Evaluation of Opiate Separation by High-Resolution Electrospray Ionization-Ion Mobility Spectrometry/ Mass Spectrometry

Size: px
Start display at page:

Download "Evaluation of Opiate Separation by High-Resolution Electrospray Ionization-Ion Mobility Spectrometry/ Mass Spectrometry"

Transcription

1 Anl. Chem. 2001, 73, Evlution of Opite Seprtion by High-Resolution Electrospry Ioniztion-Ion Mobility Spectrometry/ Mss Spectrometry Lur M. Mtz nd Herbert H. Hill, Jr.* Deprtment of Chemistry, Wshington Stte University, Pullmn, Wshington The seprtion of opites nd the primry metbolites ws evluted with ESI-IMS/MS. Seven opite molecules were nlyzed, nd spectr were shown for ech compound. The IMS seprtion of two isomers (morphine nd norcodeine) ws shown with bseline seprtion. Differences in the mobilities were found for the noncetylted, monocetylted, nd bicetylted compounds. In this study, two primry findings re reported. First, IMS cn esily seprte metbolic isomers, nd second, the twodimensionl seprtion cpbility of IMS/MS cn be employed to confidently identify nd seprte both the opites nd metbolites. Although previous IMS studies hve shown the seprtion of isomers, this is the first exmple to show the cpbility of IMS to seprte metbolic isomers (within 70 s), significnt dvntge in high-throughput screening for phrmcokinetic studies. Second, the monocetylted nd bicetylted compounds were found to form more compct ions for the sodium dducts in comprison to the protonted moleculr ions. On the bsis of the mobilities, informtion on structures nd conformtion cn be deduced when sodium nd protonted ions re compred. The high incidence of drug buse necessittes sensitive techniques for drug detection nd identifiction. 1 Heroin, morphine, nd codeine re the primrily bused opite compounds, lthough their metbolites re evluted s well for chrcteristic biologicl mrkers present hours fter intoxiction. 2 For this reson, opite seprtions ddress the nlysis of both the opites nd metbolites. 2,3 While mny different nlyticl techniques hve been employed for opite detection, 4-6 liquid chromtogrphy/ mss spectrometry (LC/MS) is currently the most commonly used * Corresponding uthor: (tel) (509) ; (fx) (509) ; (e-mil) hhhill@wsu.edu. (1) Sunshine, I.; Sutliff, J. P. Swet It Out. In Hndbook of Anlyticl Therpeutic Drug Monitoring nd Toxicology; Wong, S. H. Y., Sunshine, I., Eds.; CRC Press: Boc Rton, FL, (2) Blnchet, M.; Bru, G.; Guerret, M.; Bromet-Petit, M.; Bromet, N. J. Chromtogr., A 1999, 854, (3) Dienes-Ngy, A.; Rivier, L.; Giroud, C.; Augsburger, M.; Mngin, P. J. Chromtogr., A 1999, 854, (4) Goldberger, B. A.; Drwin, W. A.; Grnt, T. M.; Allen, A. C.; Cpln, Y. H.; Cone, E. J. Clin. Chem. 1993, 39, (5) Mitchell, J. M.; Pul, B. D.; Welch, P.; Cone, E. J. Anl. Toxicol. 1991, 15, (6) Osborne, R. Clin. Phrmcol. Ther., 1990, 47, method due to its bility to seprte metbolic isomers while chieving the required sensitivity with MS detection. 2,3 Since its inception, ion mobility spectrometry (IMS) hs been utilized s technique for detecting drugs of buse. 7 Until recently, IMS reserch for drug detection focused on field portble devices. 8,9 Both the coupling of electrospry ioniztion (ESI) to IMS 10 nd the introduction of high-resolution IMS instruments hve extended IMS pplictions to include more complex mixtures (drugs of buse, 14 chemicl wrfre gents, 15 nd tryptic digests 16,17 ). Current stte-of-the-rt IMS/MS systems hve chieved seprtion efficiencies comprble to common chromtogrphic techniques nd, therefore, re being evluted s high-resolution seprtion technique. 18 In IMS, ions re identified by mesuring the time it tkes the ion to trvel through drift tube. An ion s mobility cn be determined from the drift time nd is relted to n ion s size-tochrge rtio. Evlutions of high-resolution ESI-IMS/MS systems hve elucidted different gs-phse mobilities for mny peptide isomers 19 nd mino cid isomers (leucine nd isoleucine). 18 Although the reltionship between solution-phse geometry nd gs-phse geometries remins undertermined, 20 ion mobilities provide structurl informtion tht cn be utilized to consider (7) Krsek, F. W.; Hill, H. H., Jr.; Kim, S. H. J. Chromtogr. 1976, 117, (8) Fetterolf, D. D.; Donnelyy, B.; Lsswell, L. D. AT ONSITE 1996, 2 (1), (9) Fytche, L. M.; Hupe, M.; Kovr, J. B.; Pilon, P. J. Forensic Sci., 1992, 37, (10) Chen, Y. H.; Hill, H. H., Jr.; Wittmer, D. P. J. Microcolumn Sep. 1994, 6, (11) Wu, C.; Siems, W. F.; Asbury, G. R.; Hill, H. H., Jr. Anl. Chem. 1998, 70, (12) Dugourd, Ph; Hudgins, R. R.; Clemmer, D. E.; Jrrold, M. F. Rev. Sci. Instrum. 1997, 68, (13) Sreblus, C. A.; Li, J.; Mrshll, W. S.; Clemmer, D. E. Anl. Chem. 1999, 71, (14) Wu, C.; Siems, W. F.; Hill, H. H., Jr. Anl. Chem. 2000, 72, (15) Asbury, G. R.; Wu, C.; Siems, W. F.; Hill, H. H., Jr. Anl. Chim. Act 2000, 404, (16) Vlentine, S. J.; Countermn, A. E.; Hoglund, C. S.; Reilly, J. P.; Clemmer, D. E. J. Am. Soc. Mss Spectrom. 1998, 9, (17) Vlentine, S. J.; Countermn, A. E.; Clemmer, D. E. J. Am. Soc. Mss Spectrom. 1999, 10, (18) Asbury, G. R.; Hill, H. H., Jr. J. Microcolumn Sep. 2000, 12, (19) Wu, C.; Siems, W. F.; Klsmeer, J.; Hill, H. H., Jr. Anl. Chem. 2000, 72, (20) Hoglund-Hyzer, C. S.; Countermn, A. E.; Clemmer, D. E. Chem. Rev. 1999, 99, Anlyticl Chemistry, Vol. 73, No. 8, April 15, /c001147b CCC: $ Americn Chemicl Society Published on Web 03/13/2001

