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

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1 Availabl onlin a BCREC Wbsi: hps://bcrc.undip.ac.id Bullin of Chmical Racion Enginring & Caalysis, 13 (3) 2018, Rsarch Aricl Comparison h Nw Kinics Equaion of Noncompiiv Sorpion Cd(II) and Zn(II) ono Grn Sorbn Hors Dung Humic Acid (HD-HA) Rahma Basuki 1*, Ngaijo 1, Sri Juari Sanosa 2, Bambang Rusdiarso 2 1 Dparmn of Chmisry, Faculy of Scinc and Tchnology, Univrsiy of Jambi, Jl. Jambi-Ma Bulian Km 15, Kampus Pinang Masak, Jambi 36136, Indonsia 2 Dparmn of Chmisry, Univrsias Gadjah Mada, Skip Uara PO Box BLS 21, Yogyakara 55281, Indonsia Rcivd: 21 s Novmbr 2017; Rvisd: 28 h Jun 2018; Accpd: 3 rd July 2018; Availabl onlin: 14 h Novmbr 2018; Publishd rgularly: Dcmbr 2018 Absrac Th nw kinics quaion has bn proposd and applid o h sorpion of Cd(II) and Zn(II) ono grn sorbn hors dung humic acid (HD-HA). This work aims o sudy h nw kinics quaion and o compar is paramrs wih Lagrgrn and Ho kinics quaion in h sam sysm. HD-HA was xracd and purifid by Svnson s mhods and hn characrizd by dcion of is funcional group, UV-Vis spcra, and oal acidiy. Th sorpion sudy of his work was invsigad by bach xprimn in ph opimum 5. Langmuir s monolayr sorpion capaciy (b) of Cd(II) and Zn(II) ono HD-HA was and mol.g -1, rspcivly. Langmuir quilibrium consan (K L ) of Cd(II) and Zn(II) sorpion was 5,651 and 6,399 (mol/l) -1, rspcivly. Th kinics paramrs wr drmind by Lagrgrn, Ho, and h nw kinics quaion. Th bs linariy (R 2 ) and h mos fid sorbd mal ion in quilibrium (x ) wih h xprimnal daa was h Ho kinics quaion. Howvr, h corrc valu of sorpion ra consan (k a ) was no rally known, bcaus h k a rsuld from Ho and Lagrgrn kinics quaion can no b compard wih anohr paramr and hr is no scal o masur h corrcnss of his valu of k a. In his work, h corrcnss valu of k a of h nw kinics quaion can b masurd by k a /k d qual o K, and his K should b qual o K L. Th valus of K of Cd(II) (3,452 (mol/l) -1 ) and and Zn(II) (10,898 (mol/l) -1 ) wr qui similar wih K L. Addiionally, h valu of inrcp from linar rgrssion of his nw kinics quaion (Cd(II) = ; Zn(II) = ) was highly similar wih h manually calculaion of -ln(x /ab) (Cd(II) = ; Zn(II) = ). Ths nw kinics quaions also rval ha Lagrgrn sorpion ra consan (k Lag ) is h complx funcion of k a (ab-x 2 )/x ). Copyrigh 2018 BCREC Group. All righs rsrvd Kywords: Nw Kinics Equaion; Non-compiiv Sorpion; Cd(II) and Zn(II); Hors Dung Humic Acid (HD- HA); Lagrgrn sorpion ra How o Ci: Basuki, R., Ngaijo, Sanosa, S.J., Rusdiarso, B. (2018). Comparison h Nw Kinics Equaion of Non-compiiv Sorpion Cd(II) and Zn(II) ono Grn Sorbn Hors Dung Humic Acid (HD-HA). Bullin of Chmical Racion Enginring & Caalysis, 13 (3): (doi: /bcrc ) Prmalink/DOI: hps://doi.org/ /bcrc Inroducion In h hisory of kinics sorpion, prdicing h sorpion ra of sorba ono sorbd for a givn sysm is probably h mos imporan * Corrsponding Auhor. rhmbsq@gmail.com (R. Basuki) Tlp: , Fax: facor in sorpion sysm dsign, wih sorba rsidnc im and h racor dimnsions conrolld by h sysm s kinics [1]. A numbr of sorpion procsss for polluans hav bn sudid in ordr o find a suiabl xplanaion for h mchanisms and kinics for soring ou nvironmn soluions. In ordr o invsiga h mchanisms of sorpion, various kinic bcrc_1774_2018 Copyrigh 2018, BCREC, ISSN

2 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 476 modls hav bn suggsd. In rcn yars, adsorpion mchanisms involving kinicsbasd modls hav bn rpord. Th arlis sudy of kinic sorpion has bn dvlopd sinc pas dcad by Lagrgrn (1898) [2]. Lagrgrn prsnd a firs-ordr ra quaion o dscrib h kinics of liquid-solid phas adsorpion of oxalic acid and malonic acid ono charcoal basd on h sorpion capaciy [3]. I can b prsnd in Equaion (1). dx = k lag ( x x) (1) whr x and x (mg.g -1 ) ar h sorba sorbd a quilibrium and a im (min), rspcivly, and k lag is h psudo-firs ra consan (min -1 ). Eq. (1) was ingrad wih h boundary condiions a = 0 o =, and x = 0 o x = x, o yild linar form in Equaion (2). ln ( x x) = ln( x ) k (2) Taking rgrssion bwn ln(x -x) vs on his quaion gnras sraigh lin, whr slop is k lag and inrcp is ln(x ). To disinguish h kinic quaions, basd on sorpion capaciy from soluion concnraion, Lagrgrn s firs ordr ra quaion has bn calld psudo-firs ordr [3]. In rcn yars, i has bn widly usd o dscrib