Original Article Studies on thermodynamic properties of binary mixture of Benzene, Toluene and CCl 4 in DMSO at T = K

Size: px
Start display at page:

Download "Original Article Studies on thermodynamic properties of binary mixture of Benzene, Toluene and CCl 4 in DMSO at T = K"

Transcription

1 Avlble onlne t Interntonl Journl o Reerch n Phycl Chetry Unverl Reerch Publcton. All rght reerved Orgnl Artcle Stude on therodync properte o bnry xture o Benzene, Toluene nd CCl 4 n DMSO t T = 08.5 K Abtrct Hrh Kur * & Deepk** *Dept. o Chetry, Ch. Dev Ll Unverty, Sr (Hryn) Ind * Dept. o Chetry, Snghn Unverty, Rjthn. hroudgl@redl.co Receved Augut 0; ccepted 04 Septeber 0 Denty ( ), ultronc peed ( u ) nd xce Molr olue ( ) o bnry xture o Benzene, Toluene nd CCl 4 n DMSO hve been eured over the entre rnge o copoton t 08.5 K. Fro thee experentl reult, preter uch entropc copreblty K, ntercton preter,, Flory preter, coecent, A, tndrd devton, ( Y ), nd olr ound velocty, R hve been etted. The exce uncton hve been tted to the Redlch-Kter polynol equton. The experentl ultronc peed hve been nlyzed n ter o Jcobon Free Length Theory (FLT), Sch Collon Fctor Theory (CFT), Nooto relton, nd n Del del xture relton. Interoleculr Free Length, L, nd vlble volue,, hve been clculted ro FLT, CFT, nd therocoutc pproch or ll the three bnry lqud yte t 08.5 K. 0 Unverl Reerch Publcton. All rght reerved Key word: Ultronc peed, xce Molr olue, Sch Collon Fctor Theory, Benzene, Toluene nd DMSO. Introducton : The eureent o therodync nd coutc properte contrbute to the undertndng o the phycochecl behvour o the bnry nd ultcoponent lqud xture. xce properte o lqud yte, uch olr volue, re requred or tetng the theore o oluton, developent o eprton technque nd equpent, nd or other ndutrl pplcton. Benzene, toluene nd CCl 4 re vertle orgnc olvent whch nd ue n nuber o ndutry. Thu, tudy o phycl properte dt on the bnry xture contnng benzene, toluene nd CCl 4 hve ttrcted conderble nteret n the lterture [-]. Thu, benzene, toluene nd CCl 4 n DMSO xed olvent would enble u to hve lrge nuber o olvent wth pproprte phycochecl properte, whch cn be ued or prtculr checl proce. Moreover, lterture urvey ndcte tht no ultronc tudy on thee bnry yte hve been reported t 08.5 K. Thereore, preent tudy w undertken n order to hve deeper undertndng o the nteroleculr ntercton between the coponent o the bove three bnry lqud xture. Thu, tudy o therodync properte dt on the bnry lqud xture o Benzene; Toluene nd CCl 4 n DMSO hve ttrcted conderble nteret n our preent tudy. Reerch worker n the pt hve hown tht NMR [4, 5], IR [6-7] nd Rn pectr [8], hve been ued to tudy oleculr ntercton. The velocty eureent o the propgton o ultronc wve [9-] nd ther borpton [4, 5] hve lredy been ound to be ueul n the tudy o oleculr ntercton or norgnc, orgnc nd orgnoetllc bnry yte. Lkewe, reercher [6-] hve lo eployed ultronc eureent to look nto the portnt conequence o on-olvent ntercton or the tructure o electrolytc oluton. Reerence [, ] relted to the eld o edcne, where reerence [4-7] bed on tude on eulon/ cro eulon, polyer urctnt ntercton [8] nd ultronc detructon o urctnt [9] re only ew ce to ugget vertlty o the technque. xperentl: Benzene, toluene nd CCl 4 were procured ro Fluk- Aldrch nd DMSO ro Fcher Scentc Ltd. nd re urther pured by the ethod gven n ogel text book o prctcl orgnc chetry [0]. Pror to the experentl eureent, ll the orgnc lqud were tored n drk bottle over 0.4 n oleculr eve to reduce wter content nd were prtlly deged wth vcuu pup under ntrogen tophere. The purte o ll the ple deterned by chrotogrphc nly were better thn 0 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9

2 0.996 on olr b. Bnry xture were prepred by xng pproprte volue o the lqud coponent n the peclly degned gl bottle wth r tght Telon coted cp. The requred properte re eured on the e dy edtely ter preprng ech copoton. The uncertnty n ole rcton ± A ult requency dgtl croeter redng ultronc ntereroeter (M-8, Mttl nterpre, New Delh) opertng t,, & 4 MHz w ued to eure the ultronc velocty o the bnry lqud xture (wth n uncertnty o ±0.%) t contnt teperture o 08.5 K by ung dgtl contnt teperture wter bth. The teperture tblty ntned wthn ±0.00 K by crcultng therotted wter round the cell wth crcultng pup. In order to nze the uncertnty o the eureent, everl x re llowed to p nd ther nuber (ty) counted. All x re recorded wth the hghet wng o the needle on the croeter cle. The totl dtnce, d n (c) oved by the relector gven by d, where the wvelength. The requency, o the crytl beng ccurtely known (.0 MHz), the peed o ound, u n - clculted by ung the relton u. xce olr volue, w clculted by peclly degned double Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9 lbed gl dltoeter tted wth crocpllry (±0.0c) n the centre. The denty o oluton w eured by double r pyknoeter o bulb cpcty 0 l nd cpllry o n nternl deter o bout. The rk o the te w clbrted by double dtlled wter (conductvty le thn 0-6 oh - c - ) wth nd g c - t denty t 98.5K nd 08.5K repectvely nd benzene wth buoyncy corrected. The ccurcy o the denty reult w ±0.000 (g c - ). Beore ech ere o eureent, the ntruent w clbrted wth trple dtlled rehly deged wter. Weght eureent were perored on Mettler Toledo AB 5-S/FACT, ngle pn nlytcl blnce, wth precon o 0.0g. The dente, nd ultronc velocte, u o the pure lqud were n good greeent wth the vlue ound n the lterture nd re preented n Tble. Tble. Copron o experentl dente, o pure lqud wth lterture vlue t 98.5K, ultronc peed, u nd olr volue, 0 t 08.5K. Coponent (g c - ) u ( - ) 0 (c ol - ) xpt. Lt. xpt. Lt. t 08.5K [58] Benzene [56] Toluene [56] CCl [56] DMSO [57] 487# 48# [57] 66.5 # vlue t 98.5K Reult: Where, M, M nd u, The exce olr volue,, o the oluton were clculted ro the dente o the pure lqud nd ther xture ung the ollowng equton []: x M x M x M x M Where () x x the denty o the xture nd x, M, nd x, M, re the ole rcton, olr, nd the denty o pure coponent nd repectvely. The ollowng relton hve been ued to correlte the ound velocty, u, o the bnry lqud xture: Nooto Relton [] R xr xr u () x x x Where x, x,, nd R, R re ole rcton, olr volue, nd olr ound velocty o rt nd econd coponent, repectvely. n Del Relton [] x x. x M x M u M u M u d. x () ound velocte o u u re the olr e nd rt nd econd coponent, repectvely, nd d. x the ultronc velocty o the del xture. Jcobon Free Length Theory (FLT) [4] K ux (4) L ( x.) x Where K the Jcobon contnt whch teperture dependent only nd t vlue 64.5 t.5k. The L ( x.) the nteroleculr ree length o the bnry xture, whch gven by L. Here Y repreent the vlble volue per ole nd Y the urce re per ole nd thee y be expreed T 0 (5) Y 6 N A0 (6) Here N A the Avogdro nuber nd 0 nd T re the olr volue t zero Kelvn nd t teperture T, repectvely. The 0 cn be obtned ro the ollowng relton ung crtcl teperture T C :

