval from Aquous Soluion by using rd mud

More information

Received 28 May, 2018; Accepted 6 June, 2018.

Received 28 May, 2018; Accepted 6 June, 2018. Vol. (8), pp. xxx-xxx, Augus 8 DOI:.5897/AJEST8.xxxx Aricl Numbr: xxxxx ISSN: 996-786 Copyrigh 8 Auhor(s) rain h copyrigh of his aricl hp://www.acadmicjournals.org/ajest African Journal of Environmnal

More information

Accepted 31 January, 2012

Accepted 31 January, 2012 Inrnaional Journal of Physical Scincs Vol. 7(9), pp. 376-385, 23 Fbruary, 202 Availabl onlin a hp://www.acadmicjournals.org/ijps DOI: 0.5897/IJPS.597 ISSN 992-950 202 Acadmic Journals Full Lngh Rsarch

More information

Use of Surface Modified Silica gel factory Waste for Removal of 2,4-D Pesticide from Agricultural Wastewater: A case study

Use of Surface Modified Silica gel factory Waste for Removal of 2,4-D Pesticide from Agricultural Wastewater: A case study In. J. Environ. Rs., 6(4):995-006, Auumn 202 ISSN: 735-6865 Us of Surfac Modifid Silica gl facory Was for Rmoval of 2,4-D Psicid from Agriculural Waswar: A cas sudy Konr, S., Pal, A. 2 and Adak, A. 3*

More information

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =

More information

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees CPSC 211 Daa Srucurs & Implmnaions (c) Txas A&M Univrsiy [ 259] B-Trs Th AVL r and rd-black r allowd som variaion in h lnghs of h diffrn roo-o-laf pahs. An alrnaiv ida is o mak sur ha all roo-o-laf pahs

More information

Equilibrium sorption of divalent metal ions onto groundnut (Arachis hypogaea) shell: kinetics, isotherm and thermodynamics

Equilibrium sorption of divalent metal ions onto groundnut (Arachis hypogaea) shell: kinetics, isotherm and thermodynamics ISSN: 2410-9649 Babarind Chmisry and Onyiaocha Inrnaional / Chmisry 2(1) (2016) Inrnaional 37-46 2(1) (2016) 37-46 iscinic.org. Equilibrium sorpion of divaln mal ions ono groundnu (Arachis hypogaa) shll:

More information

ERROR ANALYSIS A.J. Pintar and D. Caspary Department of Chemical Engineering Michigan Technological University Houghton, MI September, 2012

ERROR ANALYSIS A.J. Pintar and D. Caspary Department of Chemical Engineering Michigan Technological University Houghton, MI September, 2012 ERROR AALYSIS AJ Pinar and D Caspary Dparmn of Chmical Enginring Michigan Tchnological Univrsiy Houghon, MI 4993 Spmbr, 0 OVERVIEW Exprimnaion involvs h masurmn of raw daa in h laboraory or fild I is assumd

More information

The removal of chloramphenicol from water through adsorption on activated carbon

The removal of chloramphenicol from water through adsorption on activated carbon E3S Wb of Confrncs 9, 0008 (07) EEMS 07 DOI: 0.05/3sconf/0790008 Th rmoval of chloramphnicol from war hrough adsorpion on acivad carbon Joanna Lach,*, Agniszka Ocipa-Kubicka Czsochowa Univrsiy of Tchnology,

More information

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn

More information

H is equal to the surface current J S

H is equal to the surface current J S Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion

More information

Biosorption of Cr (III) from Aqueous Solutions Using Bacterium Biomass Streptomyces rimosus

Biosorption of Cr (III) from Aqueous Solutions Using Bacterium Biomass Streptomyces rimosus In. J. nviron. Rs., 3():9-38, Spring 009 ISSN: 735-6865 Biosorpion of Cr (III) from Aquous Soluions Using Bacrium Biomass Srpomycs rimosus Sahmoun, M.N. *, Louhab, K. and Boukhiar, A. Laboraoir Maériaux,

More information

EE 434 Lecture 22. Bipolar Device Models

EE 434 Lecture 22. Bipolar Device Models EE 434 Lcur 22 Bipolar Dvic Modls Quiz 14 Th collcor currn of a BJT was masurd o b 20mA and h bas currn masurd o b 0.1mA. Wha is h fficincy of injcion of lcrons coming from h mir o h collcor? 1 And h numbr

More information

10. If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve

10. If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve 0. If p and q ar h lnghs of h prpndiculars from h origin on h angn and h normal o h curv + Mahmaics y = a, hn 4p + q = a a (C) a (D) 5a 6. Wha is h diffrnial quaion of h family of circls having hir cnrs

More information

3.9 Carbon Contamination & Fractionation

3.9 Carbon Contamination & Fractionation 3.9 arbon onaminaion & Fracionaion Bcaus h raio / in a sampl dcrass wih incrasing ag - du o h coninuous dcay of - a small addd impuriy of modrn naural carbon causs a disproporionaly larg shif in ag. (

More information

On the Speed of Heat Wave. Mihály Makai

On the Speed of Heat Wave. Mihály Makai On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.