h adsorpion of polluans from waswar in many diffrn filds. In 1995, Ho dscribd h adsorpion kinics of divaln mal ions ono pa [4], in which h chmical bonding among divaln mal ions and polar funcional groups on pa, such as: aldhyds, kons, acids, and phnolics, ar rsponsibl for h caion-xchang capaciy of h pa. Th main assumpions wr ha h adsorpion may b scond-ordr, and h ra limiing sp, may b chmical adsorpion, involving valn forcs hrough sharing or h xchang of lcrons bwn h pa and divaln mal ions. Th ra xprssion of psudo-scond ordr quaion is: dq = k Ho ( q q ) 2 (3) whr q and q (mg.g -1 ) ar h sorba sorbd a quilibrium and a im (min), rspcivly. k Ho (g.mg -1.min -1 ) is h psudo-scond ra consan. By ingraing h quaion wih h boun-dary condiions a = and q = q, i yilds linar form as in Equaion (4). q = 1 k q + 2 Ho 1 q lag (4) Rgrssion bwn /q vs on his quaion gnras sraigh lin, whr q obaind from slop and k Ho obaind from inrcp. Bfor h Ho kinics quaion, h ohr kinics quaions wr proposd by Elovich [5-6], Richi [7], Sobkowsk and Czrwinski [8], and Blanchard al. [9] quaions. Elovich s quaion was basd on h adsorpion capaciy. This work was sablishd hough h work of Zldowisch by sudying sorpion of carbon monoxid on mangans dioxid. H found ha sorbd gas was dcrasd xponnially wih an incras in h amoun of sorbd gas. I has commonly bn calld h Elovich quaion in h following yars. In 1977, Richi rpord a modl for h adsorpion of gasous sysms. Assumpions wr mad as follows: θ is h fracion of surfac sis which ar occupid by an adsorbd gas, n h numbr of surfac sis occupid by ach molcul of h adsorbd gas, and α is h ra consan. In arlir yars, Sobkowsk and Czrwinski prsnd a ra quaion for h racion of carbon dioxid adsorpion ono a plainum lcrod. Thy concludd ha h firs-ordr is only for low surfac concnraions of a solid. In 1984, Blanchard al. prsnd h ovrall xchang racion of NH4 + ions fixd in zoli by divaln mallic ions. In rcn yars, h Blanchard scond-ordr xprssion has bn usd o dscrib h kinics of xchang procsss bwn sodium ions from zoli A and cadmium, coppr, and nickl ions from soluions [10]. Th quaion and h origin ra can b sn in Tabl 1. In pas wo dcad, h Lagrgrn and Ho kinics quaion domina h sorpion kinics sudy in publicaion. Ths wo kinics sorpion quaion is h mos usd o dscrib kinics and mchanism of sorpion in any sysms [1,11-12]. In many cass, hr was waknss of using Lagrgrn and Ho kinics quaion bcaus h paramrs valu of hs kinic quaions sms o b indpndn and hav no a clar xplanaion bcaus i can no b compard wih anohr paramr and hr is no scal o masur h corrcnss of his paramrs valu. In ohr words, i can b sad ha h kinic paramr is unknown whhr i is rally corrc or no. In Lagrgrn quaion, h inrcp valu (ln x ) from rgrssion of plo ln (x -x) vs. x is nvr b sam wih ln x from manual calculaion of xprimnal daa [13]. Th valu of ra consan (k) was also changd wih changing h iniial concnraion of sorba [14]. Addiionally, hs boh kinics quaion was no drmind d- Copyrigh 2018, BCREC, ISSN

3 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 477 sorpion ra consan (k d ), whr i was imporan in quilibrium sysm. This rsarch proposd h nw kinics quaion o giv anohr viw of kinics sorpion o ovrcom ha waknss. Th paramrs obaind from his nw kinics quaion can b compard wih Langmuir daa o confirm whhr h paramrs wr rally corrc or no. Th nw kinics quaion dvlopd basd on an approach ha sorpion is a dynamic quilibrium procss and during mahmaical drivaion h availabiliy of binding sis of sorbn of Langmuir modl. Th applicabiliy of his nw kinic quaion is hn sd for h sorpion of Cd(II) and Zn(II) on humic acid (HD -HA). Ths mal ion, Cd(II) and Zn(II) known as hir disribuion in soil and war has bn o b srongly associad wih h prsnc of humic subsanc [15]. HA was also rpord o hav widly usd o rduc or limina mals in surfac war [16-20]. HA gnrally xracd from pa soil as sourc. Th usag of pa soil as sourc of HA has ngaiv ffc ha is rlas sord carbon sorag conribud o incrasing h grnhous ffc [21]. Addiionally, i can no b rnwd immdialy. To grning h sourc of HA, i can b usd hors dung ha i has high xisnc bcaus i has a dnsr and rough xur, so i is rarly usd for biogas and organic frilizr [22]. Th valuaion is carrid ou for h comparison h valu of ka of h sorpion of Cd(II) and Zn(II) on HD-HA by Lagrgrn, Ho, and his nw kinics quaion. Th sorpion kinic modl