3 0 T T Tc 0. The crtcl teperture, T C the ole rcton ddtve o the vlue o t pure coponent nd gven by the relton: C C() C() (7) T x T x T (8) The therodync nteroleculr ree length, L, n the bnry lqud xture hve been clculted ung the relton: L T x x x x 0() 0() The ultronc nteroleculr ree length L, hve lo been coputed ung the Sch relton or vlble volue : u T (0) u Where, u the ultronc velocty t teperture T nd u Sch Collon Fctor Theory (CFT) [5-6] x b xb u u x x (9) x () x Where, b nd re the geoetrc volue nd collon ctor, repectvely. The ctul volue o the olecule per ole o the lqud h been coputed ung the relton 4 b r N () Where, r the oleculr rdu whch h been coputed ung the Sch relton [6] M RT Mu r N 6 Mu RT ' M RT Mu b u RT ' b r 6 N (4) (5) ' Where, b the nder Wl contnt nd equl to our te the ctul volue o the olecule per ole o the ' lqud,.e. b 4b. The therocoutcl ethod [7-9] h lo been eployed to obtn the vlble volue, ung the relton T ' '' ' K T (6) K K ' '' The K, K, nd K re known otherl, obrc nd ochorc coutcl preter, repectvely, nd cn be expreed by the relton * ' '' S T X K K K (7) T '' X K (8) T S * T K (9) T * 4T S (0) The X known the obrc teperture coecent o nternl preure nd cn be expreed T X () ~ C Where repreent the reduced olr volue nd C the Moelwyn-Hughe preter nd cn be expreed Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9 ~ ~ T () T 4T C () T The therl expnon coecent,, h been clculted ung the equton: (4) T P The entropc copreblty hve been clculted ro Newton-Lplce equton: k (5) () u The exce entropc copreblty w ound out by ung the relton, Where, k k k (6) k d d the entropc copreblty or the del xture, w obtned ccordng to Benon nd Kyohr [40] nd Acree [4]: d T k k, T x C p, xc p, (7) Where, the volue rcton o coponent n the xture, x the correpondng ole rcton, T the bolute teperture, nd k,,, nd C p, re the entropc copreblty, the olr volue, the cubc

4 expnon coecent, nd the olr het cpcty o pure coponent repectvely. The cubc expnon coecent were obtned ro experentl denty eureent perored n our lbortory t derent teperture. The exce entropc copreblty o the bnry xture were tted wth Redlch-Kter polynol equton [4]: n j j (8) j0 k x x A ( x x ) Where, Aj re the djutble preter. Owl [4] extended the Prgogne Flory-Ptteron (PFP) theory to ette the entropc copreblte nd peed o ound o lqud xture. At gven teperture, T, the PFP theory cn be ued to clculte the olr volue, nd the olr het cpcte, C, o lqud xture the ntercton preter,, known. The ter nd T P P o ollowng equton: T cn lo be clculted by en 7 5 T. P 4 T P T. T 4 P T p (9) (0) Where,, P nd T re the chrctertc volue, preure nd teperture o the xture, repectvely nd the correpondng reduced volue. Fro thee quntte the entropc copreblty, k () P S cn be clculted ung the ollowng therodync relton: TCP S T P () P P T nd nlly the entropc copreblty relted to the peed o ound u, by the Newton-Lplce equton, k u () Tble. lue o denty, peed o ound nd dervton n peed, u o ound o bnry lqud xture t 08.5K. Where ρ 0 nd u 0 re the dente nd ultronc peed o pure olvent, ρ nd u re the denty nd ultronc peed o xture repectvely nd K the teperture dependent Jcobon contnt ( t 5 0 C). The devton preter o bnry lqud xture hve been evluted ung the generl equton: Iotherl copreblte, k T, were clculted equolr H vlue [45-46]. Once the ntercton ro therl expnon coecent, experentl preter obtned, the entropc copreblty nd entropc copreblte nd olr het cpcte. the peed o ound cn be etted. Inter oleculr ree length nd reltve octon Phycl properte o pure ubtnce lke denty, h been clculted by the ollowng orul: ultronc peed t 08.5K re hown n Tble. Speed L K K o ound, u, denty, entropc copreblty, k, nd devton n peed o ound o bnry lqud xture o u 0 benzene, toluene nd CCl RA 4 n DMSO over the derent 0 u copoton rnge t teperture o 08.5K re reported Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9 Y Y X Y X Y x Where, Y ndcte the preter uch entropc copreblty, nter oleculr ree length nd ultr onc peed: X nd X re the ode rcton o coponent Y, nd repectvely. Y, Y, nd Y x re the devton preter, preter o the coponent nd nd oberved preter repectvely. The nuber o contct te per egent o olecule, h been etted ung Bond ethod [44]. Moleculr ntercton preter or ech bnry xture w obtned by ttng the PFP theory to the correpondng experentl

5 n Tble. lue o entropc copreblte,, nteroleculr ree length, L, nd reltve octon, K Tble 4. xce olr volue, lqud xture t 08.5 K. o the bnry Tble. lue o devton n entropc copreblty K, nteroleculr ree length, L nd reltve octon R o ound o bnry lqud xture t 08.5K. A Mole Frcton - K (0 - P - ) - ( x ) (0 - ) R L A The vlue o the coecent o Redlch-Kter polynol equton or ll the bnry lqud xture long wth vlue o the tndrd devton re repreented n Tble 7 t 08.5 K. Flory preter [47, 48] o the pure copound long wth ther phycl properte re gven n Tble 8 t 08.5 K. Tble 9 gve the etted nd experentl equolr, u nd k, vlue long wth the R, o the bnry lqud xture o benzene, toluene nd CCl 4 n DMSO t 08.5 K re hown n Tble. Tble 4 how xce Molr olue o the bnry lqud xture o benzene, toluene nd CCl 4 n DMSO t 08.5 K. Tble 5 how Interoleculr Free Length, L, clculted ro Free Length Theory (FLT), Collon Fctor Theory (CFT), nd Therocoutc Approch (TAP) or benzene, toluene nd CCl 4 () + DMSO () bnry lqud xture t 08.5 K. Tble 6 how vlble volue,, clculted ro Free Length Theory (FLT), Collon Fctor Theory (CFT), nd Therocoutc Approch (TAP) or Benzene, Toluene nd CCl 4 () + DMSO () bnry lqud xture t 08.5K. ntercton preter,, or benzene, toluene nd CCl 4 n DMSO bnry lqud xture t 08.5 K. tted vlue or peed o ound nd entropc copreblty re lot dentcl to experentl reult or bnry lqud xture. Tble 0 gve theoretcl vlue o ultronc peed clculted ro FLT, CFT, Nooto nd n Del nd ngeel del xng relton nd percentge error n clculted vlue or DMSO + Benzene, Toluene nd CCl 4 t 08.5 K. Dcuon: All the yte o DMSO wth Benzene, Toluene nd CCl 4 how negtve devton through K other over entre rnge o ole rcton (Fgure ). A cler n t the ole rcton round x = , ndcte tht the xu ntercton re t tht th ole rcton rnge. 4 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9

6 Tble 5. Interoleculr Free Length (- L ), clculted ro Free Length (FLT), Collon Fctor Theory (CFT), nd Therocoutc Approch (TAP) or bnry xture t 08.5K. Tble 6. Avlble olue,, clculted ro Free Length Theory (FLT), Collon Fctor Theory (CFT), nd Therocoutc Approch (TAP) or bnry xture t 08.5K. Tble 7. lue o Preter A o the Redlch-Kter j or equton nd correpondng tndrd devton, k the bnry yte t 08.5K. Fgure. Devton n entropc copreblty (- K ) wth the ole rcton o DMSO n the bnry lqud xture o Benzene n DMSO. Fro Tble &, t oberved tht u vlue re potve whle, 5 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9 K vlue re negtve, uch trend o potve devton n peed o ound nd negtve devton n entropc copreblty qute coon [49-5]. In pure DMSO, there dpole dpole well the uul dperve ntercton. The eect o ddng non polr (benzene nd CCl 4 ) nd polr (toluene) econd coponent prrly to drupt the dpolr ntercton o the rt coponent, but when the econd coponent lo polr,

