MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000
|
|
- Neal Price
- 6 years ago
- Views:
Transcription
1 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, FOOD COMPOSITION AND ADDITIVES Liquid Chromtogrphic Determintion of Residul Nitrite/Nitrte in Foods: NMKL 1 Collbortive Study MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000 LEONARDO MERINO, ULLA EDBERG, nd GEORG FUCHS Ntionl Food Administrtion, Chemistry Division 2, PO Box 622, S Uppsl, Sweden PER ÅMAN Swedish University of Agriculturl Sciences, Box 7051, S Uppsl, Sweden Collbortors: G. Corbri; L. Dhlberg; V. D-Riz; S. Eerol; R. Gerrd; D. Grncher; S. Jensen; A. Kngro; A. Kjolby; L. Lundberg; M. Mrin; S. Melnd; B. Muriel; M. Nicols; T. Rvn; M. Tuhknen; T. Vrtil; G. Zieprth Nitrite nd nitrte re used s dditives in the food industry to provide color nd tste nd to control undesirble gs nd flvor production by nerobic bcteri by virtue of their ntimicrobil properties. The nlyticl method tht hs been widely used to determine nitrite nd nitrte involves the use of toxic cdmium. In response to request from the Nordic Committee on Food Anlysis, study ws performed to obtin n lterntive chromtogrphic method to determine residul nitrite nd nitrte in met products. The study ws done in 3 stges: (1) comprtive evlution of the performnce of 3 liquid chromtogrphic methods, (2) internl vlidtion of the selected ion chromtogrphic method, nd (3) collbortive study in which 17 lbortories from Europen countries prticipted. Furthermore, the pplicbility of the method to mtrixes other thn met nd met products ws demonstrted. The results of the collbortive study show tht the Europen Prestndrd prenv is well suited for the determintion of nitrite nd nitrte in different foods (e.g., met products, vegetbles, bby food, nd cheese). The limits of detection for nitrite nd nitrte ions re 1 nd 10 mg/kg, respectively. Recoveries of residul nitrite/nitrte rnged from 96 to 108%. Repetbility nd reproducibility were stisfctory. Received Mrch 24, Accepted by JL August 25, Nordic Committee on Food Anlysis (Secretrit Generl, c/o Veterinærinstituttet, Pb 8156 Dep., N-0033 Oslo, Norwy). Nitrite either lone or in combintion with the nitrte slt is used s curing gent for met products. The role of nitrite is to produce the chrcteristic pink color, texture, nd flvor nd, especilly, to provide protection ginst poisonous microorgnisms, such s Clostridium botulinum, which is of prticulr interest. Becuse of toxicologicl considertions, nitrite nd nitrte re the concern of gencies responsible for food sfety. Nitrite (nd nitrte s its reservoir) is precursor of the crcinogenic N-nitroso compounds. Nitrite is n unstble ion nd undergoes series of rections s soon s it is dded to food products. In n cid environment, the nitrite ion ionizes to yield nitrous cid, which further decomposes to yield nitric oxide (NO), n importnt product from the stndpoint of color fixtion in cured met. Nitric oxide rects with myoglobin to produce the red pigment nitrosomyoglobin. Time, temperture, ph, nd dditives hve n importnt effect on the depletion of nitrite in cured met. Nordin (1) reported n eqution tht reltes the rte of nitrite depletion to time, temperture, nd ph. Sen et l. (2) hd considerble losses of nitrite during nlysis of cidic smples. Fujimki et l. (3) studied the fte of nitrite in met-curing model systems tht showed the effect of sodium scorbte in the decomposition of nitrite. These fctors, besides the fct tht the nlyticl procedure itself promotes certin chemicl rections, explin why determintion of nitrite in met products is difficult. On the other hnd, Olsmn nd Cees (4) differentited between residul free nitrite nd protein-bound nitrite, nd they proposed method to estimte the protein-bound nd the residul free nitrite content of met. The principle on which the method is bsed is the relese of the bound nitrite, s described by the following rection: RS NO + HgCl 2 +H 2 O RS HgCl + HNO 2 + HCl Acording to our nlyticl objective, we were not interested in relesing nitrite from ny rection products (even though they re reservoirs for nitrosmine formtion). On the contrry, the choice of the conditions nd chemicls used in the methods we evluted ws guided by the desire to minimize the losses of or increse the numbers of free nitrite/nitrte ions present during the nlyticl procedures. Therefore, the nlyticl methods determine the residul nitrite/nitrte, i.e., the free nitrite/nitrte ions tht re present when the chemicl nlysis is initited.