was also valuad for inrcp of Lagrgrn kinics quaion (ln q ) ofn found no qual bwn ln q from xprimn [13] and h valu of k a /k d = K ofn was no sam wih Langmuir quilibrium consan (K L ). Furhrmor, sudy of h nw kinics quaion was also criically discussd in his papr. 2. Marials and Mhods 2.1 Marials All ragn usd in his work ar analyical grad, i.. sodium hydroxid, hydrochloric acid, fluorid acid, silvr nira, barium hydroxid, calcium aca monohydra, cadmium(ii) aca dihydra, and zinc aca dihydra supplid by Mrck Co. Inc. (Grmany) and usd wihou furhr purificaion. HD-HA was xracd from dry hors dung powdr from Banul, Yogyakara. As sandard of humic acid, PS-HA was xracd from pa soil from Musi Banyuasin, Souh Sumara. Exracion and purificaion was prformd according o h procdur of IHSS undr amosphric air [23]. 2.2 Insrumnaions Ths work usd Hanna Insrumn Porabl ph Mr, magnic sirrr, glass war, and Auhor(s) Rf. Origin Ra Linar form Plo Lagrgrn [2,3] Elovich [5,6] Sobkowsk and Czrwinski Tabl 1. Th summary of hisorical kinics quaions [8] dx dq = k ( x x) ln( x x) = ln( x ) klag lag = a q 2.3 q = log Wih o = 1/aa d k( ) n = 1 = k SC ( + 0 ) log0 ln(x -x) vs. q vs. log (+ 0 ) θ/(1-θ) vs. Richi [7] d a( ) n q = 1 = + 1 q q q /(q -q) vs. Blanchard al. [9] dn = K ( n ) 2 0 n 1 1/n 0 -n vs. = K n n 0 Ho [1,4] dq = k ( ) 2 Ho q q q = k q + /q vs. q Ho Copyrigh 2018, BCREC, ISSN

4 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 478 Jna ConrAA 300 Aomic Absorpion Spcroscopy (AAS) o analyz oal mal ions in sampl. Th characrizaions of hors dung humic acid (HD-HA) and pa soil humic acid (PS-HA) wr prformd by Shimadzu FTIR Prsig 21 and UV-visibl spcrophoomr (GBC Cinra 2020). 2.3 Exracion and Purificaion of HD-HA Th sorbn (HD-HA) and h sandard (PS- HA) was xracd and purifid by IHSS procdur [23] undr amosphric air. Abou 1 kg of sampl (dry hors dung powdr) was xracd basd on acidiy using 10 L NaOH 0.1 M, sirrd for 24 hours, and h filra was akn by cnrifugaion a 3000 rpm. Filra was hn addd by 0.1 M HCl o rach ph 1, savd for 12 hours unil wo layrs formd: humic acid (solid boom layr). Th crud HD-HA was sparad by cnrifugaion a 5000 rpm for 15 minus and drid a 60 C. h sam sp conducd o xrac PS-HA from dry pa soil powdr. Crud HD-HA (and PS-HA) was purifid by HCl/HF mhods. Abou 50 g of crud sorbn was addd ino 0.1 M HCl / 0.3 M HF (1:1), sirrd for 24, and h solid was akn by cnrifugd a 5000 rpm. Th Cl - rsidus in h sampl wr rmovd by washing wih disilla war and hn h sampl sd by silvr nira o dc Cl - rsidus. Purifid sampl, which was fr of Cl - ion, was hn drid a 60 C. 2.4 Characrizaion of HD-HA Funcional groups wr drmind by FT- IR prformd by mixing h wll ground of sampl wih spcroscopic grad pll KBr and prssd ino a disk. Th spcrum of absorpion band was analyzd in wavnumbr rangs of 400 o 4000 cm -1. Humificaion characrisd by UV-Vis was prformd by dissolving 10 mg of sampl in ph 11 of 100 ml disilld war. Wll mixd sampl was insrd ino a cuv and analyzd a UV-vision rgion. Ash lvl analysis indicas h minral conn in sampl. Ash lvl was drmind by insring 50 mg of sampl ino a crucibl porclain furnac a 750 C for 4 hours. Each sampl was rpad ripl and nod h changd of wigh bfor and afr furnac. Toal of acidiy was drmind by Barya indirc poniomric iraion mhod [23]. 2.5 Effc of Mdium Acidiy A firs, a sris of 50 ml of Cd(II) was prpard and hir acidiy was adjusd o 2.0, 3.0, 4.0, 5.0, and 6.0 by adding HCl soluion. Ino vry Cd(II) soluion, 10 mg of HD-HA was pourd and hn sirrd for 2 h. Afr filring hrough 100 msh mmbran filr, h concnraion of Cd(II) in suprnaan was analyzd by using AAS. Sampl and blank soluions wr analyzd undr sam condiions. Th amoun of sorbd Cd(II) was considrd o b h diffrnc bwn h iniial and h rmaining amoun in h racing soluion ach im a sampl was analyzd. Th sam procdur was conducd o ph opimum Zn(II). 2.6 Sorpion Isohrm Th sorpion isohrm xprimns wr carrid ou using a bach yp racor using 50 ml of Erlnmyr in a war bah a 25±0.01 C. As much as 10 mg of sorbns was inrac wih and sirrd in 50 ml of soluions conaining h various concnraions of 5, 10, 20, 30, 40, 50, 100, 200, and 400 mg/l of Cd(II) a ph 5.0 for 2 h and hn agd for 24 h. Afr sparaing h suprnaans, h concnraion Cd(II) in h suprnaan was drmind by AAS. Undr h sam condiion wih h sampl soluion, h blank soluion was also analyzd. Th sam procdur was prformd o h Zn(II) sampl. Th daa obaind was hn analyzd by Frundlich and Langmuir isohrm modls. 