7 Tble 8. Phycl properte reduced olr volue, crtcl preure P nd Flory preter otherl copreblty, k collon ctor, o the pure T copound t 08.5K. Tble 9. Intercton Preter,, clculted nd experentl equolr peed o ound, nd entropc copreblte, k, o the bnry yte t 08.5K. the dpole-dpole ntercton between unlke olecule ot lkely whch reult n contrcton o volue nd the xture becoe the le copreble [5-54]. The behvor o bnry lqud xture cn be explned n ter o ) phycl orce -dperon ) checl orce dpole-dpole ntercton. The orer ctor ncree the nteroleculr ree length decrbed by Jcobon [54]. Th turn, cue negtve devton n ound peed nd potve devton n copreblty. On the other hnd, the ltter ctor decree the nteroleculr pth length ledng to potve devton n ound peed nd negtve devton n copreblty nd exce olr volue,. The ctul vlue depend upon the reltve trength o two oppong eect. The oberved negtve vlue o K nd exce olr volue (Tble 4) nd potve vlue o u or thee bnry xture ply tht the pecc ntercton donte over the dperve ntercton between unlke olecule. Fro Tble 5, the negtve vlue o devton n the oleculr ree length preter ubtntve the bove rguent undoubtedly nd undenbly unvel the ct the pecc ntercton re beng opertve between the olecule o olvent nd coolvent n the nvetgted bnry xture. Snce, pckng eect nd H n nterctonl eect between the A nd B conttuent o n (A+B) xture nd dt o ll the three bnry xture re negtve throughout the copoton rnge o DMSO, th ugget tht copred to the dperon orce, negtve vlue o n generl, lwy cue ore copct pckng o the olecule due to tronger checl ntercton between the two unlke orgnc olecule. Ther repectve contrbuton to the eured dt uncton o the ole rcton o DMSO. The concluon urther orted by the ncreng vlue o reltve octon, R ncluded n Tble. All the A trend o the bove preter ndcte tht the xture re le copreble thn ther correpondng del xture. Generlly, the devton preter condered to be the relectng gent o the gntude o polrty t the te o ntercton n the olecule [55]. The nteroleculr ree length, L, cn be relted to the pce llng blty ung tht the olecule re ncopreble hrd phere hvng unor rdu. The nteroleculr ree length, L, obtned ung ree length theory (FLT) whch decree wth the ncree n ole rcton o DMSO (Tble 5). However, the L vlue obtned ro Sch collon ctor theory (CFT) ncree wth the ncree n the ole rcton o DMSO. The chnge n the lope o the other o L uncton o ole rcton n the hgher ole rcton regon predcted by FLT nd CFT how tht the entropy eect relted to the tructurl rerrngeent o olvent olecule due to drupton o dpole-dpole ntercton between lke polr olecule. However, the therocoutc pproch (TAP) predct tht the L vlue n thee bnry lqud xture decree wth ncree n the ole rcton o DMSO. The L vlue or thee bnry lqud xture obtned ro the ultronc ethod re hgher thn thoe obtned ro the ree length theory nd the therocoutcl pproch. Fgure. Devton n entropc copreblty K wth the ole rcton o DMSO n the bnry lqud xture o Toluene n DMSO. Fgure. Devton n entropc copreblty K wth the ole rcton o DMSO n the bnry lqud xture o CCl 4 nd DMSO. 6 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9

8 Tble 0. Theoretcl vlue o ultronc peed clculted ro FLT, CFT Nooto (NOM) nd n Del nd ngeel del xng relton (D) nd percentge error n clculted vlue or Benzene, Toluene nd CCl 4 () DMSO () t 08.5K. u x ( ) % error FLT CFT NOM D FLT CFT NOM D Benzene +DMSO Toluene + DMSO CCl 4 + DMSO The vlble volue,, obtned ung Free Length Theory (FLT) or the (DMSO + Benzene, Toluene nd CCl 4 ) decree wth the ncree n ole rcton o DMSO (Tble 6). However, the vlue obtned ro Sch Collon Fctor Theory (CFT) ncree wth the ncree n the ole rcton o DMSO. The chnge n the lope o the other o vlble volue uncton o ole rcton n the hgher ole rcton regon predcted by FLT nd CFT how tht the entropy eect relted to the tructurl rerrngeent o olvent olecule due to tronger dpole-dpole ntercton between unlke olecule. However, the therocoutc pproch (TAP) predct tht the vlue n thee bnry xture decree wth ncree n the ole rcton o DMSO. The tudy o tndrd devton, k, preented n Tble 7, revel tht the reult o ultronc velocty or ll the three nvetgted bnry yte cn be tctorly explned by n Del Idel Mxture relton (nu < 0.). However, the predcton o thee reult better or the DMSO wth benzene yte by the CFT orulton. Stronger dpolr ntercton between unlke olecule lo juted by the vlue o ntercton preter (Tble 9). lue o ntercton preter re low or Benzene n DMSO whch ugget dpole-nduced dpole ntercton between the DMSO nd Benzene. Theoretcl vlue o ultronc peed clculted or FLT theory how lrge percentge error n DMSO wth benzene bnry lqud xture t 08.5K (Tble 0). Theoretcl vlue o ultronc peed clculted or Nooto nd n Del nd ngeel del xng relton re lot dentcl. Thee relton how nu percentge error n theoretcl ultronc peed. Concluon : Denty ( ), ultronc velocty ( u ) nd exce olr volue ( 7 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9 ) o bnry xture o benzene, toluene nd crbon tetrchlorde n DMSO hve been eured over

9 the entre rnge o copoton nd t 08.5 K. Fro thee experentl reult, preter uch devton n entropc copreblty K, ntercton preter, Flory preter, Coecent A, tndrd devton ( Y ) nd olr ound velocty R hve been etted. The exce uncton hve been tted to the Redlch-Kter polynol equton. The experentl ultronc velocte hve been nlyzed n ter o Nooto relton, n Del del xture relton, Jcobon ree length theory nd Sch collon ctor theory. Interoleculr ree length, L, nd vlble volue,, hve been clculted ro Jcobon ree length theory, Sch collon ctor theory, nd therocoutc pproch or bnry yte t 08.5K. The oberved negtve vlue o K nd exce olr volue nd potve vlue o u or thee xture ply tht the pecc checl ntercton donte over the phycl dperve ntercton between unlke orgnc olecule. Reerence:. Anbhv, T. M., Bnerjee, K.: Denty, vcoty, rerctve ndex, nd peed o ound n bnry xture o DMSO wth ethyl cette, ethyl cette, N-propyl cette, N-butyl cette, nd -ethylbutyl--cette n the teperture ntervl ( ) K. J. Che. ng. Dt 4, (998). Hjun, W., Goukong, Z., Mngzh, C.: por-lqud qulbr o -Propnol -Propnol wth,,4- Trethylpentne t 0. kp. J. Che. ng. Dt 6, (994). Sndhu, J. S., Sngh, A.: xce olr volue o (DMSO+n n-lkn--ol) t the teperture 98.5 K. J. Che. Therodyn. 4, 8-84 (99) 4. Ln, W., Ty, S. J.: Nucler gnetc reonnce tude on the nteroleculr octon n oe bnry xture. J. Phy. Che. 74, (970) 5. Schneder, W. G., d. Hdr, D.: Hydrogen Bondng. Pergon Pre, London, 55 (959) 6. Grunwld,., Coburn, W. C.: Group contrbuton to the therodync properte o non-onc orgnc olute n dlute queou oluton. J. A. Che. Soc. 80, -5 (958) 7. Coggehll, N. D., Ser,. L.: Study o oleculr ntercton n ternry xture through ultronc peed eureent. J. A. Che. Soc. 7, (95) 8. Pentel, G. C., Mclelln, A. L.: The Hydrogen Bond, Freen nd Co, Sn Frncco 67 (960) 9. Prd, N., Prkh, S.: Solute-wter ntercton nd the olublty behvor o long-chn prn hydrocrbon. Acutc 6, -9 (976) 0. Gopl, K., Ro, N. P.: Therodync properte o queou orgnc olute relton to ther tructure. Acoutc Letter 4, 64 (98). Frnk, F., Quckenden, M. A. J., Red, D. S., Wton, B.: A derentl cloreter or the eureet o het o oluton t hgh dluton. Trn Frdy Soc. 66, 58 (970). Kulgud, M.., Ro, K. S. M.: Ultronc velocty nd vcoty o bnry lqud xture. J. Che. Soc. Frdy Trn I 75, 7-5 (979). Srvtv, T. N., Sngh, R. P., Swroop, B.: Theoretcl evluton o ultronc velocty n bnry lqud xture. Ind. J. Pure Appl. Phy., 67-7 (98) 4. Sette, D.: oluetrc properte o queou oluton o orgnc copound. III. Alphtc econdry lcohol, cyclc lcohol, prry, econdry, nd ne. Rcerc Sc. 5, (955) 5. Dvnbkht, A., Long, J., Zn, R.: Interoleculr ntercton tude o bnry xture o norgnc nd orgnoetllc coplexe. J. Phy. Che. 8, 60 (977) 6. Shr, C., Gupt, S. P.: Ultronc tude o oleculr ntercton o bnry xture o non nterctng orgnc olvent. Acoutc Letter, 66 (986) 7. Mehrotr, K. N., Updhy, S. K.: Acoutcl tude o clcu op. Acoutc Letter, 66 (987) 8. Mehrotr, K. N., Ghlut, A. S., Shr, M. J.: Ultronc tude o oleculr ntercton n the oluton o lnthnu op. Collod Interce Sc. 0, 0 (987) 9. Srvtv,. N. P.: Therodync properte o Ne+n-H xture deduced ro ultronc velocty dt. Acoutc Letter, 7-76 (988) 0. Mehrotr, K. N., Ghlut, A. S.: Stude on the cellr behvour o preodyu op. Collod nd Surce 5, 80 (989). Kur, A.: Acoutc tude o bnry xture o rotc ketone n benzene. Collod nd Surce 4, -9 (989). Scheruly, R., Scheehl, T., Gunther, A., Grnger, F., Seeger, W., Wlrth, D.: Oxdtve Stre n Chronc Obtructve Pulonry Dee. A. J. Repr. Crt. Cre. Med. 56 () 445 (997). Wnger, M. H., Wetho, Fredrch, S. W., Mollenhuer, I., Obden, M., Boenck, U.: Bo. Phy. Che. 84 () 5 (000) 4. Hckey, S., Lwrence, M. J., Hgn, S. A., Buckn,.: Anly o the phe dgr nd crotructurl trnton n phopholpd croeulon yte ung hgh-reoluton ultronc pectrocopy. Lngur () 5575 (006) 5. Becu, L., Mnnevlle, S., Coln, A.: Study o trglycerde- proten ntercton ung croeulon- ltrton ethod. Phy. Rev. Lett. 76 () 8 (006) 6. Meht, Kwljet, S. K.: Interoleculr ntercton tudy o croeulon nd eulon n DDAB/W/ol yte. Phy. Rev.. Stt. Nonln. Sot Mtter Phy. 65 (00) 7. Brllev, M., Greex, F.: ulon Polyerzton Synthe o Ctonc Polyer Ltex n n Ultronc Feld. J. Collod Interce Sc. 5 () 78 (00) 8. Alendr, D., Aprno Cllo L Me, Pert, L, : Ultronc Nebulzton or cent Delvery o Surctnt n Model o Acute Lung Injury. Ipct 8 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9