More information

Institute of Actuaries of India

Institute of Actuaries of India Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6

More information

A batch study of adsorption equilibrium and kinetic for methylene blue onto synthesized zeolite

A batch study of adsorption equilibrium and kinetic for methylene blue onto synthesized zeolite Journal of marials and Environmnal Scincs ISSN : 8-58 Copyrigh 7, Univrsiy of Mohammd Prmir Oujda Morocco JMES, 7 Volum 8, Issu, Pag 539-55 hp://www.jmarnvironsci.com/ A bach sudy of adsorpion uilibrium

More information

Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors

Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors Boc/DiPrima 9 h d, Ch.: Linar Equaions; Mhod of Ingraing Facors Elmnar Diffrnial Equaions and Boundar Valu Problms, 9 h diion, b William E. Boc and Richard C. DiPrima, 009 b John Wil & Sons, Inc. A linar

More information

Chemistry and Materials Research ISSN (Print) ISSN (Online) Vol.7 No.5, 2015

Chemistry and Materials Research ISSN (Print) ISSN (Online) Vol.7 No.5, 2015 Chmisry and Marials Rsarch ISSN 4-34 (Prin) ISSN 5-956 (Onlin) Vol.7 No.5, 5 www.iis.org Rmoval o Phnol rom Pain Waswar by Adsorpion ono Phosphoric Acid Acivad Carbon Producd rom Coconu Shll: Isohrmal

More information

Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016

Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016 Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...

More information

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th

More information

Double Slits in Space and Time

Double Slits in Space and Time Doubl Slis in Sac an Tim Gorg Jons As has bn ror rcnly in h mia, a am l by Grhar Paulus has monsra an inrsing chniqu for ionizing argon aoms by using ulra-shor lasr ulss. Each lasr uls is ffcivly on an

More information

whereby we can express the phase by any one of the formulas cos ( 3 whereby we can express the phase by any one of the formulas

whereby we can express the phase by any one of the formulas cos ( 3 whereby we can express the phase by any one of the formulas Third In-Class Exam Soluions Mah 6, Profssor David Lvrmor Tusday, 5 April 07 [0] Th vrical displacmn of an unforcd mass on a spring is givn by h 5 3 cos 3 sin a [] Is his sysm undampd, undr dampd, criically

More information

General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract

General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract Applicaion of Diffrnial... Gnral Aricl Applicaion of diffrnial uaion in - and C- circui analysis by classical mhod. ajndra Prasad gmi curr, Dparmn of Mahmaics, P.N. Campus, Pokhara Email: rajndraprasadrgmi@yahoo.com

More information

The transition:transversion rate ratio vs. the T-ratio.

The transition:transversion rate ratio vs. the T-ratio. PhyloMah Lcur 8 by Dan Vandrpool March, 00 opics of Discussion ransiion:ransvrsion ra raio Kappa vs. ransiion:ransvrsion raio raio alculaing h xpcd numbr of subsiuions using marix algbra Why h nral im

More information

Bioreduction of Thallium and Cadmium Toxicity from Industrial Wastewater using Microalgae

Bioreduction of Thallium and Cadmium Toxicity from Industrial Wastewater using Microalgae A publicaion of CHEMICAL ENGINEERING TRANSACTIONS VOL. 57, 7 Gus Ediors: Sauro Pirucci, Jiří Jaromír Klmš, Laura Piazza, Srafim Bakalis Copyrigh 7, AIDIC Srvizi S.r.l. ISBN 978-88-9568-48-8; ISSN 83-96

More information

Elementary Differential Equations and Boundary Value Problems

Elementary Differential Equations and Boundary Value Problems Elmnar Diffrnial Equaions and Boundar Valu Problms Boc. & DiPrima 9 h Ediion Chapr : Firs Ordr Diffrnial Equaions 00600 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /55 ผศ.ดร.อร ญญา ผศ.ดร.สมศ