2.7 Sorpion Kinics Th kinics xprimns also wr carrid ou using a bach yp racor using 50 ml Erlnmyr in a war bah a 25±0.01 C. Th volum of sorpion mdium was 50 ml, h iniial mal ion concnraion was 50 mg/l, h acidiy was adjusd a ph opimum; and o ach soluions, 10 mg of sorbn was addd and hn sirrd coninuously a 10, 15, 20, 25, 30, 35, 40, 45, 60, 90, and 120 minus. Th sampl was immdialy filrd hrough 100 msh filr and h concnraion of Cd(II) in h suprnaan was analyzd by using AAS mhod. Sampl and blank soluions wr analyzd undr h sam condiions. Th amoun of sorbd Cd(II) was considrd o b diffrnc bwn h iniial and h rmaining amoun in h racing soluion ach im a sampl was analyzd. Th sam procdur was prformd o Zn(II) and daa obaind was hn analyzd by hr diffrn sorpion kinics modls, i.. nw kinics quaion, Lagrgrn quaion, and Ho quaion. Copyrigh 2018, BCREC, ISSN

5 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, Rsuls and Discussion 3.1 Characrizaion of HD-HA Th dark brown powdr of sorbn (HD-HA) has h xur and apparanc highly similar o pa soil humic acid (PS-HA). Characrizaion by UV-Vis spcrophoomr of HA is smoohly dcrasd and hr ar no maximum or minimum clar pak wih incrasing wavlngh (Figur 1). Th high absorbanc mrgs in h UV rgion and hn dcras smoohly o visibl rgion. Th smooh parns from his sudy wr similar o Svnson s [23] and Agarwal s al. [24] sudy. Characrisic of amoun aromaic compounds (C=C, C=O, and C=N) and dgr of humificaion wr indicad in rang of nm. High absorbanc of UV spcra of humic subsanc was commonly usd o prdic svral molcular propris of humic subsanc. Prominn rgion should b spo approximaly a 280 nm (A2), nm (A4), and around 600 nm (A6). Th combinaion raios of his absorbanc indicas spcific characr of humic subsancs. A2/4 indicas h porion of lignin and ohr marials a h bginning of h humificaion procss [25]), whil A2/6 indicas h porion bwn humificad and nonhumificad marial. A4/6 indicas dgr of condnsaion and polymrizaion of aromaic compounds (can b usd o prdic humificaion indx) (Tabl 1). This combinaion raio of UV-Vis spcra of HD-HA and PS-HA can b usd o prdic h humificaion indx (mauriy) ha any corrlaion o conn of acidiy and sorpion capaciy. Th lowr valu of A2/6 and A4/6 rprsns a highr dgr of aromaic and mauriy of organic marial. Th raio A4/6 for HA should b lowr han 5, whil FA is rangd 6 o 8.5 [23]. A4/6 raio of PS-HA was highr han 5 (6.25) indicaing h pa soil from Musi Banyuasin sill young and humificaion sill occur. Th A4/6 raio of HD-HA was also highr han sandard and PS-HA. I is indicad ha hors dung usd in his work has no bn humificad wll. Succss purificaion maks clar h clay minrals, silicas, and disurbing mal impuriis from sorbn [23], which is covr h surfac of HD-HA. This impuriis inrac wih aciv si of HD-HA, -COOH and phnolic OH which affcd h oal acidiy and h COOH and phnolic O conn. Th lowr ash lvl indicas ha marial hav low of impuriis. Th yild of ash lvl of sorbn bfor purificaion wr abov 5 % (w/w), howvr afr purificaion procss, h rsuls of ash lvl of PS-HA and HD-HA dcras blow 5 % i and 1.20 (% w/w), rspcivly. Toal acidiy of HD-HA was also incrasd afr purificaion procss, bu i is sill blow h oal acidiy of PS-HA and rfrnc HA [23]. Th lowr oal acidiy agrs wih fac ha hors dung marial usd in his sudy is akn from opn ara and only abou 3 monh ags (Tabl 2). This rsul indicas h succssfulnss of purificaion procss. Comparison h FT-IR spcra of crud HD- HA, purifid HD-HA, crud PS-HA and purifid PS-HA showd ha boh of HD-HA and PS-HA hav high similariis in paricular wav numbr absorpion band of h funcional group (Figur 1). Thr ar fiv characrisic band of HA according o HA rfrnc [23], i cm -1 indicas O H bond wih hydrogn bond occurs inr molcul of aciv si Figur 1. Th characrisic parn of UV-Vis absorbanc (lf) and FT-IR spcra of HD-HA and PS- HA (righ) Copyrigh 2018, BCREC, ISSN