10 on G xchnge. A. J. Repr. Crt. Cre Med. 56, 445 (997) 9. Wever, L. K., Gyng, F. P. J., Le, A. Y., Rthn, Je, F. : Benzene nvronent Reerch 77 () (005) 0. Furn, B. S., Hnnord, A. J., Sth, P. W. G., Ttchell, A. R.: Textbook o Prctcl Orgnc Chetry. 98 (004). Bht, S. C., Bht, R., Dubey, G. P.: Stude on trnport nd therodync properte o bnry xture o octn--ol wth chloroor,,- dchloroethne nd,,,-tetrchloroethne t 98.5 nd 08.5 K. J. Mol. Lqud, 44() 6-7 (009). Nooto, O.: prcl orul or ound velocty n lqud xture. J. Phy. Soc. Jpn., 58 (958). n Del, W.: Therodync Properte nd eloctyo Sound,Butterworth, London,(975),Chp Jcobon, B.: Theoretcl tudy o ultronc velocty n bnry lqud xture t 0 0 C. Act Che. Scnd. A (95) 5. Sch, W.: Study o oleculr ntercton n ternry xture through ultronc peed eureent. Acoutc, 7-76 (975) 6. Sch, W.: Molekulrkutc. Sprnger erlg, Berln (96) Chp Nutch-Kuhnke R.: Stude on thero-coutc preter n bnry lqud xture o phophnc cd wth derent dluent t 0.5 K. Acoutc 5, 8-86 (965) 8. Pndey, J. D., Dev, R., Chhbr, J.: Therocoutcl pproch to the nteroleculr ree-length o lqud xture. Phy. Che. Coun. 6, 55 (00) 9. Pndey, J. D., Dubey, G. P., Shukl, B. P., Dubey, S. N.: Predcton o ultronc velocty nd nteroleculr ree-length nd ther correlton wth ntercton n bnry lqud xture. Prn J. Phy. 7 (6) 4-49 (99) 40. Benon, G. C., Kyohr, O. K.: vluton o exce entropccopreblte nd ochorc het cpcte. J. Che. Therodyn., 06 (979) 4. Acree, W..: Denty, Speed o Sound, nd Ientropc Copreblty o Trethnolne (or N- Methyldethnolne) + Wter + thnol Soluton ro t = (5 to 50) C. J. Che. ng. Dt 8, 5-6 (98) 4. Redlch, O., Kter, A. T.,: Repreentton o Therodync Properte nd the Clcton o Soluton. Indut. ng. Che. 40, (948). 4. Owl, S. L., Phlk, R. P.: Speed o ound nd entropc copreblte o nonelectrolyte lqud xture. I. Bnry xture contnng p-doxne. J. Sol. Che., 4-58 (99) 44. Bond, A.: Phycl Properte o Molecule, Lqud nd Ge, Wley, New York (968) 45. Morco, K. W.: xce enthlpy;,-doxne + cyclohexne nd,4- doxne + cyclohexne. Int. Dt Ser., Sec. A 56, (97) 46. Inglee, A., Kehn, H..: Molr exce volue nd exce het cpcte o (,,4-trchlorobenzene + n lkne). Int. Dt Ser. Sec. A (98) 47. Flory, P. J., Orwoll, R. A., rj, A., J.: Stttcl Therodync o Chn Molecule Lqud. I. An quton o Stte or Norl Prn Hydrocrbon. A. Che. Soc. 86, ( Abe, A., Flory, P. J.: The therodync properte o xture o ll, nonpolr olecule. J. A. Che. Soc. 87, (965) 49. Anbhv, T. M., Goplkrhn, B. J.: Denty, vcoty o bnry xture o N,Ndethylorde, dethyluloxde, N,Ndethylcetde, cetontrle, ethylene glycol, dethylene glycol,,4-doxne, tetrhydrourn, - ethoxyethnol, nd -ethoxyethnol t 98.5 K. Che. ng. Dt, 40, (995) 50. Anbhv, T. M., Bnerjee, K.: Denty, coty, Rerctve Index, nd Speed o Sound n Bnry Mxture o Dethyl Crbonte wth Methnol, Chloroor, Crbon Tetrchlorde, Cyclohexne, nd Dchloroethne n the Teperture Intervl ( ) K. J. Che.ng. Dt 4, (998) 5. Owl, S. L., Prjpt, K. D.: Speed o Sound, Ientropc Copreblte, nd xce Molr olue o n Alknol + Cyclolkne t 0.5 K.. Reult or Alkn--ol + Cyclohexne. J. Che. ng. Dt 4, 67-7 (998) 5. Ohouru, K. K., Murk, S, J.: Speed o ound, exce olr volue, nd entropc copreblte o xch COC H 5 + ( x)c 6 H 6, xch COC H 5 + ( x)c 6 H 5 CH, xch COC H 5 + ( x) C 6 H 5 Cl, nd xc H 5 COC H 5 + ( x)c 6 H 6 t 98.5 K. Che. Therodync 9, 7-76 (987) 5. enkteu, P., Ro, M.. P.: xce volue o ternry xture o N,N-dethylorde + ethyl obutyl ketone + -lknol t 0.5 K. Flud Phe qulbr 98, 7-78 (994) 54. Jcobon, B.: Interoleculr ree length n the lqud tte; Adbtc nd otherl copreblte. Act Ch Scnd 6, (95) 55. Internet, per dt provded n dvnced chetry developent Inc, Adelde Street, Wet Toronto-Ontro, Cnd 55. Len, P. J., enkteu, P., Ln, H. M., Lee, M. J.: xce olr enthlpe o - octnol wth ethylbenzene ethyl benzote benzene nole or ethnol t 98.5 K. J. Che. ngg. Dt 47, 768 (00) 56. Arlgupp, M. I., Jdr, C.., Anbhv, T. M.: Denty, coty, Rerctve Index, nd Speed o Sound n Bnry Mxture o DMSO wth Methnol, thnol, Propn--ol, Butn--ol, Pentn--ol, Hexn- -ol, Heptn--ol, nd Butn--ol. J. Che. ngg. Dt 44, 6- (999) 57. Agrwl, P. B., Nrwde, M. L.: Ultronc nd vcoetrc tude o ubttuted lvone, oxzole nd pyrzole n 70 % cetone-wter xture. Ind J. Che. Sec A (00). Source o upport: Nl; Conlct o nteret: None declred 9 Interntonl Journl o Reerch n Phycl Chetry 0, (): 0-9

International Journal of Chemical Science and Technology

International Journal of Chemical Science and Technology vlble onlne t http://www.urpjournl.co Interntonl Journl o Checl Scence nd Technology Unverl Reerch Publcton. ll rght reerved btrct ISSN 49-85 Orgnl rtcle Therodync tudy o bnry lqud xture o Wter nd DMSO

More information

Solubilities and Thermodynamic Properties of SO 2 in Ionic

Solubilities and Thermodynamic Properties of SO 2 in Ionic Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,

More information

v v at 1 2 d vit at v v 2a d

v v at 1 2 d vit at v v 2a d SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton

More information

Effect of Wind Speed on Reaction Coefficient of Different Building Height. Chunli Ren1, a, Yun Liu2,b

Effect of Wind Speed on Reaction Coefficient of Different Building Height. Chunli Ren1, a, Yun Liu2,b 4th Interntonl Conference on Senor, Meurement nd Intellgent Mterl (ICSMIM 015) Effect of Wnd Speed on Recton Coeffcent of Dfferent Buldng Heght Chunl Ren1,, Yun Lu,b 1 No.9 Dxuexdo. Tnghn Cty, Hebe Provnce,

More information

8. INVERSE Z-TRANSFORM

8. INVERSE Z-TRANSFORM 8. INVERSE Z-TRANSFORM The proce by whch Z-trnform of tme ere, nmely X(), returned to the tme domn clled the nvere Z-trnform. The nvere Z-trnform defned by: Computer tudy Z X M-fle trn.m ued to fnd nvere

More information

An Ising model on 2-D image

An Ising model on 2-D image School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn

More information

On generalized 2-step continuous linear multistep method of hybrid type for the integration of second order ordinary differential equations

On generalized 2-step continuous linear multistep method of hybrid type for the integration of second order ordinary differential equations Avlble onlne t www.colrreerclbrry.co Scolr Reerc brry Arcve o Apple Scence Reerc :- ttp://colrreerclbrry.co/rcve.tl ISSN 9-X CODEN USA AASRC9 On generlze -tep contnuou lner ulttep eto o ybr type or te

More information

E-Companion: Mathematical Proofs

E-Companion: Mathematical Proofs E-omnon: Mthemtcl Poo Poo o emm : Pt DS Sytem y denton o t ey to vey tht t ncee n wth d ncee n We dene } ] : [ { M whee / We let the ttegy et o ech etle n DS e ]} [ ] [ : { M w whee M lge otve nume oth

More information

Chapter Newton-Raphson Method of Solving a Nonlinear Equation

Chapter Newton-Raphson Method of Solving a Nonlinear Equation Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson

More information

Molecular interaction Study in binary mixture of DMSO with formamide and N, N-dimethylformamide

Molecular interaction Study in binary mixture of DMSO with formamide and N, N-dimethylformamide Indan Journal of Pure & Appled Phyc Vol. 55, October 2017, pp. 729-736 Molecular nteracton Study n bnary xture of DMSO wth forade and N, N-dethylforade R D Sngh a * & M Gupta b a Departent of Phyc, Babu

More information

Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units!

Kinematics Quantities. Linear Motion. Coordinate System. Kinematics Quantities. Velocity. Position. Don t Forget Units! Knemtc Quntte Lner Phyc 11 Eyre Tme Intnt t Fundmentl Tme Interl t Dened Poton Fundmentl Dplcement Dened Aerge g Dened Aerge Accelerton g Dened Knemtc Quntte Scler: Mgntude Tme Intnt, Tme Interl nd Speed

More information

Chapter Newton-Raphson Method of Solving a Nonlinear Equation

Chapter Newton-Raphson Method of Solving a Nonlinear Equation Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson

More information

Linear predictive coding

Linear predictive coding Liner predictive coding Thi ethod cobine liner proceing with clr quntiztion. The in ide of the ethod i to predict the vlue of the current ple by liner cobintion of previou lredy recontructed ple nd then

More information

Applied Statistics Qualifier Examination

Applied Statistics Qualifier Examination Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng

More information

Fitting a Polynomial to Heat Capacity as a Function of Temperature for Ag. Mathematical Background Document

Fitting a Polynomial to Heat Capacity as a Function of Temperature for Ag. Mathematical Background Document Fttng Polynol to Het Cpcty s Functon of Teperture for Ag. thetcl Bckground Docuent by Theres Jul Zelnsk Deprtent of Chestry, edcl Technology, nd Physcs onouth Unversty West ong Brnch, J 7764-898 tzelns@onouth.edu

More information

a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114

a = Acceleration Linear Motion Acceleration Changing Velocity All these Velocities? Acceleration and Freefall Physics 114 Lner Accelerton nd Freell Phyc 4 Eyre Denton o ccelerton Both de o equton re equl Mgntude Unt Drecton (t ector!) Accelerton Mgntude Mgntude Unt Unt Drecton Drecton 4/3/07 Module 3-Phy4-Eyre 4/3/07 Module

More information

When current flows through the armature, the magnetic fields create a torque. Torque = T =. K T i a

When current flows through the armature, the magnetic fields create a torque. Torque = T =. K T i a D Motor Bic he D pernent-gnet otor i odeled reitor ( ) in erie with n inductnce ( ) nd voltge ource tht depend on the ngulr velocity of the otor oltge generted inide the rture K ω (ω i ngulr velocity)

More information

Name: SID: Discussion Session:

Name: SID: Discussion Session: Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether

More information

Physics 123. Exam #1. October 11, 2006

Physics 123. Exam #1. October 11, 2006 hyscs Exa # October, 006 roble /0 roble /0 roble /0 roble 4 /0 roble 5 /0 roble 6 /0 roble 7 /0 roble 8 /0 roble 9 /0 roble 0 /0 Total /00 Free-Response robles: lease show all work n order to receve partal

More information

Ideal Gas behaviour: summary

Ideal Gas behaviour: summary Lecture 4 Rel Gses Idel Gs ehviour: sury We recll the conditions under which the idel gs eqution of stte Pn is vlid: olue of individul gs olecules is neglected No interctions (either ttrctive or repulsive)

More information

Unique Solutions R. Amazing World of Carbon Compounds. C h a p t e r. G l a n c e

Unique Solutions R. Amazing World of Carbon Compounds. C h a p t e r. G l a n c e 9. C h p t e r t G l n c e Hydrocrbons - The fundmentl orgnic compounds : All orgnic compounds contin hydrogen long with crbon. They re the fundmentl orgnic compounds lso known s "Prent" compounds. These

More information

Chapter 14. Gas-Vapor Mixtures and Air-Conditioning. Study Guide in PowerPoint

Chapter 14. Gas-Vapor Mixtures and Air-Conditioning. Study Guide in PowerPoint Chpter 14 Gs-Vpor Mixtures nd Air-Conditioning Study Guide in PowerPoint to ccopny Therodynics: An Engineering Approch, 5th edition by Yunus A. Çengel nd Michel A. Boles We will be concerned with the ixture

More information

A SIMPLE EQUATION FOR ICE SHEET THICKNESS AND ICE FORMATION/BREAKUP PREDICTION

A SIMPLE EQUATION FOR ICE SHEET THICKNESS AND ICE FORMATION/BREAKUP PREDICTION Journl o JSCE, Vol. 2, 23-213, 214 A SIMPLE EQUATION FOR ICE SHEET THICKNESS AND ICE FORMATION/BREAKUP PREDICTION Yuro YOSHIKAWA 1, Yuru WATANABE 2 nd A ITOH 3,4 1 Member o JSCE, Atnt Proeor, Dept. o Cvl

More information

Introduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015

Introduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015 Introducton to Interfacal Segregaton Xaozhe Zhang 10/02/2015 Interfacal egregaton Segregaton n materal refer to the enrchment of a materal conttuent at a free urface or an nternal nterface of a materal.

More information

Chapter 12 Lyes KADEM [Thermodynamics II] 2007

Chapter 12 Lyes KADEM [Thermodynamics II] 2007 Chapter 2 Lyes KDEM [Therodynacs II] 2007 Gas Mxtures In ths chapter we wll develop ethods for deternng therodynac propertes of a xture n order to apply the frst law to systes nvolvng xtures. Ths wll be

More information

HPLC Separation and Identification of Parabens Homologs

HPLC Separation and Identification of Parabens Homologs HPLC Separaton and Identcaton o Paraben Hoolog Experent Objectve By experent, learn the bac prncple o chroatographc analy and the bac operaton o the ntruent, and undertand the proce o data analy. Learn

More information

Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden

Position and Speed Control. Industrial Electrical Engineering and Automation Lund University, Sweden Poton nd Speed Control Lund Unverty, Seden Generc Structure R poer Reference Sh tte Voltge Current Control ytem M Speed Poton Ccde Control * θ Poton * Speed * control control - - he ytem contn to ntegrton.