2 366 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000 Experimentl Anlyticl Methods Assessed Three ion chromtogrphic methods were ssessed: (1) Wek nionic exchnger (minopropyl bonded-phse column). This liquid chromtogrphic (LC) method is bsed on the Europen Stndrd pren Prt 2 (5). (2) Strong nionic exchnger (quternry mmonium column). This method ws proposed to the Nordic Committee on Food Anlysis (NMKL) some yers go. Erlier collbortive studies showed low recoveries of nitrites in met, nd in generl the performnce of the method ws vrible. (3) Strong nionic exchnger (quternry mmonium column). This method ws proposed to the Europen Committee for Stndrdistion (CEN). This method is ctully Europen Prestndrd (6). The methods re summrized in Tble 1. Wek Anionic Exchnger Method (Aminopropyl Bonded-Phse Column) The method hs been vlidted for determintion of nitrte in vegetbles. The liquid chromtogrm of stndrd solution contining nitrite nd nitrte, ech t 5 mg/l, is shown in Figure 1. The seprtion of the peks ws indequte, but this is not shortcoming in the nlysis of vegetbles, which usully do not contin nitrite. Although the compounds were dded t the sme concentrtion, the nitrite pek is smller thn the nitrte pek. Becuse the mobile phse is ph 3, the NO 2 forms HNO 2 (pk = 3.4), llowing the possibility of nitrite losses by the following rection in cidic solution: 3HNO 2 HNO 3 +H 2 O + 2NO To void this rection, the ph of the mobile phse ws incresed from 3 to 9. At this higher ph, the mobile phse showed high molr bsorptivity t 205 nm tht interfered with the mesurement of the nlytes. The mobile phse ws chnged to 5 mm K 2 HPO 4 in 15% cetonitrile, ph 8.6 (the mobile phse from the NMKL method). No improvement ws chieved; just 1 pek ppered. No further evlutions of this method were mde becuse of its poor performnce. Strong Anionic Exchnger Methods; Comprison of NMKL nd CEN Methods The NMKL nd the CEN methods re bsed on the sme ion chromtogrphic principle, but they use different mobile phses nd preprtion procedures. Assys were performed to ssess which mobile phses nd smple preprtions give better performnce. Evlution of Mobile Phse The extrct of met product (susge) ws used for the nlyses. The extrct ws seprted on strong nionic exchnger column (IC-PAK A mm) by using 2 different mobile phses: 5 mm K 2 HPO 4 in 15% cetonitrile, ph 8.6 (NMKL mobile phse), nd buffer (boric cid, gluconic cid, lithium hydroxide, nd glycerol) in 12.5% cetonitrile, ph 6.5 (CEN mobile phse). Figure 2 shows the Tble 1. Summrized description of the nlyticl methods ssessed Smple preprtion Chromtogrphic conditions Injection volume Extrction Clrifiction Column Mobile phse Flow Detection Method 0.7 ml/min 205 nm 20 µl 57 mm K2HPO4 in 5% cetonitrile. Adjust to ph 3 with H3PO4 Aminopropyl bonded phse LiChrosorb-NH2 (Hichrom) Filter through filter pper nd membrne filter Aminopropyl 10 g smple homogenized in hot wter (50 80 C), plced in boiling wter bth 15 min 0.6 ml/min 215 nm 20 µl 5mMK2HPO4 in 15% cetonitrile, ph 8.6 IC-PAK A mm (Wters) 2 ml Crrez I nd Crrez II solutions +5mLborx solution. Filter through filter pper nd membrne filter NMKL 10 g smple g ctivted chrcol +5mLsturted borx + 50 ml wter (80 C), plced in boiling wter bth 15 min 1 ml/min 205 nm 100 µl Buffer (boric cid, gluconic cid, lithium hydroxide, glycerol) in 12.5% cetonitrile, ph 6.5 IC-PAK A HC (High Cpcity) mm (Wters) 50 ml cetonitrile. Filter through filter pper nd membrne filter CEN 10 g smple homogenized in 50 ml wter (50 60 C)
3 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, Figure 1. Chromtogrm obtined with the wek nionic exchnger column for n queous stndrd solution contining nitrite nd nitrte t 5 mg/l. resolution of the peks obtined with the NMKL nd CEN mobile phses. The CEN mobile phse (buffer in 12.5% cetonitrile, ph 6.5) shows better seprtion of the peks. In ddition, this mobile phse hs prcticl dvntge, i.e., it my be left on the chromtogrphic column s storing solvent. Smple Preprtion (Extrction nd Clrifiction) Met products, purchsed from locl supermrket, were used for the comprison. Both spiked nd unspiked met products were nlyzed. One set of smples ws extrcted nd clrified exctly s described in the CEN method. The other set of smples ws treted s described in the NMKL method with modifiction: the smple ws homogenized with wter t 60 C (not t 80 C), nd it ws not plced in boiling wter bth for 15 min. Tble 2 shows the results of the evlution. Smple preprtion ffected the recoveries of nitrite nd nitrte. The smples pretreted ccording to the CEN method gve consistently higher recoveries thn did smples pretreted ccording to the modified NMKL method. Appliction of the pired t-test showed significnt difference in the results. The theoreticl vlue of t ws lower (2.73) thn the observed t vlues for nitrite nd nitrte (4.73 nd 4.10, respectively; p = 0.05; 18 degrees of freedom). Lter ssys showed tht the deproteinizing/clering Crrez regents interfere in the nlyses (see below). Smple Preprtion nd Mtrix ph One importnt difference in the smple preprtion procedures of the NMKL nd CEN methods is tht the former extrcts the nitrite/nitrte by using borx buffer, which is intended to counterct the effect of low ph on the stbility of nitrite/nitrte. In order to evlute if the ddition of borx buffer ctully enhnced the recovery of the nlytes, some ssys were performed in which the ph of the mtrix ws chnged before the smples were spiked with nitrite nd nitrte ions. () (b) Figure 2. Seprtion of nitrite nd nitrte in susge extrct on strong nionic exchnger column: () with the NMKL mobile phse nd (b) with the CEN mobile phse.