2 possible structures Additionl peptide structurl informtion hs been elucidted from sodium dduct formtions 24,25 in which it ws found tht doubly chrged brdykinin ions tht wrpped round sodium ion formed more compct structure thn the (M + 2H) 2+ ion. Understnding the reltionship between conformtionl geometries nd biologicl citivity is importnt for not only proteins (i.e., enzymes) but drug molecules s well. As described bove, the utility of IMS/MS for discerning peptide nd protein conformtions hs been shown. The objectives of this study were to develop IMS/MS s n lterntive (fster) seprtion technique to LC/MS. Becuse IMS provides ion size informtion, structurl fetures of the opites nd metbolites were lso investigted. EXPERIMENTAL SECTION Regents nd Chemicls. The seven opite derivtives employed in this study were purchsed from Alltech Assocites (Bellefonte, PA) s 1.0 mg/ml stndrds in methnol (heroin concentrtion ws 0.10 mg/ml) nd included normorphine, norcodeine, codeine, morphine, 6-monocetyl codeine (MAC), 6-monocetyl morphine (MAM), nd heroin. All stndrd solutions were diluted to concentrtions of 100 ppm ( 300 µm) (heroin ws diluted to 50 ppm concentrtion). All solvents (wter, methnol, nd cetic cid) were obtined from J. T.Bker (Phillipsburgh, N. J.) nd were HPLC grde. Instrumenttion. A high-resolution ESI-IMS/MS instrument ws employed for ll experiments nd hs been described previously (wter-cooled ESI source, 10 high-resolution IMS/MS, 11 nd recent modifiction to the IMS/MS 18 ). The ESI source ws mintined t 14 kv resulting in +4-kV difference between the ESI source nd the trget screen. The ESI solvent composition ws 47.5%/47.5% methnol/wter with 5% cetic cid. Anlyticl stndrd delivery ws performed vi six-port (Vlco Industries, Houston, TX) injection port nd n externl (70 µl) injection loop. The IMS drift tube consisted of two regions: (1) desolvtion region (13 cm in length), which served to completely remove excess solvent molecules from the ions prior to entry into the drift region, nd the drift region (22.5 cm in length). A positive voltge (ll experiments were performed in the positive mode) of 10 kv ws pplied to the electronic ion gte, which equted to n verge drift field of 385 V/cm. Nitrogen ws employed s the drift gs nd ESI cooling gs (flow rtes of 800 nd 100 ml/min, respectively). Both IMS regions were mintined t temperture of 250 C. The IMS ws interfced to 150-QC ABB-Extrel (Pittsburgh, PA) qudrupole mss spectrometer vi 40-µm pinhole interfce. A series of six Einzel lenses were plced fter the drift tube nd were operted t the following voltges (listed in order): +8.0 (pinhole), (screen), (first element of einzel), (second element of einzel), (third element of einzel), nd V (ELFS plte). The dynode nd electron multiplier were operted t -5.0 nd 1.7 kv, respectively, nd the qudrupole mss filter ws bised t V. The current signl ws collected with Keithley model 427 mplifier (Keithley Instruments, Clevelnd, OH) nd mplified (10 9 gin), nd the signl ws sent to Lbview (Ntionl Instruments, Houston, TX) dt cquisition system. All spectr were the result of 1000 verges obtined with gte pulse width of 0.2 ms nd totl scn time of 50.0 ms. Due to overhed from Lbview dt processing, ech spectrum took 70 s to obtin. All IMS spectr presented were obtined in one of two instrumentl opertion modes: non-mss-selective nd mss-selective ion monitoring (SIM). For the first mode (rf only), the qudrupole served to trnsmit ions from the IMS drift tube to the electron multiplier. For SIM, the qudrupole selectively trnsmitted one m/z vlue from the IMS tube. Clcultions. All reduced mobility constnts (K o ) nd collision cross-section () vlues were clculted from experimentlly determined drift times (t d ). The reduced mobility constnts were clculted ccording to the following eqution: K o ) ( L2 Vt d)( 273 T )( 760) P (1) where L ws the drift region length (22.5 cm), V ws the drift voltge (8680 V), T ws the effective temperture in the drift region (523 K), nd P ws the pressure in the drift region ( Torr). The verge ion collision cross section () ws clculted from the following eqution: 26 ) ( 16N)( 3 µkt) 1/2( 2π zevt d L ) (2) 2 where z is the number of the chrges on the ion, e is the chrge of one proton, N is the number density of the drift gs, µ [) mm/ (m + M)] is the reduced mss of n ion (m) nd the neutrl drift gs (M), nd k is Boltzmnn s constnt. RESULTS AND DISCUSSION In Figure 1, the structures for the seven opite compounds studied re shown. The moleculr weight for ech compound is lso presented nd listed in the order of incresing mss. Three bused drugs (heroin, codeine, nd morphine) nd four primry metbolites were evluted. The differences in the structures were due to functionl group plcement t one or more of the three sites, R 1,R 2,orR 3. Norcodeine nd normorphine re the demethylted derivtives of codeine nd morphine, respectively. MAC nd MAM re the cetylted derivtives for codeine nd morphine, respectively. For ll seven compounds, both nonselective IMS spectr nd SIM spectr were obtined to mss identify ech ion mobility pek tht ws observed. The reduced mobility constnts (K o ) nd corresponding m/z vlues for the seven compounds re listed in Tble 1. Severl trends in ion formtion cn be elucidted from Tble 1. First, ll seven compounds formed protonted moleculr (21) Trszk, J. A.; Li, J.; Clemmer, D. E. J. Phys. Chem. B 2000, 104, (22) Countermn, A. E.; Vlentine, S. J.; Sreblus, C. A.; Henderson, S. C.; Hoglund, C. S.; Clemmer, D. E. J. Am. Soc. Mss Spectrom. 1998, 9, (23) Vlentine, S. J.; Anderson, J. G.; Ellington, A. D.; Clemmer, D. E. J. Phys. Chem. B 1997, 101, (24) Wu, C.; Klsmeier, J.; Hill, H. H., Jr. Rpid Comm. Mss Spectrom. 1999, 13, (25) Wyttenbch, T.; von Helden, G.; Bowers, M. T. J. Am. Chem. Soc. 1996, 118, (26) Revercomb, H. E.; Mson, E. A. Anl. Chem. 1975, 47, Anlyticl Chemistry, Vol. 73, No. 8, April 15,