6 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 480 HA ha maks h band widr, abou 2900 cm -1 indicas C H aliphaic srching, abou 1720 cm -1 indicas carbonyl group of COOH, abou 1600 cm -1 indicas phi of aromaic alkn and aromaic rings of quinons which form hydrogn bond wih OH group, and abou 1200 cm -1 indicas srching of C O from COOH group. Addiional sharp pak commonly mrgd a 2330 cm -1 which is no com from HA, bu com from C=O srching of carbon dioxid rappd in KBr pll. Similar band as a characrisic of HA was also rpord by Baro and Bagla in sudy of xracion HA from dry cow dung powdr [26,28]. 3.2 Effc of Mdium Acidiy Acidiy is a funcion of amoun H + in soluion mdium. I has high ffc on h form of chmical subsanc or mal subsanc in aquous mdium [27]. Lowr ph (high acidiy) affcs in dcrasing h mal ions ha aachd in aciv si of sorbn as a rsul of compiion bwn H + which h consquncs is high concnraion of unsorbd mal ions in soluion. Th rsul off his work indicas ha h concnraion of boh sorbd Cd(II) and Zn(II) nd o incrass wih h dcrasing of mdium acidiy (Figur 2). A highr ph mdium, amoun of hydronium (H + ) ion was proonad and ld o srong inracion among hydrogn and funcional group of inrmolcular HD-HA. In ohr word, h aciv si of HD- HA was dcd in COOH or OH form which caus h surfac has posiivly chargd and lads o rpulsion bwn mal ions and funcional group of HD-HA. Causd by his rpulsion, h mal ions (Cd and Zn) which sorbd in HD-HA was vry low. This condiion maks aachd mal ions on sorbn vry low. Thr is no significan diffrncs bwn sorbd Cd(II) and Zn(II), alhough h Zn(II) sms lil highr sorbd han h Cd(II). This rsul can b compard o prvious sudy ha h Zn(II) was sorbd highr han Cd(II). Whn h ph of mdium acidiy highr han 2, HD- HA s aciv si, -COOH and phnolic OH sar o b dproonad ha ld o wakning in hydrogn bonds and h surfac covr wih ngaiv charg. As a rsul, mal ion, Cd(II), and Zn(II) ar asir o inrac wih aciv si of HD-HA and maks mal ion highly sorbd Tabl 2. Th absorbanc raio of UV-Vis spcra, ash lvl, and oal acidiy of HD-HA compard o PS-HA and Humic Acid rfrnc Marials A280/A472 (A2/4) Absorbanc Raio A280/A664 (A2/6) A472/A664 (A4/6) Ash Lvl (% w/w) HD-HA PS-HA Toal Acidiy (mol.kg -1 ) Humic Acid [14] Fulvic Acid [14] Figur 2. Effc of mdium acidiy on h disribuion of Zn(II) (lf) and Cd(II) (righ) in h prsnc of HD-HA Copyrigh 2018, BCREC, ISSN

7 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 481 on sorbn. This condiion is good for mal ion, bu i is poor for HD-HA bcaus i bgins o dissolvd and o form liquid phas, and i is hard o b sparad. Opimum ph was balanc condiion bwn mal ions and HD-HA (sorbn) condiion. Th opimum ph of sorpion Zn(II) and Cd(II) was occurrd in ph 5. Th opimum ph 5 was also suggsd by Rahmawai and Sanosa [18] and Burhan [28]. 3.3 Sorpion Isohrm Drminaion of capaciy and sorpion nrgy of mal ions on HD-HA was plod using Langmuir and Frundlich isohrm modls. Langmuir isohrm modl was drivd from modl dscribd as follow: A + S A*S A im = 0 : a=c o b - Sorbd : m m m In quilibrium: a-m=c b-m m whr a = C o is iniial concnraion of mal ion A (mol/l); b is sorpion capaciy (mol/g); m is amoun mal ion A sorbd pr gram sorbn, S in quilibrium (mol/g); and a-m=c is concnraion mal ion A in quilibrium (mol/l). From ha modl, quilibrium consan, K, can b wrin in Equaion (5). K = A* S m = A S ( b m) C Equaion (5) can b rarranging: KCb m = 1+ KC (5) (6) Linar form of Equaion (6) was wll-known calld as Langmuir isohrm [29] modl ha can b wrin as: C 1 1 = + C m Kb b (7) Frundlich isohrm [30] form is m = K F C n. This modl can b wriing as linar form: log m = log K + 1 log n F C (8) whr C is h quilibrium concnraion in soluion; b is Langmuir s sorpion capaciy; K rprsns Langmuir s consan of quilibrium; m is mal sorbd pr gram sorbn a quilibrium; B is Frundlich s sorpion capaciy and, n is consans. Th applicaion of h wo modls was rsuld h sorpion paramrs shown in Figur 3. Th Langmuir isohrm is dsignd for monolayr sorpion of spcis on a homognous surfac wih h sam sorpion nrgy for all aciv si rgardlss of h dgr of covrag, whil h Frundlich is for mulilayr sorpion on hrognous surfac wih h frquncy of sis associad wih fr nrgy of sorpion dcras xponnially wih h incras of fr nrgy. Sorpion capaciy of Cd(II) and Zn(II) was and mol/g, rspcivly. Compard wih Cd(II), Zn(II) hav highr sorpion capaciy (Tabl 3). Sorpion capaciy of Cd(II) on HD- HA is lss compard wih anohr HA from ohr sourc as sudid by Rahmawai and Sanosa (HA from Rawa Pning pa soil, b = mol/g) [18] and highr han Burhan (HA from dry cow dung powdr, b = mol/g) [28]. This can b xplaind by wo rason, firsly aomic radii for Cd(II) acually highr han Zn(II) (1.4 Å and 1.1 Å, rspcivly), bu in hydra condiions Zn(II) has highr radii han