4 368 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000 Tble 2. methods Recovery of nitrite nd nitrte from met products pretreted ccording to the CEN nd modified NMKL Nitrite Nitrte CEN NMKL CEN NMKL Smple mg/kg % mg/kg % mg/kg % mg/kg % Pork susge b NF c NF Pork susge + std b Beef b NF NF NF NF Beef + std Hm NF NF NF NF Hm + std Pte b NA d NF NA 16 Pte + std b NA NA Chorizo Chorizo + std Bcon NF NF NF NF Bcon + std Hot dog b Slmi NF NF NF NF Mortdell + std NA NA b c d Std = stndrd. Men of 2 results. NF = not found. NA = not nlyzed. A slmi smple with ph < 5 ws spiked directly nd fter ph djustment with borx, borx plus 1M NOH, nd 5M NOH. The smples were extrcted ccording to the NMKL nd CEN methods. The results re shown in Tble 3. From Tble 3 it cn be concluded tht the higher the ph of the mtrix, the higher the recovery obtined. From n nlyticl point of view, the results suggest tht the difference in the ph of the extrction procedures of the methods hs minor influence on recovery, compred with the initil ph of the mtrix. Europen Prestndrd s Horizontl Method; Anlysis of Vegetbles nd Diry Products Vegetbles (onion, crrot, potto, cucumber, spinch, nd lettuce) were nlyzed in prllel by using the wek nionic exchnger column (5) nd the strong nionic exchnger column (6). The chromtogrms (Figure 3) show tht for certin vegetbles (i.e., crrot, onion, nd potto), which normlly hve very low concentrtion of nitrte, the strong nionic exchnger column is the only one cpble of seprting this ion. The seprtion obtined by using the wek nionic exchnger column (Figure 3) did not llow clcultion of the nitrte concentrtion. However, in the cses for which both methods chieved good chromtogrphic seprtion (i.e., cucumber, lettuce, nd spinch), the concentrtions of nitrte were the sme (dt not shown). A cheese smple ws lso nlyzed. Good seprtion nd recovery were obtined. Method Vlidtion: A Simple nd Prcticl Experimentl Design Bsed on Anlysis of Vrince (ANOVA) Mny guidelines hve been written, most of them describing interesting spects of the elements of the vlidtion procedure, but the experimentl designs to estimte these prmeters re omitted or pertin to severl replicte nlyses of different smples. In generl, good experimentl design would enble the nlyst to estimte most of the prmeters with minimum of nlyses. This tsk is fcilitted by the interreltion between the elements of the vlidtion. However, the diverse pproches in the literture give the impression tht to consistently follow the vlidtion procedure proposed, n nlyst must undertke enormous nd tedious work (7), but this is not the cse. Wilson nd Chessemn (8) proposed n experimentl design using ANOVA to give n estimte of precision, bis, nd limit of detection. The design specifies tht nlyses ought to be performed in severl btches over period of 1 2 weeks. Ech btch consists of replicte nlyses of blnks (limit of detection), stndrd solutions (sensitivity, linerity, nd rnge), nd both spiked nd unspiked smples (recovery). To estimte precision over concentrtion rnge, t lest
5 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, Tble 3. Influence of mtrix ph on recovery of nitrite spike Nitrite CEN NMKL Smple ph mg/kg % mg/kg % Slmi (sl.) 4.57 NF NF Sl. + stndrd (std) Sl. + borx (bx) + std Sl. + bx + 1M NOH + std Sl. + 5M NOH + std 10.4 NA b b NF = not found. NA = not nlyzed. 2 stndrd solutions re recommended for the upper nd lower concentrtions of interest. The dvntge of this pproch is tht it estimtes the within-btch stndrd devition s pooled vlues from ll the btches. This pproch is of prcticl importnce becuse it provides resonble indiction of wht is chievble. In ddition, this bsic experimentl design includes the internl reproducibility (between-btches stndrd devition, S b ), which hs n importnt consequence in reltion to the distinction between the vlidtion requirement of single lbortory nd of regultory body. Actully, prerequisite for the cceptnce of method s officil by committees or regultory gencies is estimtion of its performnce through collbortive study. Becuse collbortive study is n expensive nd work-intensive tsk, it is not suitble option for ll lbortories. However, by estimting the internl reproducibility, the nlyst obtins preliminry informtion bout the reproducibility of the method, i.e., the robustness under the best conditions. One generl point is worth noting here. The vlidtion procedure should consist of the nlysis of n portions in m btches. It is recommended tht n = 2 nd m = The product m n should never be < 10; 20 is better. Such design encourges the use of sttistic criterion to estimte the number of nlyses, to help to prevent n rbitrry nd inpproprite decision. A detiled discussion of the ANOVA s pplied to method vlidtion is beyond the scope of the present rticle, but the prcticl utility of ANOVA should not be overlooked. To put it more simply, its role in the experimentl design of the vlidtion method should be similr to the importnce it hs when interlbortory studies re conducted (9). Vlidtion of the Europen Prestndrd prenv The ppliction rnge, linerity, precision, detection limit, nd percent recovery were determined for the method. The procedure ws s follows: Foods (susge, corned beef, hm, chorizo, cheese, potto, nd bby food) purchsed from locl supermrket were homogenized nd spiked (except potto nd chorizo) with different concentrtions of ni- () (b) Figure 3. Chromtogrms obtined from nlyses of crrot smples using () wek nionic exchnger column (CEN, Prt 2, 1998) nd (b) strong nionic exchnger column (CEN, Prt 4, 1998).
6 370 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000 Tble 4. Btch Nitrite nd nitrte found in susge (mg/kg) NO - 2 NO - 3 Test 1 Test 2 Test 1 Test trite nd nitrte ions (dt not shown). Smples were stored t 4 C during the study. Six stndrd solutions of nitrite nd nitrte were used to clculte the clibrtion curve. In ddition, 2 replicte stndrd solutions of lower (0.5 mg/l) nd upper (20 mg/l) concentrtions were nlyzed s smples. The test consisted of the nlyses of replicte smples (n = 2) in ech btch (m = 5). The totl of 10 nlyses (m n = 10) gives resonble minimum number of degrees of freedom for the clcultion of the within-btch stndrd devition (S w ) nd between-btches stndrd devition (S b ) for ech smple. Results nd Discussion Linerity nd Rnge Linerity ws ddressed by prepring stndrd solutions of nitrite nd nitrte t 6 levels (0.5, 1.0, 3.0, 5.0, 10.0, nd 20.0 mg/l). Stndrds were injected in rndom order into the chromtogrph. A liner regression nlysis of nlyte concentrtion vs pek response ws performed. The coefficients of determintion (r 2 ) for nitrite nd nitrte were nd , respectively. The upper concentrtion of the rnge is equivlent to 400 mg nitrite nd/or nitrte/kg smple. Precision nd Internl Reproducibility As n exmple of the repetbility obtined on precision, only the results for the susge smple re shown in Tbles 4 nd 5. The results of the ANOVA re given in Tble 5. The criticl vlue of F (P = 0.01, n 1 =4,n 2 = 5) is 11.4, which is less thn nd 44.6, the F vlues for nitrite nd nitrte, respectively. The F-test showed tht there is significnt difference between the within-btch nd between-btches stndrd devitions; this difference is explined by the instbility of the nlytes (Figure 4). A prerequisite for the experimentl design bsed on ANOVA is the stbility of the smple. Unfortuntely, we were unble to chieve n cceptble level of control over the instbility of the nlytes through the use of borx, time, nd low temperture. Thus, the only wy to estimte the reproducibility of the method ws through n interlbortory study (see below, Collbortive Study). Limit of Detection nd Limit of Determintion The NMKL Procedure No. 4 (10) estblishes tht the detection nd determintion limits re clculted by multiplying the stndrd devition of the blnk by 3 nd 10, respectively. Becuse the studied method filed to detect n nlyticl response for the blnk smple, the stndrd devition of the stndrd solution of lowest concentrtion (0.5 mg/l) ws used to clculte these limits (11). Thus, the detection limits of nitrite nd nitrte re 1 nd 10 mg/kg, respectively. Bis nd Recovery Test The experimentl recovery is obtined from the difference between 2 mesurements (smple nd spiked smples), ccording to the following reltionship: Recovery, % = (totl nlyte found nlyte originlly present) 100/nlyte spike The recovery rnges for nitrite nd nitrte estimted immeditely fter smple preprtion (dte not reported) were % nd %, respectively. The poor recovery of the lter btches ws ttributed to the instbility of the nlytes. Identifiction of Systemtic Errors: Constnt-Type nd Reltive-Type Errors According to Linnig et l. (12), reltive-type nd constnt-type systemtic errors re ssocited with the slope nd intercept of plot of found vs dded concentrtion of the nlyte, respectively. They lso stte tht the effect of reltive-type error is generlly more importnt in the determintion of mjor components, wheres constnt-type errors re more serious in the determintion of trce components. The Tble 5. Summry of sums of squres nd degrees of freedom for susge smples Smple Source of vribility Sums of squres Degrees of freedom Men squres (MS) F Susge NO - 2 Between-btches (B) (MSB) 6852 Within-btch (W) (MSW) Susge NO - 3 Between-btches Within-btch F = (MSB)/(MSW).
7 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, Figure 4. Rte of depletion of nitrite nd nitrte spikes in hm. bility to use the method to nlyze other foods, which usully hve low concentrtions of nitrte nd nitrite (bby food, cheese), mde it necessry to identify these systemtic errors. An experiment ws performed. Minced met smples were spiked with different concentrtions of nitrite nd nitrte ions. The smples were nlyzed immeditely fter preprtion. Exmintion of the rtio vlues (columns 3 nd 5, Tble 6) shows tht the nitrite rtios re distributed round vlue close to unity, wheres the nitrte rtios decrese when the mount of nlyte increses. This difference suggests the presence of constnt-type systemtic error in the results of the nitrte nlyses. A correction fctor should be used, if meningful results re to be obtined. The intercept of the regression line for nitrte is 13.4 (Figure 5). This vlue could be n dequte correction fctor for the constnt-type error in the nlyses for residul nitrte in minced met. On the other hnd, there is no definitive criterion for judging whether the intercept is n dequte correction fctor for the nlyses for nitrite, becuse the observed intercept flls into the confidence intervl of the clculted intercept (dt not shown). The existence of reltive-type systemtic error (error proportionl to the mount of smple nlyzed) is relted to slope different from unity. Nitrite nd nitrte stright lines show slopes of 1.10 nd 1.09, respectively, which indicte reltive error of bout 10%. Comprison of Ion Chromtogrphic (CEN-Prt 4) nd Spectrophotometric (CEN-Prt 3) Methods for Determintion of Nitrite in Minced Met Spiked minced met smples were nlyzed for nitrite by both methods. The spectrophotometric method is bsed on Tble 6. Results of nlyses of spiked minced met smples for nitrite nd nitrte Nitrite Nitrte NO - + NO- 2 3 dded, mg/kg Found, mg/kg Rtio, found/dded Found, mg/kg Rtio, found/dded Ech vlue is the men of 2 results.
8 372 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000 Figure 5. Effect of experimentl errors in nitrte determintion. dizotiztion of sulfnilmide by nitrite, followed by coupling with N-(1-nphthyl)ethylenedimine dichloride to form n zo dye, which is mesured spectrophotometriclly t 540 nm (13). The pired t-test did not give significnt difference (columns 2 nd 3, Tble 7). Furthermore, nother portion ws nlyzed simultneously by the sme ion chromtogrphic method using cetonitrile nd the Crrez solution, which re the clrifiction solutions of the CEN nd NMKL methods, respectively (columns 3 nd 4, Tble 7). The results show the disturbing effect of Crrez solution when the ion chromtogrphic method is used. These results gree very well with those of previous nlyses performed during the evlution of the methods tht led to the choice of the Europen Prestndrd (Tble 2). Therefore, the Crrez solution is not recommended s clrifying solution for the ion chromtogrphic method. Collbortive Study Prticipting Lbortories, Test Mterils, nd Sttisticl Procedure A totl of 17 lbortories prticipted in the collbortive studies I nd II. The prticipting lbortories were in Denmrk, Estoni, Finlnd, Frnce, Germny, Itly, Norwy, Spin, nd Sweden. The procedure estblished by AOAC INTERNATIONAL to conduct collbortive study ws followed (14). If cidic, the test mterils were neutrlized with solution of 5M NOH nd spiked with sturted solution of borx to increse the ph. The test mterils were sent by courier in freeze-box. Recommendtions were given to the prticipnts to store the test mterils in refrigertor (4ºC) nd strt the nlysis in the morning on the sme dy. Ech lbortory ws provided well in dvnce with the written version of the method, the schedule, instructions, etc. Tble 7. Comprison of residul nitrite levels in minced met s determined by 2 different methods Found, mg/kg Spectrophotometry Liquid chromtogrphy NO NO- 3 dded, mg/kg Crrez solution Acetonitrile Crrez solution ND b b Ech vlue is the men of 2 results. ND = not detected.