3 Tble 1. Reduced Mobility Vlues nd Mss Identities for Ions Formed from Seven Opite Compounds compound ion M - 18 M + 1 M + 23 M - 59 (M - H 2O) + (MH) + (M + N) + (M - COOCH 3) + normorphine K o (cm 2 V -1 s -1 ) m/z morphine K o (cm 2 V -1 s -1 ) m/z norcodeine K o (cm 2 V -1 s -1 ) m/z codeine K o (cm 2 V -1 s -1 ) m/z monocetyl morphine K o (cm 2 V -1 s -1 ) m/z monocetyl codeine K o (cm 2 V -1 s -1 ) m/z heroin K o (cm 2 V -1 s -1 ) m/z Identified s M - 43 ion for heroin. Figure 1. Structure of seven opite compounds evluted in this study. ion nd six of seven formed sodium dduct (except norcodeine). The noncetylted opites (normorphine, morphine, codeine, nd norcodeine) lso formed n (M - 18) + ion which is thought to be the loss of wter (M - H 2 O) +. Similrly, ions contining cetyl groups, MAM, MAC, nd heroin, formed (M - 59) + ions which corresponds to the loss of n cetyl group (COOCH 3 ). In ddition, the ESI of heroin formed fourth ion, (M - 43) +, the loss of COCH 3 group. The moleculr decompositions re similr to results from previous IMS studies tht utilized rdioctive sources for ioniztion of opites 27 nd for other drug molecules contining hydroxyl groups. 28 In contrst, studies using ESI-MS hve shown tht only the protonted ions were observed in the mss spectrum. 2,3 (27) Lwrence, A. H. Anl. Chem. 1988, 58, (28) Lwrence, A. H. Anl. Chem. 1989, 59, Figure 2. Nonselective ESI-IMS/MS spectr of four noncetylted compounds: () normorphine, (b) morphine, (c) norcodeine, nd (d) codeine. Products ion for ech compound were mss identified to be (1) (M - H 2O) +, (2) MH +, nd (3) (M + N) +. Although similr frgmenttion hs been seen by incresed skimmer voltges in ESI-MS, the unique mobilities for the decomposition products indicted tht the frgmenttion occurred prior to beginning the ion mobility experiment. The difference in the ioniztion process is not obvious, lthough fundmentl understnding of the difference would enble mnipultion of experimentl prmeters to gin moleculr informtion. Bsed on these structurl observtions nd distinguishing functionl group losses, the following results re broken into two groupings: noncetylted opites nd cetylted opites Anlyticl Chemistry, Vol. 73, No. 8, April 15, 2001