More information

4. Which of the following organs develops first?

4. Which of the following organs develops first? Biology 4. Which of h following organs dvlops firs? (A) Livr (C) Kidny (B) Har (D) Noochord 12. During mbryonic priod, animals rpa mbryonic sags of hir ancsors. This law is calld (A) Flokin s law (B) Biognic

More information

Control System Engineering (EE301T) Assignment: 2

Control System Engineering (EE301T) Assignment: 2 Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also

More information

Final Exam : Solutions

Final Exam : Solutions Comp : Algorihm and Daa Srucur Final Exam : Soluion. Rcuriv Algorihm. (a) To bgin ind h mdian o {x, x,... x n }. Sinc vry numbr xcp on in h inrval [0, n] appar xacly onc in h li, w hav ha h mdian mu b

More information

Chapter 12 Introduction To The Laplace Transform

Chapter 12 Introduction To The Laplace Transform Chapr Inroducion To Th aplac Tranorm Diniion o h aplac Tranorm - Th Sp & Impul uncion aplac Tranorm o pciic uncion 5 Opraional Tranorm Applying h aplac Tranorm 7 Invr Tranorm o Raional uncion 8 Pol and

More information

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is 39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h

More information

Mundell-Fleming I: Setup

Mundell-Fleming I: Setup Mundll-Flming I: Sup In ISLM, w had: E ( ) T I( i π G T C Y ) To his, w now add n xpors, which is a funcion of h xchang ra: ε E P* P ( T ) I( i π ) G T NX ( ) C Y Whr NX is assumd (Marshall Lrnr condiion)

More information

Logistic equation of Human population growth (generalization to the case of reactive environment).

Logistic equation of Human population growth (generalization to the case of reactive environment). Logisic quaion of Human populaion growh gnralizaion o h cas of raciv nvironmn. Srg V. Ershkov Insiu for Tim aur Exploraions M.V. Lomonosov's Moscow Sa Univrsi Lninski gor - Moscow 999 ussia -mail: srgj-rshkov@andx.ru

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 8: Electron Configurations and Periodicity Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how

More information

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to: Rfrncs Brnank, B. and I. Mihov (1998). Masuring monary policy, Quarrly Journal of Economics CXIII, 315-34. Blanchard, O. R. Proi (00). An mpirical characrizaion of h dynamic ffcs of changs in govrnmn spnding

More information

The Optimal Timing of Transition to New Environmental Technology in Economic Growth

The Optimal Timing of Transition to New Environmental Technology in Economic Growth h Opimal iming of ransiion o Nw Environmnal chnology in Economic Growh h IAEE Europan Confrnc 7- Spmbr, 29 Vinna, Ausria Akira AEDA and akiko NAGAYA yoo Univrsiy Background: Growh and h Environmn Naural

More information

Single Electron Devices for Logic Applications

Single Electron Devices for Logic Applications Sinl Elcron Dvics for Loic Applicaions Rza M. Rad UMB Basd on pas 45-441 441 of Nanolcronics and Informaion Tchnoloy,, Rainr Wasr Inroducion Scalin down MOSFETs has bn fundamnal in improvin h prformanc

More information

Midterm exam 2, April 7, 2009 (solutions)

Midterm exam 2, April 7, 2009 (solutions) Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions

More information

Electronic Supplementary Information (ESI)

Electronic Supplementary Information (ESI) Elctronic Supplmntary Matrial (ESI) for RSC Advancs. This journal is Th Royal Socity of Chmistry 2015 Elctronic Supplmntary Information (ESI) Bouqut-lik calcium sulfat dihydrat: a highly fficint adsorbnt

More information

Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule

Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -

More information

Physics 160 Lecture 3. R. Johnson April 6, 2015

Physics 160 Lecture 3. R. Johnson April 6, 2015 Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison conomics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 4/25/2011 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 21 1 Th Mdium Run ε = P * P Thr ar wo ways in which

More information

B) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of

B) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of Sampl Final 00 1. Suppos z = (, y), ( a, b ) = 0, y ( a, b ) = 0, ( a, b ) = 1, ( a, b ) = 1, and y ( a, b ) =. Thn (a, b) is h s is inconclusiv a saddl poin a rlaiv minimum a rlaiv maimum. * (Classiy

More information

Modelling of three dimensional liquid steel flow in continuous casting process

Modelling of three dimensional liquid steel flow in continuous casting process AMME 2003 12h Modlling of hr dimnsional liquid sl flow in coninuous casing procss M. Jani, H. Dyja, G. Banasz, S. Brsi Insiu of Modlling and Auomaion of Plasic Woring Procsss, Faculy of Marial procssing

More information

Wave Equation (2 Week)