9 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, Sttisticl Anlysis The bsis of the outliers test is to determine if the cndidte outlier vlues re consistent with the Gussin distribution ssumed priori. The outliers exclusion ws done with the Cochrn test nd the single nd double Grubbs tests t the 2.5% rejection level. The Cochrn test is for the removl of lbortories showing significntly greter vribility mong replictes (blind duplictes). The Grubbs test is for the removl of lbortories with extreme vlues. The Horrt vlues were used to judge the relibility of the method. The Horrt vlue for reproducibility is the observed (RSD R ) vlue divided by the RSD R vlue clculted from the Horwitz eqution t the concentrtion of interest (RSD R =2 (1 0.5logC) ). If the Horrt vlue is 2, then the method my be ssumed to hve stisfctory reproducibility (15). This is the cceptbility criterion. Collbortive Study I Results were received from 13 lbortories (Tble 8). Dt for the test mterils were rounded without decimls. The test mterils were the following: A = susge smple spiked with low concentrtion of nitrite nd nitrte; B, D = susge smple spiked with high concentrtion of nitrite nd nitrte; C = bby food smple spiked with nitrite nd nitrte; E = cbbge smple; nd Std = 10 mg NO - 2 /L nd 10 mg NO- 3 /L. The results from lbortories 9 nd 11 were considered s invlid dt.when the outliers tests were pplied to ll lbortories, lbortories 9 nd 11 hd the most outliers. Furthermore, the results of the check stndrd solution were significntly different from those of other lbortories. Becuse the effect of retining rel outlier is usully more serious thn the effect of rejecting vlid point, the decision to eliminte ll results of these lbortories s invlid dt is correct. Vlid dt re the vlues tht the collbortor hs no reson to suspect s being wrong (14). The outliers tests were pplied to the results of the remining lbortories. Lbortory 2 hd Grubbs outliers in 4 of 5 nlyses for nitrte. Lbortory 4 hd Grubbs outlier for the susge smple (test mteril A). In ll nlyses of the preliminry collbortive study, the precision (repetbility nd reproducibility) ws stisfctory. Tble 8. Reported vlues of nitrite nd nitrte from collbortive study I NO - 2, mg/kg NO - 3, mg/kg Lbortory code Std, mg/l A B C D E Std, mg/l A B C D E b 210 b 173 b 210 b b c c b Accepted results No. of outliers Men d SD r e SD R RSD R, % f Horrt vlue b c d e f Std = stndrd. Grubbs outlier. Invlid dt. SD r = repetbility stndrd devition (clculted for the blind duplicte test mterils). SD R = reproducibility stndrd devition. RSD R, % = reproducibility reltive stndrd devition.
10 374 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, 2000 Collbortive Study II Results were received from 15 lbortories (Tble 9). The test mterils were the following: F, K = slmi smple spiked with low concentrtion of nitrite nd nitrte; G = lettuce smple; H = pté smple spiked with nitrite nd nitrte; I = slmi smple spiked with nitrite nd nitrte; J = cheese smple; nd Std = 5 mg NO - /L nd 5 mg NO- 2 3 /L. Lbortories 9 nd 11 hd Cochrn outliers. Lbortories 3, 4, 8, 9, 11, 13, nd 14 hd Grubbs outliers. Test mterils G nd J contined only nitrte. However, some lbortories reported very low concentrtion of nitrite. When the retention times were checked, most of them showed significnt difference from retention times reported by the other lbortories. These results (which could indicte the presence of interfering substnces) were considered s invlid dt. On the bsis of the Horrt vlues, 3 out of 10 did not fulfill the cceptnce criterion (see Tble 9, Horrt vlues; vlues re not given for test mterils G nd J, which hd nitrite concentrtion below the limit of detection). Two comments should be mde. First, test mterils F nd K were the sme (blind duplictes). In one cse the cceptnce criterion ws fulfilled, nd in the other cse it ws not. Second, the concentrtion of the nitrite spike in the test mterils ws very close to the limit of determintion (5 nd 25 mg/kg for nitrite nd nitrte ions, respectively, vlues obtined in the vlidtion performed by our lbortory), nd obviously the uncertinty is higher t this level. Tble 9. Reported vlues of nitrite nd nitrte from collbortive study II NO - 2, mg/kg NO - 3, mg/kg Lbortory code Std, mg/l F G H I J K Std, mg/l F G H I J K b c c c c b c c c c d b c c c c c c c c Accepted results No. of outliers Men <LOD e <LOD f SD r g SD R RSD R, % h Horrt vlue b c d e f g h Std = stndrd. Test mterils F nd K gve Cochrn outliers (nitrite). Grubbs outlier. Excess dt reported. LOD = limit of detection. SD r = repetbility stndrd devition. SD R = reproducibility stndrd devition. RSD R,% = reproducibility reltive stndrd devition.