4 Tble 2. Mesured Collision Cross Sections of Four Noncetylted Opite Compounds nd Reltive Increse with Additionl Functionl Groups nd Ionic Size ion NM M NC (M - H 2O) Å Å Å Å 2 V% MH Å Å Å Å 2 V% (M + N) Å Å Å 2 Reltive increse in collision cross section from previous row/ column to next. C Tble 3. Mesured Collision Cross Sections of Monocetylted nd Bicetylted Opite Compounds nd Reltive Increse with Additionl Functionl Groups nd Ionic Size ion MAM MAC HER (M - COOCH 3) Å Å Å 2 V% MH Å Å Å 2 V% (M + N) Å Å Å 2 V% (M - COCH 3) 144 Reltive increse in collision cross section from previous row/ column to next. Figure 3. SIM ESI-IMS/MS spectr showing seprtion of two isomers: (1) morphine nd (2) norcodeine; m/z 267 (M - H 2O) +, 286 MH +, nd z 308 (M + N) +. IMS Spectr for Noncetylted Opites. Nonselective ESI- IMS/MS spectr for the four noncetylted opites re shown in Figure 2. Although not presented in Figure 2, ech observed mobility pek ws lso mss identified to determine the ion identity nd ech is lbeled s (1) (M - H 2 O) +, (2) MH +, nd (3) (M + N) + for the four compounds: () normorphine, (b) morphine, (c) norcodeine, nd (d) codeine. Although the ion formtion for the four opites is similr, there re differences in the reltive responses tht llude to structurl dependences on ion formtion in ESI. First, the overll signl intensities for normorphine nd morphine MH + ions were 60% less thn those observed for codeine nd norcodeine. The structurl difference in the two groups is methyl group on the R 1 oxygen group (refer to Figure 1). Signl intensity rtios (M - 18:M + 1, M + 1:M + 23) were found to be greter for codeine nd norcodeine, s well. The ddition of the methyl group on the R 1 group seems to hve n ffect on ESI ion signl intensity. The formtion of ll three ions (loss of wter, protonted ion, nd sodium dduct) ws incresed by the methyl ddition nd cn be observed by specultion in Figure 2 ( nd b compred to c nd d). As seen in Figure 2, incresing ion msses correlted with longer drift times nd, hence, lower K o vlues. Although this Figure 4. () Nonselective nd (b) SIM ESI-IMS/MS spectr of 6-monocetyl codeine; m/z 282 (M - COOCH 3) +, 342 MH +, nd 364 (M + N) +. generl reltionship ws expected nd observed, the reltive increse for ech compound ws dependent on the moleculr structure. Both the collision cross sections nd percent increse in cross section re listed in Tble 2 for the four compounds. For normorphine, ddition of sodium to the molecule incresed the collision cross section by 1.4%. In comprison, both morphine nd codeine collision cross sections incresed (ddition of sodium) by 2.7%. This difference in collision cross section due to the sodium ddition indicte tht there could be differences in the plcement of sodium on the molecule. Although morphine (Figure 2b) nd norcodeine (Figure 2c) were isomers, differing in the plcement of methyl group (R 3 on morphine, R 1 on norcodeine), inspection of the IMS spectr for the two compounds shows tht the drift times were different for the two ions. This difference ws further elucidted by prepring the two isomers in mixture nd evluting their seprtion. Figure 3 shows the SIM spectr for ech ion formed Anlyticl Chemistry, Vol. 73, No. 8, April 15,

5 Figure 5. () Nonselective nd (b) SIM ESI-IMS/MS spectr of 6-monocetyl morphine; m/z 266 (M-COOCH 3) +, m/z 328 MH +, nd m/z 350 (M+N) +. Figure 6. () Nonselective nd (b) SIM ESI-IMS/MS spectr of heroin; m/z 310 (M - COOCH 3) +, 327 (M - COCH 3) +, 370 MH +, nd 392 (M + N) +. for the two isomeric compounds: (1) morphine nd (2) norcodeine. It cn be seen tht, for both the (M - H 2 O) + nd MH + ions, the morphine ions drifted fster thn the norcodeine ions. Bseline seprtion ws esily obtinble for the two isomers, demonstrting significnt dvntge of IMS seprtion. IMS Spectr for Acetylted Opites. In Tble 3, the collision cross sections for the three cetylted molecules re shown. As expected, the ions tht lost COOCH 3 (59) group hd lower collision cross section thn the MH + ion which differed by pproximtely 12-15%. Acetyltion of either oxygen tom (R 1 for MAM nd MAC, R 1 nd R 2 for heroin) ltered the reltive mobilities for the MH + ion nd sodium dduct. In Figure 4, both the nonselective () nd SIM (b) IMS/MS spectr for MAC re shown. In the top nonselective IMS spectr, only two peks re observed. Upon mss identifying ech pek (b), it ws determined tht the pek t 25 ms correlted to the M - 59 ion nd the lrger pek t 28 ms is due to both the protonted moleculr ion (28.2 ms) nd sodium dduct (28.4 ms). The two ion collision cross sections (161 nd 162 Å 2, respectively) differ by 0.6% compred to 2.7% for the noncetylted counterprt, codeine. The ffect of the sodium on ion conformtion hd n even greter impct on the ion mobility spectrum of MAM nd heroin. In Figure 5, similr ion mobility representtion is shown for MAM (, nonselective mode; b, SIM mode). While the decetylted ion drifts for 24 ms, both the protonted nd sodited ions hve drift times of 27 ms. The interction with the sodium tom ppers to be even stronger for the MAM molecule, nd the two ions (protonted nd sodited ions) re pproximtely the sme size. Figure 7. Grph showing reltionship between m/z nd K o vlues for opite ions: (f) MH +,(O) (M+ N) +,(9) (M- H 2O) +, nd (b) (M - COOCH 3). The replcement of the methyl group on MAC with COCH 3 results in the formtion of heroin. In Figure 6, both the nonselective nd SIM IMS spectr re shown. Comprison of the lower two SIM spectr (m/z 370 (MH + ) nd 392 (M + N) + ) shows tht the sodium dduct drifted fster in the ion mobility tube thn the protonted ion. This implies tht the sodited ion ctully formed smller structure (lower collision cross section) thn the moleculr ion. Upon inspection of the structures (see Figure 1) nd the mobility results, it suggests tht the electronegtive oxygen groups due to cetyltion my interct with the sodium to form compcted ion. Seprtion of Opites by ESI-IMS/MS. Although IMS mobilities nd m/z vlues re not completely independent, the higher resolution of our instrument enbles smll differences in mobilities to be mesured. In Figure 7, the mesured K o vlues 1668 Anlyticl Chemistry, Vol. 73, No. 8, April 15, 2001