Cd(II) (6 Å and 5 Å, rspcivly). On of h sorbd mchanism mal ions ono funcional group in HD-HA is war bridg [27]. This mchanism can b provd from raio monolayr sorpion capaciy of Cd(II) and Zn (II) closly mach wih raio hydra radii for Cd(II) and Zn(II), ha was 5 : 6. Scondly, Zn (II) has srongr acid characrisic han Cd (II), so ha Zn(II) was mor suiabl wih funcional group of HD-HA which has mor hard bas characrisic. I is provd from comparison bwn Langmuir monolayr sorpion capaciy and Frundlich mulilayr sorpion capaciy for Cd(II) is 19.9 ims grar and Zn (II) is 64.6 ims grar. Addiionally, Zn(II) has grar sorpion nrgy han Cd(II) (Tabl 4). Humic acid has many aciv sid as O- (nola), -COOH (carboxylic), -NH (amid), -O- (hr), C=O (carbonyl), c. Among h aciv sid, h oxygn conaining funcional groups such as -O- and -COO - is h mos raciv funcional groups [27]. FT-IR sudis showd ha -COO - plays an imporan rol in mal complxaion. If w assum -COO - is h rsponsibl group for h adsorpion of mal ions, hn h capaciy (monolayr or mononrgy) Langmuir adsorpion may indica h numbr of his group. Bcaus mal ions occupy h aciv si, h srongs inracion occupis firs and hn h aciv sid wih lowr nrgy. Manwhil, h capaciy (mulilayr or muli-nrgy) indicas h Frundlich adsorp- Copyrigh 2018, BCREC, ISSN

8 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 482 (a) (b) (c) (d) Figur 3. Frundlich isohrm sorpion of Zn(II) (a) and Cd(II) (c) ono HD-HA and Langmuir isohrm sorpion of Zn(II) (b) and Cd(II) (d) ono HD-HA Marials Tabl 3. Funcional group conn and oal acidiy of varid HA HD-HA (This Work) PS-HA (This Work) Toal Acidiy (cmol/kg) 415,3 565,0 Carboxyla (cmol/kg) 166,3 208,2 -OH phnolic (cmol/kg) 249,0 356,8 Cow Dung-HA [20] 96,7 7,3 89,4 PS-HA [7] 715,8 326,6 426,2 PS-HA [14] 560,0-890,0 150,0 570,0 20,0 490,0 Tabl 4. Sorpion capaciy (b), nrgy (E), and consan of quilibrium (K) obaind from Langmuir isohrm as wll as sorpion capaciy (B) obaind from Frundlich isohrm for h sorpion of Cd(II) ono HD-HA Sorpion paramrs Mal Langmuir Frundlich ions b K (mol/l) -1 E a R 2 B n R 2 (10-3 mol/g) (kj/mol) (10-2 mol/g) Cd(II) , Zn(II) , a E= -RT ln K Copyrigh 2018, BCREC, ISSN

9 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 483 ion capaciy -COO- and all aciv sid oghr. Inracions wr occurrd allgdly as lcrosaic forcs bwn h mal ions wih aciv sis of HD-HA. FT-IR spcra can provid lil informaion abou h lcrosaic inracion bwn sorba and sorbn (Figur 4). Th wakning of h C=O absorpion of -COOH on wav numbr 1720 cm -1 afr inracion wih Cd(II) indicas h physical inracion of C=O group on h HD-HA acid wih Cd(II). 3.4 Th Nw Kinics Equaion Considring h sorpion of mal ions on sorbn is an quilibrium procss as illusrad as follow: A + S A*S A im, = 0 a b - A im, = a-x b-x x whr A is a mal ions; S is an sorbn (HD- HA); k a is h sorpion ra consan, and k d is dsorpion ra consan. If a is h iniial concnraion of mal A (mol/l), b is h Langmuir sorpion capaciy (mol/l) and x is h numbr of A is adsorbd on h S (mol/l), from h sam drivaion as Langmuir, h quaion ra can b wrin in Equaion (9). r ads = dx = k a ( a x)( b x) k x A quilibrium, dx/=0, so ha: d (9) k d k = a ( a x )( b x ) Subsiuing Eq. (9) ino Eq. (10) yilds: dx = k a I can b simplify b a simpl form: (10) (11) (12) A = 0, sorpion has no occurd y, so k a is 0 and mal ion of A has no bn adsorbd on sorbn S, so x = 0. Taking ingraion for h q. (12) wih limi (ab) o (ab-x x), 0 o (x), and 0 o, so Eq. (12) can b wrin as: Ingraion rsuls: Rarrangd Eq. (14) givs: Or in anohr form: x k x a ( a x)( b x) ( a x )( b x ) dx ( ab x x)( x x) ab x x k = x a ( ) dx + ( ) dx = 2 ab 2 x ab ab x x ab x ( x x) x x ln ( ab xx) ( x x) 1 x = ka ab ab x x ab x ln = k a x x x ln ( x x) x = ln a ab x x 2 ( ab x x) ab 1 2 x x ln ab 1 ab x ka x k (13) (14) (15) (16) Th Eq. (16) is surprisingly h sam as Lagrgrn quaion, ln (q -q ) = ln(q ) - k lag, whr q and x has h sam uni (mol/l). Thus allgdly linariy of Eq. (16) is similar o h linariy Lagrgrn psudo-firs ordr. Th sam plo bwn Eq. (16) wih a Lagrgrn psudofirs-ordr modl is ln (x -x) vrsus gnras rlaionships, k lag = k a ((ab-x 2 )/x ). If h Eq. (16) givs a sraigh lin, h inrcp ln q from Lagrgrn has a valu qual o ln (x (abx 2 ))/ab) and answrd qusions Aharoni and Sparks [13] why h paramr ln q always hav diffrn valus wih ln q obaind from xprimnal daa. Figur 4. FT-IR spcra of HD-HA bfor and afr inracion wih mal ions, Cd(II) and Zn(II) 3.5 Sorpion Kinics If Eq. (15) is applid, plo ln ((ab-x x)/(x -x)) vs gnras sraigh lin and h valu of k a can b drmin from slop. Inrcp was ln (x /ab) and should no b diffrn wih Copyrigh 2018, BCREC, ISSN