More information

concentration of the chemical species A to activity as shown below:

concentration of the chemical species A to activity as shown below: Fundmentl of Anlyticl Chemitry: th ed. Chpter Chpter - Activity, A, i the effective concentrtion of chemicl ecie A in olution. The ctivity coefficient, A, i the numericl fctor necery to convert the molr

More information

Chemistry 163B Absolute Entropies and Entropy of Mixing

Chemistry 163B Absolute Entropies and Entropy of Mixing Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) PPENDIX : H f, G f, U S (no Δ, no su f ) Chemstry 163 solute Entropes nd Entropy of Mxng Hº f Gº f Sº 1 hrd Lw

More information

Quick Visit to Bernoulli Land

Quick Visit to Bernoulli Land Although we have een the Bernoull equaton and een t derved before, th next note how t dervaton for an uncopreble & nvcd flow. The dervaton follow that of Kuethe &Chow ot cloely (I lke t better than Anderon).

More information

13 Design of Revetments, Seawalls and Bulkheads Forces & Earth Pressures

13 Design of Revetments, Seawalls and Bulkheads Forces & Earth Pressures 13 Desgn of Revetments, Sewlls nd Bulkheds Forces & Erth ressures Ref: Shore rotecton Mnul, USACE, 1984 EM 1110--1614, Desgn of Revetments, Sewlls nd Bulkheds, USACE, 1995 Brekwters, Jettes, Bulkheds nd

More information

Model Fitting and Robust Regression Methods

Model Fitting and Robust Regression Methods Dertment o Comuter Engneerng Unverst o Clorn t Snt Cruz Model Fttng nd Robust Regresson Methods CMPE 64: Imge Anlss nd Comuter Vson H o Fttng lnes nd ellses to mge dt Dertment o Comuter Engneerng Unverst

More information

x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions

x=0 x=0 Positive Negative Positions Positions x=0 Positive Negative Positions Positions Knemtc Quntte Lner Moton Phyc 101 Eyre Tme Intnt t Fundmentl Tme Interl Defned Poton x Fundmentl Dplcement Defned Aerge Velocty g Defned Aerge Accelerton g Defned Knemtc Quntte Scler: Mgntude Tme Intnt,

More information

2. Work each problem on the exam booklet in the space provided.

2. Work each problem on the exam booklet in the space provided. ECE470 EXAM # SOLUTIONS SPRING 08 Intructon:. Cloed-book, cloed-note, open-mnd exm.. Work ech problem on the exm booklet n the pce provded.. Wrte netly nd clerly for prtl credt. Cro out ny mterl you do

More information

4. More general extremum principles and thermodynamic potentials

4. More general extremum principles and thermodynamic potentials 4. More generl etremum prncples nd thermodynmc potentls We hve seen tht mn{u(s, X )} nd m{s(u, X)} mply one nother. Under certn condtons, these prncples re very convenent. For emple, ds = 1 T du T dv +

More information

A Tale of Friction Student Notes

A Tale of Friction Student Notes Nae: Date: Cla:.0 Bac Concept. Rotatonal Moeent Kneatc Anular Velocty Denton A Tale o Frcton Student Note t Aerae anular elocty: Intantaneou anular elocty: anle : radan t d Tanental Velocty T t Aerae tanental

More information

Acoustic Properties of Gasoline and Its Binary Liquid Mixtures with Kerosene

Acoustic Properties of Gasoline and Its Binary Liquid Mixtures with Kerosene 2018 IJSRST Volume 4 Issue 7 Print ISSN: 2395-6011 Online ISSN: 2395-602X Themed Section: Science nd Technology Acoustic Properties of Gsoline nd Its Binry iquid Mixtures with Kerosene ABSTRACT 1 Ajy R.

More information

ATTRIBUTE SELECTION AND INTRUSION DETECTION FOR KNOWLEDGE-BASED AUTHENTICATION SYSTEMS

ATTRIBUTE SELECTION AND INTRUSION DETECTION FOR KNOWLEDGE-BASED AUTHENTICATION SYSTEMS TTRIBTE SELECTIO D ITRSIO DETECTIO FOR OWLEDGE-BSED THETICTIO SYSTES Drgn olć, Brnlv Vunovć, Ch guyen Fculty of Technology, nverty of Portouth nglee Buldng, nglee Rod, Portouth, Hnt, PO 3DJ nted ngdo [drgn.nolc,

More information

Prediction of Ultrasonic Velocity in Binary Mixtures of a Nuclear Extractant and Monocarboxylic Acids using Several Theoretical Models

Prediction of Ultrasonic Velocity in Binary Mixtures of a Nuclear Extractant and Monocarboxylic Acids using Several Theoretical Models Predcton of ltrasonc Velocty n Bnary Mxtures of a Nuclear Extractant and Monocarboxylc Acds usng Several Theoretcal Models R. K. Mshra 1, B. Dala 1*, N. Swan 2 and S.K. Dash 3 1 BSH, Gandh Insttute of

More information

ECEN 5807 Lecture 26

ECEN 5807 Lecture 26 ECEN 5807 eture 6 HW 8 due v D Frdy, rh, 0 S eture 8 on Wed rh 0 wll be leture reorded n 0 he week of rh 5-9 Sprng brek, no le ody: Conlude pled-dt odelng of hghfrequeny ndutor dyn n pek urrentode ontrolled

More information

Analysis of Geometric, Zernike and United Moment Invariants Techniques Based on Intra-class Evaluation

Analysis of Geometric, Zernike and United Moment Invariants Techniques Based on Intra-class Evaluation 0 Ffth Interntonl Conference on Intellgent Systes, odellng nd Sulton Anlyss of Geoetrc, ernke nd Unted oent Invrnts Technques Bsed on Intr-clss Evluton ohd Wf srudn *, Shhrul z Ykob, Roze Rzf Othn, Iszdy

More information

PHYSICS 211 MIDTERM I 22 October 2003

PHYSICS 211 MIDTERM I 22 October 2003 PHYSICS MIDTERM I October 3 Exm i cloed book, cloed note. Ue onl our formul heet. Write ll work nd nwer in exm booklet. The bck of pge will not be grded unle ou o requet on the front of the pge. Show ll

More information

The gravitational field energy density for symmetrical and asymmetrical systems

The gravitational field energy density for symmetrical and asymmetrical systems The ravtatonal eld enery denty or yetrcal and ayetrcal yte Roald Sonovy Techncal Unverty 90 St. Peterbur Rua E-al:roov@yandex Abtract. The relatvtc theory o ravtaton ha the conderable dculte by decrpton

More information

Thermomechanical Stress in the Evolution of Shear of Fiber-Matrix Interface Composite Material

Thermomechanical Stress in the Evolution of Shear of Fiber-Matrix Interface Composite Material Mterls Scences nd Applctons, 0,, 399-403 do:0.436/s.0.505 Publshed Onlne My 0 (http://www.scp.org/journl/s) 399 Theroechncl Stress n the voluton o Sher o Fber-Mtrx Interce Coposte Mterl Dll eoun Boureg,

More information

Chapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A.

Chapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A. Chapter 3 Gas Mxtures Study Gude n PowerPont to accopany Therodynacs: An Engneerng Approach, 5th edton by Yunus A. Çengel and Mchael A. Boles The dscussons n ths chapter are restrcted to nonreactve deal-gas

More information

20.2. The Transform and its Inverse. Introduction. Prerequisites. Learning Outcomes

20.2. The Transform and its Inverse. Introduction. Prerequisites. Learning Outcomes The Trnform nd it Invere 2.2 Introduction In thi Section we formlly introduce the Lplce trnform. The trnform i only pplied to cul function which were introduced in Section 2.1. We find the Lplce trnform

More information

Local and Total Entropy Production and Heat and Water Fluxes in a One-Dimensional Polymer Electrolyte Fuel Cell

Local and Total Entropy Production and Heat and Water Fluxes in a One-Dimensional Polymer Electrolyte Fuel Cell 9020 J. Phy. Che. B 2005, 09, 9020-9033 Locl n otl Entropy Proucton n Het n Wter Fluxe n One-Denonl Polyer Electrolyte Fuel Cell Sgne Keltrup* n Auun Røore Deprtent of Chetry, Noregn UnVerty of Scence

More information

Let us look at a linear equation for a one-port network, for example some load with a reflection coefficient s, Figure L6.

Let us look at a linear equation for a one-port network, for example some load with a reflection coefficient s, Figure L6. ECEN 5004, prng 08 Actve Mcrowve Crcut Zoy Popovc, Unverty of Colordo, Boulder LECURE 5 IGNAL FLOW GRAPH FOR MICROWAVE CIRCUI ANALYI In mny text on mcrowve mplfer (e.g. the clc one by Gonzlez), gnl flow-grph

More information

Phys101 Lecture 4,5 Dynamics: Newton s Laws of Motion

Phys101 Lecture 4,5 Dynamics: Newton s Laws of Motion Phys101 Lecture 4,5 Dynics: ewton s Lws of Motion Key points: ewton s second lw is vector eqution ction nd rection re cting on different objects ree-ody Digrs riction Inclines Ref: 4-1,2,3,4,5,6,7,8,9.