6 Although, some mobility peks overlp in the nonselective IMS spectr, ech SIM spectr (for the protonted moleculr ions) re shown in Figure 8b nd cn be identified by ech ion s unique K o :m/z reltionship. The complementry seprtion cpbilities of IMS nd MS enble opites s well s other smll drug molecules to be efficiently seprted. Figure 8. () Nonselective ESI-IMS/MS spectr of morphine mixtures contining normorphine, morphine, nd cetyl morphine. (1) (M - H 2O) + normorphine, (2) MH + normorphine, (3) (M - H 2O) + morphine, (4) (M - COOCH 3) + cetyl morphine, (5) MH + morphine, (6) (M + N) + normorphine, (7) (M + N) + morphine, (8) MH + cetyl morphine, nd (9) (M + N) + cetyl morphine. (b) SIM ESI-IMS/MS spectr of the three compounds; SIM spectr for ech compound re SIM spectr of protonted moleculr ion. for the opite ions were grphed with ech ion s corresponding m/z vlue. For ll but two sets of ions, ech ion hd unique m/z nd/or K o vlue. Therefore, the two-dimensionl seprtion cpbility of IMS/MS ws relized. Figure 8 shows n ESI-IMS/MS seprtion of morphine nd its two primry metbolites, normorphine nd cetyl morphine. CONCLUSIONS The results of this study show two beneficil fetures of ESI- IMS/MS s tool for opite seprtion. First, with our highresolution instrument, the two-dimensionl seprtion of the three opites nd metbolites ws relized. Becuse IMS seprtes ions on the bsis of size/chrge density, it ws found tht the predominnt ions hd unique K o :m/z vlue. Not only ws the seprtion possible, but the seprtion ws performed in 70 s. This is significnt enhncement in nlysis times nd could produce higher smple throughput. Metbolic isomers were found to be esily seprted nd hd substntilly different mobilities. In mny phrmcokinetic studies, the cpbility of identifying isomers is importnt nd this work shows tht the unique seprtion of IMS could contribute to these type of studies. The findings of this study lso lluded to more fundmentl contributions of IMS. The difference in moleculr ion nd sodited ion mobilities provided insights into the underlying conformtions of the ions nd, subsequently, the molecules themselves. Heroin ws found to form more compct structure when ssocited with sodium ion thn the protonted ion. This study provides n exmple of the size nd conformtion informtion tht cn be determined by determining ion mobilities. Received for review September 26, Accepted Jnury 11, AC001147B Anlyticl Chemistry, Vol. 73, No. 8, April 15,

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses

More information

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler)

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler) CHE 309: Chemicl Rection Engineering Lecture-8 Module 2: Rte Lw & Stoichiomtery (Chpter 3, Fogler) Topics to be covered in tody s lecture Thermodynmics nd Kinetics Rection rtes for reversible rections

More information

New data structures to reduce data size and search time

New data structures to reduce data size and search time New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute

More information

CHM Physical Chemistry I Chapter 1 - Supplementary Material

CHM Physical Chemistry I Chapter 1 - Supplementary Material CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion

More information

Part 1. Normal Saturated Fatty Acids

Part 1. Normal Saturated Fatty Acids MASS SPECTRA OF METHYL ESTERS OF FATTY ACIS Prt 1. Norml Sturted Ftty Acids Methyl esters re by fr the most widely used ftty cid derivtives for nlysis in CH3 OOC generl, nd gret del of informtion is vilble

More information

Vibrational Relaxation of HF (v=3) + CO

Vibrational Relaxation of HF (v=3) + CO Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,

More information

Strategy: Use the Gibbs phase rule (Equation 5.3). How many components are present?

Strategy: Use the Gibbs phase rule (Equation 5.3). How many components are present? University Chemistry Quiz 4 2014/12/11 1. (5%) Wht is the dimensionlity of the three-phse coexistence region in mixture of Al, Ni, nd Cu? Wht type of geometricl region dose this define? Strtegy: Use the

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

SUMMER KNOWHOW STUDY AND LEARNING CENTRE

SUMMER KNOWHOW STUDY AND LEARNING CENTRE SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18

More information

Psychrometric Applications

Psychrometric Applications Psychrometric Applictions The reminder of this presenttion centers on systems involving moist ir. A condensed wter phse my lso be present in such systems. The term moist irrefers to mixture of dry ir nd

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

A Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System

A Signal-Level Fusion Model for Image-Based Change Detection in DARPA's Dynamic Database System SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 16-0, Orlndo FL. (Minor errors in published version corrected.) A Signl-Level Fusion Model for Imge-Bsed

More information

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA Hrris: Quntittive Chemicl Anlysis, Eight Edition CHAPTER 08: MONOPROTIC ACIDBASE EQUILIBRIA CHAPTER 08: Opener A CHAPTER 08: Opener B CHAPTER 08: Opener C CHAPTER 08: Opener D CHAPTER 08: Opener E Chpter

More information

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es

More information

Problem 22: Buffer solutions 1. The equilibrium, which governs the concentration of H + within the solution is HCOOH! HCOO + H + + Hence K

Problem 22: Buffer solutions 1. The equilibrium, which governs the concentration of H + within the solution is HCOOH! HCOO + H + + Hence K Problem : Buffer solutions. The equilibrium, hich governs the concentrtion of H ithin the solution is HCOOH! HCOO H [HCOO ] 4 Hence. [HCOOH] nd since [HCOOH] 0.00 M nd [HCOO ] 0.50 M -4 0.00 4..8 M 0.50

