Korean Journal of Environmental Agriculture Korean J Environ Agric (2011) Online ISSN: 2233-4173 Vol. 30, No. 2, pp. 179-188 DOI : 10.5338/KJEA.2011.30.2.179 Print ISSN: 1225-3537 Research Article Open Access 불확도추정을통한토마토페이스트에서카드뮴및납분석의오차발생요인규명 김지영, 김영준, 1 류지혁, 이지호, 김민지, 강대원, 임건재, 홍무기, 신영재, 2 김원일 * 국립농업과학원농산물안전성부, 1 서울대학교농생명공학부 WCU 바이오모듈레이션전공, 2 단국대학교환경원예학과 A Study on the Factors Causing Analytical Errors through the Estimation of Uncertainty for Cadmium and Lead Analysis in Tomato Paste Ji-Young Kim, Young-Jun Kim 1, Ji-Hyock Yoo, Ji-Ho Lee, Min-Ji Kim, Dae-Won Kang, Geon-Jae Im, Moo-Ki Hong, Young-Jae Shin 2 and Won-Il Kim* (Department of Agro-Food Safety, National Academy of Agricultural Science, Rural Development Administration, Suwon 441-707, Korea, 1 WCU Biomodulation Major, Department of Agricultural Biotechnology, Seoul National University, Seoul 151-921, Korea, 2 Department of Environmental Horticulture, Dankook University, Cheonan 330-714, Korea) Received: 12 May 2011 / Accepted: 17 June 2011 c The Korean Society of Environmental Agriculture Abstract BACKGROUND: This study aimed to estimate the measurement associated with determination of cadmium and lead from tomato paste by ICP/MS. The sources of measurement (i.e. sample weight, final volume, standard weight, purity, molecular weight, working standard solution, calibration curve, recovery and repeatability) in associated with the analysis of cadmium and lead were evaluated. METHODS AND RESULTS: The guide to the expression of was used for the GUM (Guide to the expression of Uncertainty in Measurement) and Draft EURACHEM/CITAC (EURACHEM: A network of organization for analytical chemistry in Europe/ Co-Operation on International Traceability in Analytical Chemistry) Guide with mathematical calculation and statistical analysis. The components were evaluated by either Type A or Type B methods and the combined standard were calculated by statistical analysis using several factors. Expected of cadmium and lead was 0.106±0.015 mg/kg (k=2.09) and 0.302±0.029 mg/kg (k=2.16), on basis of 95% confidence of Certified Reference Material (CRM) which was within certification range of 0.112±0.007 mg/kg for cadmium (k=2.03) and 0.316±0.021 mg/kg for lead (k=2.01), respectively. CONCLUSION(s): The most influential components in the of heavy metals analysis were confirmed as recovery, standard calibration curve and standard solution were identified as the most influential components causing of heavy metal analysis. Therefore, more careful consideration is required in these steps to reduce of heavy metals analysis in tomato paste. Key Words: Cadmium, Lead, Measurement, Uncertainty, Tomato paste 서론 * 교신저자 (Corresponding author): Tel: +82-31-290-0527 Fax: +82-31-290-0506 E-mail: wikim721@korea.kr 농산물중중금속은오염원의분포가광범위하고농산물에는미량존재하고있지만 (Lee et al., 1996; Huang et al., 179