More information

Lecture 4: Piecewise Cubic Interpolation

Lecture 4: Piecewise Cubic Interpolation Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml

More information

The heat budget of the atmosphere and the greenhouse effect

The heat budget of the atmosphere and the greenhouse effect The het budget of the tmosphere nd the greenhouse effect 1. Solr rdition 1.1 Solr constnt The rdition coming from the sun is clled solr rdition (shortwve rdition). Most of the solr rdition is visible light

More information

ψ ij has the eigenvalue

ψ ij has the eigenvalue Moller Plesset Perturbton Theory In Moller-Plesset (MP) perturbton theory one tes the unperturbed Hmltonn for n tom or molecule s the sum of the one prtcle Foc opertors H F() where the egenfunctons of

More information

The influence of Stern layer conductance on the. dielectrophoretic behaviour of latex nanospheres

The influence of Stern layer conductance on the. dielectrophoretic behaviour of latex nanospheres The nfluence of Stern layer conductance on the delectrophoretc behavour of latex nanophere Mchael Pycraft Hughe* Bomedcal Engneerng Group, Unverty of Surrey, Guldford, GU2 7XH, UK Ncola Gavn Green Boelectronc

More information

V E L O C I T Y a n d V E L O C I T Y P R E S S U R E I n A I R S Y S T E M S

V E L O C I T Y a n d V E L O C I T Y P R E S S U R E I n A I R S Y S T E M S V E L O C I T Y n d V E L O C I T Y R E S S U R E I n A I R S Y S T E M S A nlysis of fluid systes using ir re usully done voluetric bsis so the pressure version of the Bernoulli eqution is used. This

More information

CURVE FITTING LEAST SQUARES METHOD

CURVE FITTING LEAST SQUARES METHOD Nuercl Alss for Egeers Ger Jord Uverst CURVE FITTING Although, the for of fucto represetg phscl sste s kow, the fucto tself ot be kow. Therefore, t s frequetl desred to ft curve to set of dt pots the ssued

More information

PHYSICS. (c) m D D m. v vt. (c) 3. Width of the river = d = 800 m m/s. 600m. B 800m v m,r. (b) 1000m. v w

PHYSICS. (c) m D D m. v vt. (c) 3. Width of the river = d = 800 m m/s. 600m. B 800m v m,r. (b) 1000m. v w PHYSICS T. T 8 k/hr = /s, ' Hz, ' 7 Hz T. r D D D,. r D D. D. D.... g/c. Width o the rier = d = 8 w /s B 8,r P O. sin t cos., on the copring this eqution, with sin t cos k =, k =. k. /s w Q. =, 9 9 = 8,

More information

Two-Layered Model of Blood Flow through Composite Stenosed Artery

Two-Layered Model of Blood Flow through Composite Stenosed Artery Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-9466 Vol. 4, Iue (December 9), pp. 343 354 (Prevouly, Vol. 4, No.) Applcaton Appled Mathematc: An Internatonal Journal (AAM) Two-ayered Model

More information

Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 10 - Phase Equilibria and Polymer Blends February 7, 2001

Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 10 - Phase Equilibria and Polymer Blends February 7, 2001 Checal Engneerng 60/60 Polyer Scence and Engneerng Lecture 0 - Phase Equlbra and Polyer Blends February 7, 00 Therodynacs of Polyer Blends: Part Objectves! To develop the classcal Flory-Huggns theory for

More information

Math 2142 Homework 2 Solutions. Problem 1. Prove the following formulas for Laplace transforms for s > 0. a s 2 + a 2 L{cos at} = e st.

Math 2142 Homework 2 Solutions. Problem 1. Prove the following formulas for Laplace transforms for s > 0. a s 2 + a 2 L{cos at} = e st. Mth 2142 Homework 2 Solution Problem 1. Prove the following formul for Lplce trnform for >. L{1} = 1 L{t} = 1 2 L{in t} = 2 + 2 L{co t} = 2 + 2 Solution. For the firt Lplce trnform, we need to clculte:

More information

Thermodynamics Lecture Series

Thermodynamics Lecture Series Therodynac Lecture Sere Dynac Enery Traner Heat, ork and Ma ppled Scence Educaton Reearch Group (SERG) Faculty o ppled Scence Unvert Teknolo MR Pure utance Properte o Pure Sutance- Revew CHPTER eal: drjjlanta@hotal.co

More information

Volumetric And Acoustic Properties Of Binary Liquid Mixtures Of Acetonitrile With 2-Ethoxyethanol And 2-Butoxyethanol At Different Temperatures

Volumetric And Acoustic Properties Of Binary Liquid Mixtures Of Acetonitrile With 2-Ethoxyethanol And 2-Butoxyethanol At Different Temperatures Volue 3 Iue 9, Augut 2016 ISSN: 23944404 Voluetric And Acoutic Propertie Of Binary Liquid Mixture Of Acetonitrile With 2thoxyethanol And 2Butoxyethanol At Different Teperature Rahul Singh Abalika Intitute

More information

Analysis of error propagation in profile measurement by using stitching

Analysis of error propagation in profile measurement by using stitching Ay o error propgto proe eureet y ug ttchg Ttuy KUME, Kzuhro ENAMI, Yuo HIGASHI, Kej UENO - Oho, Tuu, Ir, 35-8, JAPAN Atrct Sttchg techque whch ee oger eureet rge o proe ro eer eure proe hg prty oerppe

More information

Chapter One Mixture of Ideal Gases

Chapter One Mixture of Ideal Gases herodynacs II AA Chapter One Mxture of Ideal Gases. Coposton of a Gas Mxture: Mass and Mole Fractons o deterne the propertes of a xture, we need to now the coposton of the xture as well as the propertes

More information

Department of Economics, Niigata Sangyo University, Niigata, Japan

Department of Economics, Niigata Sangyo University, Niigata, Japan Appled Matheatcs, 0, 5, 777-78 Publshed Onlne March 0 n ScRes. http://www.scrp.org/journal/a http://d.do.org/0.6/a.0.507 On Relatons between the General Recurrence Forula o the Etenson o Murase-Newton

More information

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses

More information

APPENDIX 2 LAPLACE TRANSFORMS

APPENDIX 2 LAPLACE TRANSFORMS APPENDIX LAPLACE TRANSFORMS Thi ppendix preent hort introduction to Lplce trnform, the bic tool ued in nlyzing continuou ytem in the frequency domin. The Lplce trnform convert liner ordinry differentil

More information

r = cos θ + 1. dt ) dt. (1)

r = cos θ + 1. dt ) dt. (1) MTHE 7 Proble Set 5 Solutions (A Crdioid). Let C be the closed curve in R whose polr coordintes (r, θ) stisfy () Sketch the curve C. r = cos θ +. (b) Find pretriztion t (r(t), θ(t)), t [, b], of C in polr

More information

The Number of Rows which Equal Certain Row

The Number of Rows which Equal Certain Row Interntonl Journl of Algebr, Vol 5, 011, no 30, 1481-1488 he Number of Rows whch Equl Certn Row Ahmd Hbl Deprtment of mthemtcs Fcult of Scences Dmscus unverst Dmscus, Sr hblhmd1@gmlcom Abstrct Let be X

More information

Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]

Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B] Conept of Atvty Equlbrum onstnt s thermodynm property of n equlbrum system. For heml reton t equlbrum; Conept of Atvty Thermodynm Equlbrum Constnts A + bb = C + dd d [C] [D] [A] [B] b Conentrton equlbrum

More information

APPROXIMATE INTEGRATION

APPROXIMATE INTEGRATION APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be

More information

Introduction to Numerical Integration Part II

Introduction to Numerical Integration Part II Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w

More information

Scattering of two identical particles in the center-of. of-mass frame. (b)

Scattering of two identical particles in the center-of. of-mass frame. (b) Lecture # November 5 Scatterng of two dentcal partcle Relatvtc Quantum Mechanc: The Klen-Gordon equaton Interpretaton of the Klen-Gordon equaton The Drac equaton Drac repreentaton for the matrce α and

More information

DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)

DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x) DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng

More information

INTERPOLATION(1) ELM1222 Numerical Analysis. ELM1222 Numerical Analysis Dr Muharrem Mercimek

INTERPOLATION(1) ELM1222 Numerical Analysis. ELM1222 Numerical Analysis Dr Muharrem Mercimek ELM Numercl Anlss Dr Muhrrem Mercmek INTEPOLATION ELM Numercl Anlss Some of the contents re dopted from Lurene V. Fusett, Appled Numercl Anlss usng MATLAB. Prentce Hll Inc., 999 ELM Numercl Anlss Dr Muhrrem