More information

Fundamentals of Analytical Chemistry

Fundamentals of Analytical Chemistry Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electron-pir cceptor (Lewis) hrcteristic

More information

1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is:

1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is: th 9 Homework: Reding, M&F, ch. 15, pp. 584-598, 602-605 (clcultions of ph, etc., for wek cids, wek bses, polyprotic cids, nd slts; fctors ffecting cid strength). Problems: Nkon, ch. 18, #1-10, 16-18,

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

CIT and QIT with a Periodic Impulsional Potential

CIT and QIT with a Periodic Impulsional Potential Adv. Studies Theor. Phys., Vol. 6, 2012, no. 6, 285-291 nd with Periodic Impulsionl Potentil S. Seddighi Chhrborj srkhosh@mth.upm.edu.my Islmic Azd University, Science nd Reserch Brnch Deprtment of Mthemtics,

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

Review of Calculus, cont d

Review of Calculus, cont d Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some

More information

The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O

The International Association for the Properties of Water and Steam. Release on the Ionization Constant of H 2 O IAPWS R-7 The Interntionl Assocition for the Properties of Wter nd Stem Lucerne, Sitzerlnd August 7 Relese on the Ioniztion Constnt of H O 7 The Interntionl Assocition for the Properties of Wter nd Stem

More information

Predict Global Earth Temperature using Linier Regression

Predict Global Earth Temperature using Linier Regression Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id

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

7/19/2011. Models of Solution Chemistry- III Acids and Bases

7/19/2011. Models of Solution Chemistry- III Acids and Bases Models of Solution Chemistry- III Acids nd Bses Ionic Atmosphere Model : Revisiting Ionic Strength Ionic strength - mesure of totl concentrtion of ions in the solution Chpter 8 1 2 i μ ( ) 2 c i z c concentrtion

More information

9-1 (a) A weak electrolyte only partially ionizes when dissolved in water. NaHCO 3 is an

9-1 (a) A weak electrolyte only partially ionizes when dissolved in water. NaHCO 3 is an Chpter 9 9- ( A ek electrolyte only prtilly ionizes hen dissolved in ter. NC is n exmple of ek electrolyte. (b A Brønsted-ory cid is cule tht dontes proton hen it encounters bse (proton cceptor. By this

More information

UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237 - Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII

UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY. CH237 - Chemical Thermodynamics and Kinetics. Tutorial Sheet VIII UNIVERSITY OF MALTA DEPARTMENT OF CHEMISTRY CH237 - Chemicl Thermodynmics nd Kinetics Tutoril Sheet VIII 1 () (i) The rte of the rection A + 2B 3C + D ws reported s 1.0 mol L -1 s -1. Stte the rtes of

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

8.2 ESTIMATING DETENTION VOLUMES

8.2 ESTIMATING DETENTION VOLUMES 8.. Plnning versus Design number of detention bsin plnning methods hve been proposed in the professionl literture. These provide estimtes of the reuired volume of detention storge. The outlet structure

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Scientific notation is a way of expressing really big numbers or really small numbers.

Scientific notation is a way of expressing really big numbers or really small numbers. Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific

More information

Rates of chemical reactions

Rates of chemical reactions Rtes of chemicl rections Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) 2 5 2 2 n(1 α) 2αn

More information

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs

MATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching

More information

The Regulated and Riemann Integrals

The Regulated and Riemann Integrals Chpter 1 The Regulted nd Riemnn Integrls 1.1 Introduction We will consider severl different pproches to defining the definite integrl f(x) dx of function f(x). These definitions will ll ssign the sme vlue

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

4.4 Areas, Integrals and Antiderivatives

4.4 Areas, Integrals and Antiderivatives . res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order

More information

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus

Unit #9 : Definite Integral Properties; Fundamental Theorem of Calculus Unit #9 : Definite Integrl Properties; Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl

More information

Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons

Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1.

More information

Name Solutions to Test 3 November 8, 2017

Name Solutions to Test 3 November 8, 2017 Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier

More information

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3

I1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3 2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is

More information

1 ST ROUND, SOLUTIONS

1 ST ROUND, SOLUTIONS ST ROUND, SOLUTIONS Problem (Lithuni) Self destructing pper ( points) Solution ( ) ( ) ( ) [Al HO OH ) ph pk lg [Al H O ( ) ( ) [Al H O OH [Al ( ).9 [Al H O.9.47 [Al ( ) ( ) ( ) [Al H O OH.9 pk ph lg.

More information

Chapter 6 Notes, Larson/Hostetler 3e

Chapter 6 Notes, Larson/Hostetler 3e Contents 6. Antiderivtives nd the Rules of Integrtion.......................... 6. Are nd the Definite Integrl.................................. 6.. Are............................................ 6. Reimnn

More information

Chem 130 Second Exam

Chem 130 Second Exam Nme Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding. Red ech

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

Terminal Velocity and Raindrop Growth

Terminal Velocity and Raindrop Growth Terminl Velocity nd Rindrop Growth Terminl velocity for rindrop represents blnce in which weight mss times grvity is equl to drg force. F 3 π3 ρ L g in which is drop rdius, g is grvittionl ccelertion,

More information

A signalling model of school grades: centralized versus decentralized examinations

A signalling model of school grades: centralized versus decentralized examinations A signlling model of school grdes: centrlized versus decentrlized exmintions Mri De Pol nd Vincenzo Scopp Diprtimento di Economi e Sttistic, Università dell Clbri m.depol@unicl.it; v.scopp@unicl.it 1 The

More information

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0) 1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this