180 KIM et al. 2007), 사람에게이행되었을때쉽게분해되지않고축적되기쉽다 (Suh et al., 1982). 따라서, 카드뮴과납에대한기준규격설정도지속적으로이루어지고있으며중금속이함유된식품등에많은관심이증가하고있다 (Lee et al., 2005). 최근농산물을포함한식품의국제무역이급증하는추세이므로중금속기준치초과여부및기준치근처에서발생하는오차에대한적부판정시불확도는매우중대한사항으로여겨지고있으므로신뢰성있는분석능력이요구되고있다 (Ok et al., 2009; Chen et al., 2009). 특히, 농산물중중금속등과같이미량함유되어있는화합물의분석시오차로인하여결과의차이가발생할수있으므로측정결과의신뢰도는매우중요하다. 숙련된시험원이공인된실험방법에의한농산물중중금속분석시, 매번동일한결과를산출하기는현실적으로어렵다. 따라서, 측정에있어서시료전처리, 기기분석, 결과해석등은시험기관또는시험원마다상이하므로이를최소화하기위한연구가수행되고있다 (Jun et al., 2004). 실질적으로불확도가표현되지않는분석결과는신뢰도에관한지표가없으므로신뢰성여부에대한의문이생기게되기때문에이러한일련의과정을측정불확도를통해추정할수있다. 측정불확도는측정대상으로부터합리적으로추정된값들의분산된상태를규정하는측정결과와관련된매개변수를의미하며, 결과값의불확실성정도, 분석결과가참값에얼마나근접하느냐에따른의심과타당성으로정의한다 (Kim and Kim, 2003). 정확한분석결과및측정불확도를산출하기위해서시험분석및교정결과의품질에대한척도 (Lee et al., 2008) 로측정불확도표현지침인 GUM(Guide to the expression of Uncertainty in Measurement) 과 EURACHEM에근거하여수학적처리및통계방법을이용할수있다 (ISO, 1995, Ellison et al., 2000). GUM에의한측정불확도계산은결과값의함수, 표준불확도의계산, 합성표준불학도, 확장불확도의계산을통하여통계적추정을제시하고있으며 (Ok et al., 2009), 이지침은국제도량형위원회 (CIPM) 가중심이되어측정불확도평가와표현에있어세계적으로널리채택되어확대적용되고있다 (NIST, 1993). KOLAS(Korea Laboratory Accreditation Scheme) 국제공인시험기관에서의경우, 한국표준과학원으로부터발간된 1998년측정불확도표현지침을근거로측정불확도산출및평가를의무화하고있다. 또한, 최근 FAO/WHO 합동식품규격위원회 (The Joint FAO/WHO Codex Alimentarius Commission) 시료채취분과에서도분석결과에대한신뢰성향상을위해측정불확도에대한논의가진행중이다 (Codex, 2011). 그외에도옥수수유중 pp'-dde에대한측정불확도평가 (Kim et al., 1999), 야채음료중비타민 C 불확도산출 (Kim and Kim, 2003), 성장기용조제식중비타민 C분석 (Jun et al., 2005), 밀에서데옥시니발레놀분석의측정불확도산정 (Ok et al., 2009), 조제분유중비타민 A 분석의측정불확도비교산정 (Lee et al., 2008) 연구등측정불확도와 관련한많은연구가있었다. 그러나, 농산물중중금속분석과관련된다양한시험방법및성분에있어서정확한불확도인자선정이나합리적인오차발생원인규명에대해서는연구가부족한실정이다. 본연구에서는토마토페이스트를대상으로카드뮴및납을분석할때오차원인을파악함에있어시료양, 표준물질, 분석방법, 분석기기, 시험원, 검정곡선, 희석배수, 재현성, 반복성등분석시영향을줄수있는요인들을알아보고이들을수치화하여최종실험결과및측정불확도에미치는영향을산출하고자한다. 재료및방법 실험재료본실험에서사용된농산물시료는국내농산물중카드뮴및납의규격과유사한카드뮴 0.112±0.007 (k=2.03) mg/kg, 납 0.316±0.021 (k=2.01) mg/kg의인증값을가지고있는인증표준물질 (CRM: Certified Reference Material) 토마토페이스트 (BC084a, LGC, Teddington, UK) 를사용하였으며, 표준품은 Merck (Merck KGaA, Darmstadt, Germany) 에서구입하여사용하였다. 전처리에사용한 70% HNO 3 (Dong Woo Fine Chem. Co. Ltd., Iksan, Korea) 와 H 2O 2 (Dong Woo Fine Chem. Co. Ltd., Iksan, Korea) 는 Electronic grade를사용하였다. 모든실험기구는파이렉스, 폴리테트라플로로에틸렌재질을사용하였으며, 초순수는 Millipore water purification system (Le Montsur-Lausanne, Switzerland) 에의해 18.0 MΩ수준으로정제된물을사용하였다. 표준품및시료무게측정을위한저울 (Precisa, XT220A, Swiss) 및피펫은교정기관에서교정하여불확도를추정하였다. 시료전처리및분석조건카드뮴및납의분석은식품공전 (KFDA, 2010) 과 AOAC Method(AOAC, 2000) 의시험방법을이용하여분석하였다. 분석을위해서마이크로웨이브분해는시료약 2.0 g을 HNO 3 7 ml와 H 2O 2 1~2 ml를가한후, Microwave Digestion System (ETHOS, Milestone, Italy) 을사용하였으며, 1,000 W에서 15분간 80 C까지상승시킨후, 5분간온도를유지하고 1분간 150 C까지상승시킨후, 5분간유지하고다시 5분간 180 C까지상승시킨후 20분간유지하여분해하였다. 카드뮴및납함량분석을위해표준원액 5.0 mg/l stock solution을만든후, 2% HNO 3 용액으로희석하여 5~50 µg/l 농도범위로조제하였고, ICP/MS (Agilent 7500a, Tokyo, Japan) 를이용하여측정하였다 (Table 1). 불확도추정방법 GUM(ISO, 1995) 과 EURACHEM(Ellison et al., 2000) 에근거하여모델관계식을설정하고, 각각의불확도요인들로부터불확도를추정하였다.