10 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 484 from calculaion ln (x /ab) from xprimnal daa. Th valu of k d can b drmind from Eq. (10), and if w divid k a wih k d yilds quilibrium consan, K, in which h valu of K should no b diffrn from K of isohrm Langmuir. Kinics profil of sorbd mal ions as funcion of im can b sn in Figur 5. This xprimn usd 10 mg sorbn and 50 ml of Cd(II) and Zn(II) 50 mg/l, so iniial concnraion of Cd(II), a Cd = mol/l (Ar Cd = 112.4) and iniial concnraion of Zn, a Zn = mol/l (Ar Zn = 65.4). Sorpion quilibrium rach afr 120 minu inracion, yildd sorpion Cd(II), x (Cd) and Zn(II), x (Zn) a quilibrium was mol/l and mol/l, rspcivly. Sorpion capaciy, b of Zn(II) and Cd(II) from Langmuir isohrm, is and mol/g, rspcivly. If w assum b is a spcis, i inracs wih mal ions A in crain volum, so w can chang b ino mol/l uni as a, so b = mol/l. Plo daa ino hr kinics xprssion, i.. Lagrgrn psudo-firs ordr [2], Ho psudo-scond ordr [1], and his nw kinics quaion [14], can b sn in Tabl 5. In many publicaions abou kinics quaion sudy, linariy (R 2 ) of linar rgrssion is on of h mos suiabl paramr of any kinics quaion [31-34]. In his work, h bs linariy was Ho kinics quaion (R 2 in Cd(II) sorpion = 0.995; Zn(II) = 0.999). Th mos fid calculaion of x wih xprimnal valu of x was also achivd by Ho kinics quaion. Th closnss of xprimnal valu of x of Cd(II) and Zn(II) was and mol/l, rspcivly, and calculaion valu of Ho kinics quaion of Cd(II) and Zn(II) was and mol/l, rspcivly, as sn in Tabl 5. Th bs linariy (R 2 ) and h mos fid x bwn xprimn and calculaion confirmd by Shla al. [31]. Th Ho kinics quaion was also h mos fid linar rgrssion in h mos adsorpion sysm [31-34]. Howvr, xplanaion abou h kinics quaion islf is rarly discussd. On of hm, sorpion ra consan (k a ) was rsuld from Ho and Lagrgrn kinics quaion. Ths boh valu of k a, afr quad h uni, was always diffrn. This valu of k a was indpndn and can no Figur 5. Sorpion profil of Cd(II) and Zn(II) on HD-HA as a funcion of inracion im Tabl 5. Th comparison of linariy and kinics sorpion paramrs of 50 ml mal ions 50 mg/l ono 10 mg HD-HA in ph 5 a minu Mal ions x (mol/l) 10-4 R 2 Psudo-firs ordr (Lagrgrn) k lag (min -1 ) 10-2 x (mol/l) 10-5 R 2 Psudo-scond ordr (Ho) k Ho (min -1 (mol/l) -1 ) 10 3 x (mol/l) 10-4 R 2 Nw kinics quaion k a (min -1 (mol/l) -1 ) k d (min -1 ) 10-2 Cd(II) Zn(II) x (mol/l) 10-4 Tabl 6. Comparison paramrs bwn manually calculaion and linar rgrssion of nw kinics quaion Mal ions Exprimn -ln (x /ab) of nw kinics quaion Calculaion from Inrcp rgrssion k a /k d =K k a /k d =K from rgrssion (mol/l) -1 K from Langmuir q. (mol/l) -1 Inrcp of plo ln (x -x) vs ln q of Lagrgrn quaion Calculaion ln(x (abx 2 ))/ab) k lag from Lagrgrn q. (min -1 ) k lag and k a Cd(II) ,452 5, Zn(II) ,898 6, k lag from k lag =k a (ab-x 2 )/x ) (min -1 ) Copyrigh 2018, BCREC, ISSN

11 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 485 b compard wih anohr paramr. Thr is no scal o say ha h paramr (k a ) was rally corrc. Th corrlaion paramrs for h Lagrgrn and Ho kinics quaion wr low and h calculad x valus obaind from h Lagrgrn kinic quaions ar no rasonabl valus [32]. In his work, bsid h paramrs of nw kinics quaions has good corrlaion o Langmuir daa, h paramrs can also b compard among calculaion and xprimnal daa (Tabl 6). Applicaion of Eq. (15) as h nw kinics quaion on sorpion daa of Cd(II) and Zn(II) ono HD-HA rsuls good linariy bwn ln ((ab-x x)/(x -x)) vs, which R 2 highr han Lagrgrn psudo-firs ordr xprssion (Figur 6). Bs linariy obaind by Ho psudo-scond ordr xprssion which R 2 = for Zn(II) and for Cd(II). This vidnc provs ha Ho kinics xprssion has suiabl condiion of xprimn comparison bwn iniial concnraion of mal ions (a) and sorpion capaciy (b) which is approximaly 2:3 for Cd(II) and 1:4 for Zn(II). Howvr, boh Ho and Lagrgrn hav no good rlaionship wih daa from Langmuir sorpion isohrm. Sorpion ra consan, k a, rsuld from slop in Eq. (15), was (min -1 (mol/l) -1 ) for Zn(II) and (min -1 (mol/l) -1 ) for Cd(II). Manwhil, dsorpion ra