More information

CBE 291b - Computation And Optimization For Engineers

CBE 291b - Computation And Optimization For Engineers The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn

More information

Problem Set 3 Solutions

Problem Set 3 Solutions Chemistry 36 Dr Jen M Stndrd Problem Set 3 Solutions 1 Verify for the prticle in one-dimensionl box by explicit integrtion tht the wvefunction ψ ( x) π x is normlized To verify tht ψ ( x) is normlized,

More information

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by. NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with

More information

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from

More information

SESSION 2 Exponential and Logarithmic Functions. Math 30-1 R 3. (Revisit, Review and Revive)

SESSION 2 Exponential and Logarithmic Functions. Math 30-1 R 3. (Revisit, Review and Revive) Mth 0-1 R (Revisit, Review nd Revive) SESSION Eponentil nd Logrithmic Functions 1 Eponentil nd Logrithmic Functions Key Concepts The Eponent Lws m n 1 n n m m n m n m mn m m m m mn m m m b n b b b Simplify

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

Acids and Bases. H + (aq) + Cl - (aq) 100 molecules HCl 100 H+ ions Cl- ions 100% HCl molecules dissociate in water.

Acids and Bases. H + (aq) + Cl - (aq) 100 molecules HCl 100 H+ ions Cl- ions 100% HCl molecules dissociate in water. Acids nd Bses Acids: in generl cid is the substnce tht produces H ions when it is dissolved in wter. Acids cn be divided into two different clsses: Strong cid: is one tht completely dissocites into its

More information

Freely propagating jet

Freely propagating jet Freely propgting jet Introduction Gseous rectnts re frequently introduced into combustion chmbers s jets. Chemicl, therml nd flow processes tht re tking plce in the jets re so complex tht nlyticl description

More information

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40 Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since

More information

Chapter E - Problems

Chapter E - Problems Chpter E - Prolems Blinn College - Physics 2426 - Terry Honn Prolem E.1 A wire with dimeter d feeds current to cpcitor. The chrge on the cpcitor vries with time s QHtL = Q 0 sin w t. Wht re the current

More information

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.

u( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph. nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $

More information

A New Grey-rough Set Model Based on Interval-Valued Grey Sets

A New Grey-rough Set Model Based on Interval-Valued Grey Sets Proceedings of the 009 IEEE Interntionl Conference on Systems Mn nd Cybernetics Sn ntonio TX US - October 009 New Grey-rough Set Model sed on Intervl-Vlued Grey Sets Wu Shunxing Deprtment of utomtion Ximen

More information

Set up Invariable Axiom of Force Equilibrium and Solve Problems about Transformation of Force and Gravitational Mass

Set up Invariable Axiom of Force Equilibrium and Solve Problems about Transformation of Force and Gravitational Mass Applied Physics Reserch; Vol. 5, No. 1; 013 ISSN 1916-9639 E-ISSN 1916-9647 Published by Cndin Center of Science nd Eduction Set up Invrible Axiom of orce Equilibrium nd Solve Problems bout Trnsformtion

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More information

FEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS

FEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS XIX IMEKO orld Congress Fundmentl nd Applied Metrology September 6 11, 2009, Lisbon, Portugl FEM ANALYSIS OF ROGOSKI COILS COUPLED ITH BAR CONDUCTORS Mirko Mrrcci, Bernrdo Tellini, Crmine Zppcost University

More information

Key for Chem 130 Second Exam

Key for Chem 130 Second Exam Nme Key for Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding.

More information

CHAPTER 20: Second Law of Thermodynamics

CHAPTER 20: Second Law of Thermodynamics CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het

More information

Supplementary Material (ESI) for Soft Matter This journal is The Royal Society of Chemistry Supplementary data

Supplementary Material (ESI) for Soft Matter This journal is The Royal Society of Chemistry Supplementary data Supplementry Mteril (ESI) for Soft Mtter This journl is The Royl Society of hemistry 009 Supplementry dt Quntifying Hydrogel Response using Lser Light Scttering. Joshu M. G. Swnn, Wim Brs b, Jonthn R.

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.

3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression. SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd

More information

Applicable Analysis and Discrete Mathematics available online at

Applicable Analysis and Discrete Mathematics available online at Applicble Anlysis nd Discrete Mthemtics vilble online t http://pefmth.etf.rs Appl. Anl. Discrete Mth. 4 (2010), 23 31. doi:10.2298/aadm100201012k NUMERICAL ANALYSIS MEETS NUMBER THEORY: USING ROOTFINDING

More information

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph?

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph? 95. Which of the following descries the net ionic rection for the hydrolysis of NH4Cl( s)? A. NH4 ( q) Cl & ( q) NH4Cl( s) B. NH Cl & 4 ( s) NH4 ( q) Cl ( q) C. Cl ( q) H O & 2 ( l) HCl( q) OH ( q) D.

More information

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2009

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2009 University of Wshington Deprtment of Chemistry Chemistry Winter Qurter 9 Homework Assignment ; Due t pm on //9 6., 6., 6., 8., 8. 6. The wve function in question is: ψ u cu ( ψs ψsb * cu ( ψs ψsb cu (

More information

Recitation 3: More Applications of the Derivative

Recitation 3: More Applications of the Derivative Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech

More information

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction Lesson : Logrithmic Functions s Inverses Prerequisite Skills This lesson requires the use of the following skills: determining the dependent nd independent vribles in n exponentil function bsed on dt from

More information

Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION

Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Experiment 9: DETERMINATION OF WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly.