11 MERINO ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 83, NO. 2, Conclusions Nitrite determintion with the wek nionic exchnger column, CEN-Prt 2 (5), is not suitble. This method is not relible for the nlysis of certin vegetbles with low concentrtions of nitrte. The ph of the mtrix t the time of the ddition of nitrite/nitrte hs the gretest influence on the stbility of these ions; the higher the ph, the better the recovery. Smple extrction with buffer hs minor influence, compred with the ph of the mtrix. Recoveries of nitrite from met products, vegetbles, cheese, nd bby food rnged from 96 to 108% with CEN-Prt 4 (6). The corresponding rnge for nitrte recovery ws %. The detection limits for nitrite nd nitrte ions were 1 nd 10 mg/kg, respectively. The limits of determintion were 5 nd 25 mg/kg for nitrite nd nitrte ions, respectively. Constnt-type nd reltive-type systemtic errors were found in the nlysis for nitrite nd nitrte in minced met. To obtin ccurte nlyticl results, correction of this systemtic error is necessry. Reltive-type errors were pproximtely 10% for both nlytes. In generl, the performnce of the method differs when nitrite nd nitrte re determined. Better performnce is obtined for nitrite determintions. The study shows tht the method cn be pplied to the nlysis of foods other thn met nd met products, e.g., bby food, vegetbles, nd cheese. In nlyses for nitrite, no sttisticlly significnt difference ws found between the methods studied, CEN-Prt 4 (6) nd the spectrophotometric method, CEN-Prt 3 (13). The precision of the method fulfills the criteri recommended by AOAC INTERNATIONAL (14) nd the Europen Committee for Stndrdiztion (15); therefore, CEN-Prt 4 (6) is suitble for the determintion of nitrte nd/or nitrte in vrious kinds of mtrixes. Acknowledgments We thnk the following lbortories for their prticiption: Anstlten veterinärmedicin och livsmedel, Helsinki, Finlnd Chemisches Untersuchungsmt Minz, Minz, Germny Ministere de L Agriculture (CNEVA), Misons, Frnce Centre Technique de l Slison (CTSCCV), Misons, Frnce ENVL-Lbo Chrles FLACHT, Mrcy L Etoile, Frnce Institute of Food Reserch nd Nutrition, Ringsted, Denmrk Helsingin ympäristölbortorio, Helsinki, Finlnd Joensuun kupungin eli.-j ympäristölb, Joensuun, Finlnd Lbortorio Arbitrl-Agrolimentrio, Mdrid, Spin Lb. Interrégionl de l Concurrence (DGCCRF), Illkirch Grffenstden, Frnce Næringsmiddeltillsyn for Midt-Roglnd, Forus, Norwy Ntionl Food Administrtion, Uppsl, Sweden Dnish Met Reserch Institute, Roskilde, Denmrk Sttens Lbortorium A/S, Holstebro, Denmrk Stzione Sperim. Ind. Conserve Alimentri, Prm, Itly Swedish Met Reserch Institute, K vlinge, Sweden Trtu Public Helth Service, Trtu, Estoni References (1) Nordin, H.R. (1969) J. Technol. Aliment. 2, (2) Sen, N.P., Young, C.L., & McPherson, M. (1979) J. Assoc. Off. Anl. Chem. 62, (3) Fujimki, M., Emi, M., & Okitni, A. (1975) Agric. Biol. Chem. 39, (4) Olsmn, W., & Cees, M. (1977) Z. Lebensm. Unters. Forsch. 164, (5) Europen Committee for Stndrdiztion (CEN) (1998) Europen Stndrd pr ENV Prt 2, HPLC/IC Method for the Determintion of Nitrte Content of Vegetbles nd Vegetble Products, Brussels, Belgium (6) Europen Committee for Stndrdiztion (CEN) (1998) Europen Prestndrd pr ENV Prt 4, IC Method for the Determintion of Nitrte nd Nitrite Content of Met Products, Brussels, Belgium (7) EURACHEM Drft 1.0 (1996) Method Vlidtion, A Lbortory Guide, LGC, with the support of the UK DTI VAM inititive, Middlesex, UK (8) Wilson, A.L., & Chessemn, R.V. (1978) Mnul on Anlyticl Qulity Control for the Wter Industry, Technicl Report Tr66, Wter Reserch Center, Bucks, UK (9) Thompson, M., & Wood, R. (1993) J. AOAC Int. 76, (10) Nordic Committee on Food Anlysis (1996) NMKL Procedure No. 4, Vlidtion of Chemicl Anlyticl Methods, NMKL, Espoo, Finlnd (11) Kirchmer, C.J. (1988) in Estimtion of Detection Limits for Environmentl Anlyticl Procedures, Ch. 4, Americn Chemicl Society, Wshington, DC, pp (12) Linnig, F., Mndel, J., & Peterson, J.M. (1954) Anl. Chem. 26, (13) Europen Committee for Stndrdiztion (CEN) (1998) Europen Prestndrd pr ENV Prt 3, Spectrometric Determintion of Nitrte nd Nitrite Content of Met Products fter Enzymtic Reduction of Nitrte to Nitrite, Brussels, Belgium (14) AOAC INTERNATIONAL (1995) J. AOAC Int. 78, 143A 160A (15) CEN/TC 275/WG 7 N 103 (1997) Report of the 6th Meeting of the CEN/TC 275/WG 7 N 103, Annex B, Secretrit DIN, Berlin, Germny
12 376 JOURNAL OF AOAC INTERNATIONAL VOL. 82, NO. 2, 2000
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 informationThe goal of this study was to compare the performance of
676 WHEELER ET AL.: JOURNAL OF AOAC INTERNATIONAL VOL. 85, NO. 3, 2002 FOOD COMPOSITION AND ADDITIVES Isoltion of Light Filth from Ground Oregno nd Ground Mrjorm: A Modifiction Using Isopropnol s Deftting
More informationAcceptance 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 informationExperiment 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 informationThe steps of the hypothesis test
ttisticl Methods I (EXT 7005) Pge 78 Mosquito species Time of dy A B C Mid morning 0.0088 5.4900 5.5000 Mid Afternoon.3400 0.0300 0.8700 Dusk 0.600 5.400 3.000 The Chi squre test sttistic is the sum of
More informationNon-Linear & Logistic Regression
Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More informationStudent Activity 3: Single Factor ANOVA
MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether
More informationChapter 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 informationTests 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 informationDetermination of Anions in Acid Rain by Ion Chromatography
Appliction Updte 16 Determintion of Anions in Acid Rin by Ion Chromtogrphy INTRODUCTION The increse in cidity of wet nd dry tmospheric depositions hs been ttributed to the increse of SO 2 nd NO 2 emissions
More informationCBE 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 informationNUMERICAL 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 informationLECTURE 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 informationExperiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION
Experiment 9: 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. Prt II: The
More information1. 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 informationHydronium 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 informationNew 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 informationFundamentals 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 information2008 Mathematical Methods (CAS) GA 3: Examination 2
Mthemticl Methods (CAS) GA : Exmintion GENERAL COMMENTS There were 406 students who st the Mthemticl Methods (CAS) exmintion in. Mrks rnged from to 79 out of possible score of 80. Student responses showed
More informationEvaluation of Approximate Methods for Calculating the Limit of Detection and Limit of Quantification
Environ. Sci. Technol. 1999, 33, 2291-2295 Evlution of Approximte Methods for Clculting the Limit of Detection nd Limit of Quntifiction MICHAEL E. ZORN, ROBERT D. GIBBONS, AND WILLIAM C. SONZOGNI*, Wter
More informationThe 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 informationComparison Procedures