Wave Equation (2 Week) Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Section 5 Exercises, Problems, and Solutions. Exercises:

Section 5 Exercises, Problems, and Solutions. Exercises: Scion 5 Exrciss, Problms, and Soluions Exrciss: 1. Tim dpndn prurbaion hory provids an xprssion for h radiaiv lifim of an xcid lcronic sa, givn by τ R : τ h- R 4 c 4(E i - E f ) µ fi, whr i rfrs o h xcid

More information

Let s look again at the first order linear differential equation we are attempting to solve, in its standard form:

Let s look again at the first order linear differential equation we are attempting to solve, in its standard form: Th Ingraing Facor Mhod In h prvious xampls of simpl firs ordr ODEs, w found h soluions by algbraically spara h dpndn variabl- and h indpndn variabl- rms, and wri h wo sids of a givn quaion as drivaivs,

More information

Modeling and Experimental Investigation on the Internal Leakage in a CO2 Rotary Vane Expander

Modeling and Experimental Investigation on the Internal Leakage in a CO2 Rotary Vane Expander urdu Univrsiy urdu -ubs Inrnaional Comprssor Enginring Confrnc School of chanical Enginring 2008 odling and Exprimnal Invsigaion on h Inrnal Lakag in a CO2 Roary Van Expandr Bingchun Yang Xi an Jiaoong

More information

ROLE OF SAWDUST IN THE REMOVAL OF IRON FROM AQUEOUS SOLUTION

ROLE OF SAWDUST IN THE REMOVAL OF IRON FROM AQUEOUS SOLUTION AJSTD Vol. 23 Issu 3 pp. 223-229 (2006) ROLE OF SAWDUST IN THE REMOVAL OF IRON FROM AQUEOUS SOLUTION H.B. Snin *, O. Subhi, R. Rosliza, N. Kancono, M.S. Azhar, S. Hasiah, and W.B. Wan Nik Faculty of Scinc

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd

More information

Arturo R. Samana* in collaboration with Carlos Bertulani*, & FranjoKrmpotic(UNLP-Argentina) *Department of Physics Texas A&M University -Commerce 07/

Arturo R. Samana* in collaboration with Carlos Bertulani*, & FranjoKrmpotic(UNLP-Argentina) *Department of Physics Texas A&M University -Commerce 07/ Comparison of RPA-lik modls in Nurino-Nuclus Nuclus Procsss Aruro R. Samana* in collaboraion wih Carlos Brulani* & FranjoKrmpoicUNLP-Argnina *Dparmn of Physics Txas A&M Univrsiy -Commrc 07/ 0/008 Aomic

More information

Lagrangian for RLC circuits using analogy with the classical mechanics concepts

Lagrangian for RLC circuits using analogy with the classical mechanics concepts Lagrangian for RLC circuis using analogy wih h classical mchanics concps Albrus Hariwangsa Panuluh and Asan Damanik Dparmn of Physics Educaion, Sanaa Dharma Univrsiy Kampus III USD Paingan, Maguwoharjo,

More information

Real time estimation of traffic flow and travel time Based on time series analysis

Real time estimation of traffic flow and travel time Based on time series analysis TNK084 Traffic Thory sris Vol.4, numbr.1 May 008 Ral im simaion of raffic flow and ravl im Basd on im sris analysis Wi Bao Absrac In his papr, h auhor sudy h raffic parn and im sris. Afr ha, a im sris

More information

Azimuthal angular correlations between heavy flavour decay electrons and charged hadrons in pp collisions at s = 2.76 TeV in ALICE

Azimuthal angular correlations between heavy flavour decay electrons and charged hadrons in pp collisions at s = 2.76 TeV in ALICE Azimuhal angular corrlaions bwn havy flavour dcay lcrons and chargd hadrons in pp collisions a s = 2.76 TV in ALICE DEEPA THOMAS FOR THE ALICE COLLABORATION INTERNATIONAL SCHOOL OF SUBNUCLEAR PHYSICS ERICE,

More information

Asymptotic Solutions of Fifth Order Critically Damped Nonlinear Systems with Pair Wise Equal Eigenvalues and another is Distinct

Asymptotic Solutions of Fifth Order Critically Damped Nonlinear Systems with Pair Wise Equal Eigenvalues and another is Distinct Qus Journals Journal of Rsarch in Applid Mahmaics Volum ~ Issu (5 pp: -5 ISSN(Onlin : 94-74 ISSN (Prin:94-75 www.usjournals.org Rsarch Papr Asympoic Soluions of Fifh Ordr Criically Dampd Nonlinar Sysms

More information