More information

Physics 116C Solution of inhomogeneous ordinary differential equations using Green s functions

Physics 116C Solution of inhomogeneous ordinary differential equations using Green s functions Physics 6C Solution of inhomogeneous ordinry differentil equtions using Green s functions Peter Young November 5, 29 Homogeneous Equtions We hve studied, especilly in long HW problem, second order liner

More information

Week 10: Line Integrals

Week 10: Line Integrals Week 10: Line Integrls Introduction In this finl week we return to prmetrised curves nd consider integrtion long such curves. We lredy sw this in Week 2 when we integrted long curve to find its length.

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

Period #2 Notes: Electronic Structure of Atoms

Period #2 Notes: Electronic Structure of Atoms Period # Notes: Electronic Structure of Atoms The logicl plce (for civil engineers) to begin in describing mterils is t the tomic scle. The bsic elements of the tom re the proton, the neutron, nd the electron:

More information

Hydronium or hydroxide ions can also be produced by a reaction of certain substances with water:

Hydronium or hydroxide ions can also be produced by a reaction of certain substances with water: Chpter 14 1 ACIDS/BASES Acids hve tste, rect with most metls to produce, rect with most crbontes to produce, turn litmus nd phenolphthlein. Bses hve tste rect very well well with most metls or crbontes,

More information

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt

More information

The Moving Center of Mass of a Leaking Bob

The Moving Center of Mass of a Leaking Bob The Moving Center of Mss of Leking Bob rxiv:1002.956v1 [physics.pop-ph] 21 Feb 2010 P. Arun Deprtment of Electronics, S.G.T.B. Khls College University of Delhi, Delhi 110 007, Indi. Februry 2, 2010 Abstrct

More information

#6A&B Magnetic Field Mapping

#6A&B Magnetic Field Mapping #6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by

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

New Expansion and Infinite Series

New Expansion and Infinite Series Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University

More information

CAPACITORS AND DIELECTRICS

CAPACITORS AND DIELECTRICS Importnt Definitions nd Units Cpcitnce: CAPACITORS AND DIELECTRICS The property of system of electricl conductors nd insultors which enbles it to store electric chrge when potentil difference exists between

More information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1 Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of

More information

INTERACTION BETWEEN THE NUCLEONS IN THE ATOMIC NUCLEUS. By Nesho Kolev Neshev

INTERACTION BETWEEN THE NUCLEONS IN THE ATOMIC NUCLEUS. By Nesho Kolev Neshev INTERACTION BETWEEN THE NUCLEONS IN THE ATOMIC NUCLEUS By Nesho Kolev Neshev It is known tht between the nucleons in the tomic nucleus there re forces with fr greter mgnitude in comprison to the electrosttic

More information

Chem 130 Third Exam Key

Chem 130 Third Exam Key Nme Chem 130 Third Exm Key On the following pges re eight questions tht consider topics rnging from precipittion solubility, cid bse, nd oxidtion reduction rections to metl lignd complexes nd coordintion

More information

Temperature influence compensation in microbolometer detector for image quality enhancement

Temperature influence compensation in microbolometer detector for image quality enhancement .26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*

More information

CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD

CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD CONTRIBUTION TO THE EXTENDED DYNAMIC PLANE SOURCE METHOD Svetozár Mlinrič Deprtment of Physics, Fculty of Nturl Sciences, Constntine the Philosopher University, Tr. A. Hlinku, SK-949 74 Nitr, Slovki Emil:

More information

On the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou

On the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou On the Uncertinty of Sensors Bsed on Mgnetic Effects E. ristoforou, E. Kyfs, A. Kten, DM Kepptsoglou Ntionl Technicl University of Athens, Zogrfou Cmpus, Athens 1578, Greece Tel: +3177178, Fx: +3177119,

More information

Higher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors

Higher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors Vectors Skill Achieved? Know tht sclr is quntity tht hs only size (no direction) Identify rel-life exmples of sclrs such s, temperture, mss, distnce, time, speed, energy nd electric chrge Know tht vector

More information

Chem 130 Third Exam. Total /100

Chem 130 Third Exam. Total /100 Nme Chem 130 Third Exm On the following pges you will find eight questions covering vries topics rnging from precipittion solubility, cid bse, nd oxidtion reduction rections to metl lignd complexes nd

More information

Poly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents

Poly(vinylamine) Microgels: ph-responsive Particles with High Primary Amine Contents SUPPLEMENTARY INFORMATION Poly(vinylmine) Microgels: ph-responsive Prticles with High Primry Amine Contents Sineent Thioonro, Cory Berkln, Amir H. Milni, Rein Ulijn c n Brin R. Suners, * Polymer Science

More information

ROB EBY Blinn College Mathematics Department

ROB EBY Blinn College Mathematics Department ROB EBY Blinn College Mthemtics Deprtment Mthemtics Deprtment 5.1, 5.2 Are, Definite Integrls MATH 2413 Rob Eby-Fll 26 Weknowthtwhengiventhedistncefunction, wecnfindthevelocitytnypointbyfindingthederivtiveorinstntneous

More information

Families of Solutions to Bernoulli ODEs

Families of Solutions to Bernoulli ODEs In the fmily of solutions to the differentil eqution y ry dx + = it is shown tht vrition of the initil condition y( 0 = cuses horizontl shift in the solution curve y = f ( x, rther thn the verticl shift

More information

INTRODUCTION TO INTEGRATION

INTRODUCTION TO INTEGRATION INTRODUCTION TO INTEGRATION 5.1 Ares nd Distnces Assume f(x) 0 on the intervl [, b]. Let A be the re under the grph of f(x). b We will obtin n pproximtion of A in the following three steps. STEP 1: Divide

More information