Comprison Procedures Single Fctor, Between-Subects Cse /8/ Comprison Procedures, One-Fctor ANOVA, Between Subects Two Comprison Strtegies post hoc (fter-the-fct) pproch You re interested in discovering
More informationState 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 informationDRINKING-WATER- QUALITY DATA:
A New Approch to DRINKING-WATER- QUALITY DATA: Lowest- Concentrtion Minimum Reporting Level Downloded vi 148.51.3.83 on July 10, 018 t 00:43:18 (UTC). See https://pubs.cs.org/shringguidelines for options
More informationModule 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 informationCHAPTER 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 informationScientific 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 informationWhich 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 informationProblem 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 informationADVANCEMENT 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 informationMIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model:
1 2 MIXED MODELS (Sections 17.7 17.8) Exmple: Suppose tht in the fiber breking strength exmple, the four mchines used were the only ones of interest, but the interest ws over wide rnge of opertors, nd
More informationReview 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 informationNew 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 informationUser's Guide of the Inter-Batch Physico-Chemical Variability Calculator
User's Guide of the Inter-Btch Physico-Chemicl Vribility Clcultor Scope The Inter-Btch Physico-Chemicl Vribility (IBPCV) Clcultor enbles to test if the beteenbtch vribility of the physico-chemicl chrcteristics
More information1 Online Learning and Regret Minimization
2.997 Decision-Mking in Lrge-Scle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in
More informationUNIVERSITY 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 informationEstimation of the particle concentration in hydraulic liquid by the in-line automatic particle counter based on the CMOS image sensor
Glyndŵr University Reserch Online Conference Presenttion Estimtion of the prticle concentrtion in hydrulic liquid by the in-line utomtic prticle counter bsed on the CMOS imge sensor Kornilin, D.V., Kudryvtsev,
More informationHybrid Group Acceptance Sampling Plan Based on Size Biased Lomax Model
Mthemtics nd Sttistics 2(3): 137-141, 2014 DOI: 10.13189/ms.2014.020305 http://www.hrpub.org Hybrid Group Acceptnce Smpling Pln Bsed on Size Bised Lomx Model R. Subb Ro 1,*, A. Ng Durgmmb 2, R.R.L. Kntm
More informationMath 31S. Rumbos Fall Solutions to Assignment #16
Mth 31S. Rumbos Fll 2016 1 Solutions to Assignment #16 1. Logistic Growth 1. Suppose tht the growth of certin niml popultion is governed by the differentil eqution 1000 dn N dt = 100 N, (1) where N(t)
More informationDesign and Analysis of Single-Factor Experiments: The Analysis of Variance
13 CHAPTER OUTLINE Design nd Anlysis of Single-Fctor Experiments: The Anlysis of Vrince 13-1 DESIGNING ENGINEERING EXPERIMENTS 13-2 THE COMPLETELY RANDOMIZED SINGLE-FACTOR EXPERIMENT 13-2.1 An Exmple 13-2.2
More informationCHEMICAL KINETICS
CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy
More information13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
More informationChapter 17: Additional Aspects of Aqueous Equilibria
1 Chpter 17: Additionl Aspects of Aqueous Equilibri Khoot! 1. Adding Br to sturted queous solution of decreses its solubility in wter. BSO 4, Li CO 3, PbS, AgBr. Which of the following mitures could be
More informationJim Lambers MAT 169 Fall Semester Lecture 4 Notes
Jim Lmbers MAT 169 Fll Semester 2009-10 Lecture 4 Notes These notes correspond to Section 8.2 in the text. Series Wht is Series? An infinte series, usully referred to simply s series, is n sum of ll of
More information9-1 (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 information8.2 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 informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More informationProperties 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 informationPredict 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 informationA 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 informationThe Predom module. Predom calculates and plots isothermal 1-, 2- and 3-metal predominance area diagrams. Predom accesses only compound databases.
Section 1 Section 2 The module clcultes nd plots isotherml 1-, 2- nd 3-metl predominnce re digrms. ccesses only compound dtbses. Tble of Contents Tble of Contents Opening the module Section 3 Stoichiometric
More informationData Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading
Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3d-Vritionl Method
More information8 Laplace s Method and Local Limit Theorems
8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved
More informationA Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE
Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of
More informationMATHS 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 informationGoals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite
Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More informationCu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect.
CHEM 1122011 NAME: ANSWER KEY Vining, Exm # SHORT ANSWER QUESTIONS ============= 4 points ech ============ All work must be shown. 1. Wht re [H O ] nd [OH ] for solution tht hs ph of 9.0? Choose one. ()
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils
More informationOn 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 informationContinuous Random Variables
STAT/MATH 395 A - PROBABILITY II UW Winter Qurter 217 Néhémy Lim Continuous Rndom Vribles Nottion. The indictor function of set S is rel-vlued function defined by : { 1 if x S 1 S (x) if x S Suppose tht
More informationDuality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below.
Dulity #. Second itertion for HW problem Recll our LP emple problem we hve been working on, in equlity form, is given below.,,,, 8 m F which, when written in slightly different form, is 8 F Recll tht we
More informationOrganic 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 informationPart 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 informationDriving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d
Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More informationShear and torsion interaction of hollow core slabs
Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction
More informationEntropy ISSN
Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl
More informationUnit #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 informationDepartment of Physical Pharmacy and Pharmacokinetics Poznań University of Medical Sciences Pharmacokinetics laboratory
Deprtment of Physicl Phrmcy nd Phrmcoinetics Poznń University of Medicl Sciences Phrmcoinetics lbortory Experiment 1 Phrmcoinetics of ibuprofen s n exmple of the first-order inetics in n open one-comprtment
More informationFind this material useful? You can help our team to keep this site up and bring you even more content consider donating via the link on our site.