More information

Exponents and Powers

Exponents and Powers EXPONENTS AND POWERS 9 Exponents nd Powers CHAPTER. Introduction Do you know? Mss of erth is 5,970,000,000,000, 000, 000, 000, 000 kg. We hve lredy lernt in erlier clss how to write such lrge nubers ore

More information

Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations

Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations Cter. Runge-Kutt nd Order Metod or Ordnr Derentl Eutons Ater redng ts cter ou sould be ble to:. understnd te Runge-Kutt nd order metod or ordnr derentl eutons nd ow to use t to solve roblems. Wt s te Runge-Kutt

More information

Analysis of Variance and Design of Experiments-II

Analysis of Variance and Design of Experiments-II Anly of Vrne Degn of Experment-II MODULE VI LECTURE - 8 SPLIT-PLOT AND STRIP-PLOT DESIGNS Dr Shlbh Deprtment of Mthemt & Sttt Indn Inttute of Tehnology Knpur Tretment ontrt: Mn effet The uefulne of hvng

More information

STABILITY and Routh-Hurwitz Stability Criterion

STABILITY and Routh-Hurwitz Stability Criterion Krdeniz Technicl Univerity Deprtment of Electricl nd Electronic Engineering 6080 Trbzon, Turkey Chpter 8- nd Routh-Hurwitz Stbility Criterion Bu der notlrı dece bu deri ln öğrencilerin kullnımın çık olup,

More information

The Representation of Multi-component Adsorption in Reservoir Simulation of CO 2 Sequestration in Coal and Enhanced Coalbed Methane Recovery

The Representation of Multi-component Adsorption in Reservoir Simulation of CO 2 Sequestration in Coal and Enhanced Coalbed Methane Recovery The Representton of Mult-component Adsorpton n Reservor Smulton of CO 2 Sequestrton n Col nd Enhnced Colbed Methne Recovery 59 Zhejun Pn nd LD Connell CSIRO Petroleum, Prvte Bg 1, Clyton South, Vctor,

More information

A RADIANT AIR-CONDITIONING SYSTEM USING SOLAR-DRIVEN LIQUID DESICCANT EVAPORATIVE WATER COOLER

A RADIANT AIR-CONDITIONING SYSTEM USING SOLAR-DRIVEN LIQUID DESICCANT EVAPORATIVE WATER COOLER Journl of Engneerng Scence nd Technology Vol 1, No 2 (2006) 139-157 School of Engneerng, Tylor Unverty College A RADIANT AIR-CONDITIONING SYSTEM USING SOLAR-DRIVEN LIQUID DESICCANT EVAPORATIVE WATER COOLER

More information

Chemical Reaction Engineering

Chemical Reaction Engineering Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce. Lst Lecture Energy Blnce Fundmentls F 0 E 0 F E Q W

More information

C Nuclear Magnetic Resonance

C Nuclear Magnetic Resonance Inherent Difficulties Low bundnce of 13 C (1.1% vs, 99.9% for 1 H) Lower gyromgnetic rtio (1/4 tht of 1 H) - 13 C: 67.28 vs. 1 H 267.53-1/2 1,000,000 nuclei t 60 MHz E ΔE +1/2 1,000,009 nuclei t 60 MHz

More information

OXFORD H i g h e r E d u c a t i o n Oxford University Press, All rights reserved.

OXFORD H i g h e r E d u c a t i o n Oxford University Press, All rights reserved. Renshw: Mths for Econoics nswers to dditionl exercises Exercise.. Given: nd B 5 Find: () + B + B 7 8 (b) (c) (d) (e) B B B + B T B (where 8 B 6 B 6 8 B + B T denotes the trnspose of ) T 8 B 5 (f) (g) B

More information

Rel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited

More information

Linear Open Loop Systems

Linear Open Loop Systems Colordo School of Me CHEN43 Trfer Fucto Ler Ope Loop Sytem Ler Ope Loop Sytem... Trfer Fucto for Smple Proce... Exmple Trfer Fucto Mercury Thermometer... 2 Derblty of Devto Vrble... 3 Trfer Fucto for Proce

More information

Part I: Basic Concepts of Thermodynamics

Part I: Basic Concepts of Thermodynamics Prt I: Bsic Concepts o Thermodynmics Lecture 4: Kinetic Theory o Gses Kinetic Theory or rel gses 4-1 Kinetic Theory or rel gses Recll tht or rel gses: (i The volume occupied by the molecules under ordinry

More information

Calculate the efficiency associated with one rotation of the axle

Calculate the efficiency associated with one rotation of the axle We cn clculte the efficiency of one rottion of the xle by exining the work one. k Mx Your Rie: Workheet hi ctivity will tke you through the tep neee to optiize the work ue in your ouetrp cr. ollow thi

More information

? plate in A G in

? plate in A G in Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0

More information

Substitution Matrices and Alignment Statistics. Substitution Matrices

Substitution Matrices and Alignment Statistics. Substitution Matrices Susttuton Mtrces nd Algnment Sttstcs BMI/CS 776 www.ostt.wsc.edu/~crven/776.html Mrk Crven crven@ostt.wsc.edu Ferur 2002 Susttuton Mtrces two oulr sets of mtrces for roten seuences PAM mtrces [Dhoff et

More information

The Thermodynamics of Aqueous Electrolyte Solutions

The Thermodynamics of Aqueous Electrolyte Solutions 18 The Thermodynmics of Aqueous Electrolyte Solutions As discussed in Chpter 10, when slt is dissolved in wter or in other pproprite solvent, the molecules dissocite into ions. In queous solutions, strong

More information

Artificial Intelligence Markov Decision Problems

Artificial Intelligence Markov Decision Problems rtificil Intelligence Mrkov eciion Problem ilon - briefly mentioned in hpter Ruell nd orvig - hpter 7 Mrkov eciion Problem; pge of Mrkov eciion Problem; pge of exmple: probbilitic blockworld ction outcome

More information

What's Your Body Composition?

What's Your Body Composition? Wht' Your Body Compoition? DETERMINING YOUR BODY FAT The firt tep determ your compoition i clculte your body ft percente of your tl weiht. Refer now the workheet for comput your percente of body ft. (The

More information

Jackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell

Jackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell Jckson 2.26 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: The two-dimensionl region, ρ, φ β, is bounded by conducting surfces t φ =, ρ =, nd φ = β held t zero

More information

UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II

UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )

More information

Mathematics Extension 1

Mathematics Extension 1 04 Bored of Studies Tril Emintions Mthemtics Etension Written by Crrotsticks & Trebl. Generl Instructions Totl Mrks 70 Reding time 5 minutes. Working time hours. Write using blck or blue pen. Blck pen

More information

LECTURE 23 SYNCHRONOUS MACHINES (3)

LECTURE 23 SYNCHRONOUS MACHINES (3) ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURE 3 SYNCHRONOUS MACHINES (3) Acknowledgent-Thee hndout nd lecture note given in cl re bed on teril fro Prof. Peter Suer ECE 330 lecture note. Soe lide

More information

Problems (Show your work!)

Problems (Show your work!) Prctice Midter Multiple Choice 1. A. C 3. D 4. D 5. D 6. E 7. D 8. A 9. C 9. In word, 3.5*10 11 i E. 350 billion (I nubered 9 twice by itke!) 10. D 11. B 1. D 13. E 14. A 15. C 16. B 17. A 18. A 19. E

More information

Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations

Dynamics of Linked Hierarchies. Constrained dynamics The Featherstone equations Dynm o Lnke Herrhe Contrne ynm The Fethertone equton Contrne ynm pply ore to one omponent, other omponent repotone, rom ner to r, to ty tne ontrnt F Contrne Boy Dynm Chpter 4 n: Mrth mpule-be Dynm Smulton

More information

Lecture 11. Chapter 7. - Thermodynamic Web - Departure Functions - Review Equations of state (chapter 4, briefly)

Lecture 11. Chapter 7. - Thermodynamic Web - Departure Functions - Review Equations of state (chapter 4, briefly) Lecture 11 Chpter 5 - Thermodnmc We - Deprture unctons - Revew Equtons of stte (chpter 4, refl) Chpter 6 - Equlrum (chemcl potentl) * ure Component * Mtures Chpter 7 - ugct (chemcl potentl fugct equlrum

More information

Organic Acids - Carboxylic Acids

Organic Acids - Carboxylic Acids Orgnic Acids - rboxylic Acids Orgnic cids - crboxylic cid functionl group rboxylic cids re redily deprotonted by bses such s NO eg 3 O O - + O - + O 3 O O Acid Bse onjugte Bse onjugte Acid This rection

More information