consan, k d, rsuld from Eq. (10) was min -1 for Zn(II) and min -1 for Cd(II). If w divid k a wih k d from his nw kinics quaion yilds quilibrium consan, K, which was 3,452 (mol/l) -1 for Cd(II) and 10,898 (mol/l) -1 for Zn(II). From Langmuir daa, i was obsrvd ha sorpion quilibrium consan, K L Cd(II) and Zn(II) was 5,651 and 6,399 (mol/l) -1 ), rspcivly. Th comparison valu bwn K from nw kinics quaion and K L from Langmuir daa shows ha sorpion Cd(II) has closr valu (3,452 (mol/l) -1 o 5,651 (mol/l) -1 ) han sorpion Zn(II) (10,898 (mol/l) -1 o 6,399 (mol/l) -1 ). This vidnc provs ha h paramr of nw kinic quaion can b confirmd wih Langmuir isohrm daa. Th valu of quilibrium consan in boh K from nw kinics quaion and K L from Langmuir isohrm should b qual. From our prvious work, h diffrncs of his valu K and K L gnras from raio of iniial concnraion of sorba (a) and sorpion capaciy (b) [14]. Bcaus h k a, k d, and x ar h funcion of a and b [14]. I migh b h corrc ha raio of a and b gnras h qual K and K L. Addiionally, vry sorbn and sorba has h own his raion for qualiy of K and K L. Th valus of k a, k d, and x from nw kinics quaion can b sn in Tabl 4. Th valu of k a, k d, K, and E of Zn(II) was highr han k a, k d, K, and E of Cd(II). Th highr valu of k a, k d, and K was causd by suiabiliy hard-hard characrisic bwn Zn(II) and funcional group of HD-HA. Th highr valu of k a and k d mans ha Zn(II) sorbd fasr han Cd(II), bu Zn(II) also dsorbd grar hn Cd(II). I was provd ha in 60 h minus, Zn(II) has rachd h quilibrium, bu Cd(II) sorpion sill incrass ill mor 120 h minu (Figur 5). Th suiabiliy of hard-hard characrisic bwn Zn(II) and funcional group of HD-HA lad h fasr sorpion, bu h biggr hydra radii of Zn(II) (6 Å) han Cd(II) (5 Å) caus h sorpion capaciy of Cd(II) highr han Zn(II) (Tabl 4). Smallr hydra radii of Cd(II) han Zn(II) lads o highr amoun of sorbd Cd(II). Aharoni and Sparks [13] sad ha inrcp from Lagrgrn linar rgrssion, ln q always hav diffrn valus wih calculad ln q obaind from xprimnal daa. In h sam uni (mol L -1 ) of q. (16) and Lagrgrn kinics quaion w can conclud ha ln q of Lagrgn kinics quaion is a mor complx funcion of iniial mal ion concnraion (a), sorpion capaciy (b), and sorbd mal ion a quilibrium (x ). Th vidnc of his samn was calculaion of ln (x (ab-x 2 ))/ab) giv narly clos valu wih ln q from Lagrgrn quaion (Tabl 6). Eq. (16) provs ha k lag was a complx funcion from k a ((ab-x 2 )/x ). This rsul answrd qusion by Aharoni and Spark [13], ha inrcp should hav similar valu bwn calculaion and rgrssion. Ths rsuls provs ha h nw kinics quaion has mor advanags in drmining sorpion ra consan, k a, dsorpion ra consan, k d, and quilibrium consan, K, from singl s daa comparing boh Lagrgrn and Ho kinics xprssion. This nw kinics quaion also has good rlaion bwn paramrs rsuld from manually calculaion and linar rgrssion, which was no ownd by ohr kinics quaion. 4. Conclusions I was obviously obsrvd from physical apparanc, oal acidiy, UV-Vis, and FT-IR sudy ha hors dung can b sourc of humic acid. I was provd ha his nw kinics quaion hav good rlaion bwn paramrs rsuld from manually calculaion and linar rgrssion, which is no sn on ohr sorpion kinics quaion. Th nw kinics quaion Copyrigh 2018, BCREC, ISSN

12 Bullin of Chmical Racion Enginring & Caalysis, 13 (3), 2018, 486 was succssfully applid o drmin h valu of inrcp of h wll-known Lagrgrn quaion which has narly clos valu wih calculaion of ln ((x (ab-x 2 ))/ab), h valu of quilibrium consan, K = k a /k d from proposd kinics xprssion which fairly clos wih quilibrium consan from Langmuir isohrm modl (K L ), and inrcp of his nw kinics quaion (-ln (x /ab)) was narly clos wih -ln (x /ab) from h calculaion. Addiionally, his nw kinics quaion has mor advanags in drmining sorpion paramrs, i.. k a, k d, and K from singl s daa comparing boh Lagrgrn and Ho kinics xprssion. Acknowldgmns W hank o Minisry of Rsarch, Tchnology and Highr Educaion, Th Rpublic of Indonsia hrough Graduad Scholarship for Domsic Educaion (BPP-DN) conrac numbr /E4.4/2013 for financ his work. Figur 6. Linariy from rgrssion of psudo-firs ordr Lagrgrn, psudo-scond Ho, and h kinics quaion of Zn(II) (lf-from abov o down, rspcivly) and Cd(II) (righ-from abov o down, rspcivly) ono HD-HA Copyrigh 2018, BCREC, ISSN

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