Find this mteril useful? You cn help our tem to keep this site up nd bring you even more content consider donting vi the link on our site. Still hving trouble understnding the mteril? Check out our Tutoring
More informationMarkscheme May 2016 Mathematics Standard level Paper 1
M6/5/MATME/SP/ENG/TZ/XX/M Mrkscheme My 06 Mthemtics Stndrd level Pper 7 pges M6/5/MATME/SP/ENG/TZ/XX/M This mrkscheme is the property of the Interntionl Bcclurete nd must not be reproduced or distributed
More informationSUMMER 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 informationImproper Integrals. Type I Improper Integrals How do we evaluate an integral such as
Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph
More informationCONTRIBUTION 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 informationCredibility Hypothesis Testing of Fuzzy Triangular Distributions
666663 Journl of Uncertin Systems Vol.9, No., pp.6-74, 5 Online t: www.jus.org.uk Credibility Hypothesis Testing of Fuzzy Tringulr Distributions S. Smpth, B. Rmy Received April 3; Revised 4 April 4 Abstrct
More informationName 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 informationPsychrometric 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 informationThe 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 informationf(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral
Improper Integrls Every time tht we hve evluted definite integrl such s f(x) dx, we hve mde two implicit ssumptions bout the integrl:. The intervl [, b] is finite, nd. f(x) is continuous on [, b]. If one
More informationChapter 5 : Continuous Random Variables
STAT/MATH 395 A - PROBABILITY II UW Winter Qurter 216 Néhémy Lim Chpter 5 : Continuous Rndom Vribles Nottions. N {, 1, 2,...}, set of nturl numbers (i.e. ll nonnegtive integers); N {1, 2,...}, set of ll
More informationWhen, Ti(IV)-Fe(III) and Ti(IV)-Zr(IV) binary mixtures were passed through the column at ph
Electronic Supplementry Mteril (ESI) for RSC Advnces. This journl is The Royl Society of Chemistry 2014 Supplementry dt: The distribution co-efficient (K d ) t different ph hs been computed (eq. 2) nd
More informationApplicable 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 informationLecture INF4350 October 12008
Biosttistics ti ti Lecture INF4350 October 12008 Anj Bråthen Kristoffersen Biomedicl Reserch Group Deprtment of informtics, UiO Gol Presenttion of dt descriptive tbles nd grphs Sensitivity, specificity,
More informationVyacheslav Telnin. Search for New Numbers.
Vycheslv Telnin Serch for New Numbers. 1 CHAPTER I 2 I.1 Introduction. In 1984, in the first issue for tht yer of the Science nd Life mgzine, I red the rticle "Non-Stndrd Anlysis" by V. Uspensky, in which
More informationSession Trimester 2. Module Code: MATH08001 MATHEMATICS FOR DESIGN
School of Science & Sport Pisley Cmpus Session 05-6 Trimester Module Code: MATH0800 MATHEMATICS FOR DESIGN Dte: 0 th My 06 Time: 0.00.00 Instructions to Cndidtes:. Answer ALL questions in Section A. Section
More information20 MATHEMATICS POLYNOMIALS
0 MATHEMATICS POLYNOMIALS.1 Introduction In Clss IX, you hve studied polynomils in one vrible nd their degrees. Recll tht if p(x) is polynomil in x, the highest power of x in p(x) is clled the degree of
More informationChapter 0. What is the Lebesgue integral about?
Chpter 0. Wht is the Lebesgue integrl bout? The pln is to hve tutoril sheet ech week, most often on Fridy, (to be done during the clss) where you will try to get used to the ides introduced in the previous
More informationDesign Data 1M. Highway Live Loads on Concrete Pipe
Design Dt 1M Highwy Live Lods on Concrete Pipe Foreword Thick, high-strength pvements designed for hevy truck trffic substntilly reduce the pressure trnsmitted through wheel to the subgrde nd consequently,
More informationProbabilistic Investigation of Sensitivities of Advanced Test- Analysis Model Correlation Methods
Probbilistic Investigtion of Sensitivities of Advnced Test- Anlysis Model Correltion Methods Liz Bergmn, Mtthew S. Allen, nd Dniel C. Kmmer Dept. of Engineering Physics University of Wisconsin-Mdison Rndll
More informationPhysics 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 information4.4 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 informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More informationAPEF Acids and Bases - Answers
APEF Acids nd Bses - Answers 1. It requires 3.0 ml of 0.0500 mol/l NOH(q) to neutrlize 100.0 ml of gstric juice. We cn ssume tht HCl(q) is the only cid present in gstric juice. ) Clculte the concentrtion
More informationEnergy Consideration
Energy Considertion It hs been noted tht the most common brkes employ friction to trnsform the brked system's mechnicl energy, irreversibly into het which is then trnsferred to the surrounding environment
More informationThe 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 informationMATH SS124 Sec 39 Concepts summary with examples
This note is mde for students in MTH124 Section 39 to review most(not ll) topics I think we covered in this semester, nd there s exmples fter these concepts, go over this note nd try to solve those exmples
More informationPre-Session Review. Part 1: Basic Algebra; Linear Functions and Graphs
Pre-Session Review Prt 1: Bsic Algebr; Liner Functions nd Grphs A. Generl Review nd Introduction to Algebr Hierrchy of Arithmetic Opertions Opertions in ny expression re performed in the following order:
More informationUsing air lines as references for VNA phase measurements
Using ir lines s references for VNA phse mesurements Stephen Protheroe nd Nick Ridler Electromgnetics Tem, Ntionl Physicl Lbortory, UK Emil: Stephen.protheroe@npl.co.uk Abstrct Air lines re often used
More informationChapter 16 Acid Base Equilibria
Chpter 16 Acid Bse Equilibri 16.1 Acids & Bses: A Brief Review Arrhenius cids nd bses: cid: n H + donor HA(q) H(q) A(q) bse: n OH donor OH(q) (q) OH(q) Brønsted Lowry cids nd bses: cid: n H + donor HA(q)
More information