A Study on the Factors Causing Analytical Errors through the Estimation of Uncertainty for Cadmium and Lead Analysis in Tomato Paste181 Table 1. The Conditions of ICP-MS measurement Parameter Value RF Power 1150W Neublizer 0.98 L/min Auxillary 1.3 L/min Plasma 16 L/min Lens voltage 7.75 V Lead, Cadmium Ion monitored Cd 111, Pb 208 모델관계식설정토마토페이스트중카드뮴및납의함량을산출하기위한식은식 (1) 과같이설정하였고, 농도산출단계에서불확도산출관계식은식 (2) 로설정하였다. 또한, 전체적인불확도요인및인자들에대한세부내용을 Fig. 1에나타내었다. 측정시저울및기기의안정성등과같은불확도는평균값의표준불확도를적용하여 A Type 표준불확도로평가하였으며, 저울, 플라스크, 피펫등의교정성적서상의결과를사용하는경우나반복측정하지않는경우는 B Type 표준불확도로평가하였다 (ISO, 1995). 자유도는 KOLAS에서발간한측정결과의불확도산정및표현을위한지침에따라구하였으며 (KOLAS, 2000), 반복측정시자유도를 n-1로계산하였고직선의절편과기울기는 n-2로계산하여불확도를산출하였다. 검정곡선의불확도검정곡선의경우, 표준용액을여러농도로희석하여작성하였으며, 1차회귀식 (3) 을사용하였으며, 상대표준불확도는식 (4-6) 을이용하여산출하였다. C spl = (A j-b 0 ) B l (1) A j : j th measurement of the area of the calibration standard B 0 : Intercept of the calibration curve B l : Slope of calibration curve C spl : Concentration of sample C spl = C spl FW spl Wspl = (A j-b 0 ) FW spl W spl B l (2) FW spl : Final weight of sample (g) W spl : Weight of sample (g) 요인별측정값과표준불확도 여러번측정하여평균값을측정값으로사용할경우, 무게 A j = C i B l + B 0 (3) (4) S= n [A j -(B o +B l C j )] 2 i=1 n-2 (5) n Sxx = (C j - C) 2 (6) j=1 Fig. 1. Fish bone diagram of sources in cadmium and lead analysis.
182 KIM et al. A j : j th measurement of the area of the calibration standard C i : Concentration of th ith calibration standard B l : Slope of the calibration curve B 0 : Intercept of the calibration curve P : Number of measurement to determination C 0 n : Number of measurement for the calibration C 0 : Concentration of cadmium and lead for the calibration 감응계수감응계수는각측정량의불확도인자가전체결과값에영향을미치는정도를나타내는것으로식 (7) 과같이나타내었다. c i f x i ( y) i x i (7) 합성표준불확도 측정결과가여러개의다른입력량으로부터구해질때이측정결과의표준불확도를합성표준불확도로표현하였으며, 이는식 (8) 에준하여, ISO guide에따라감응계수를이용하여산출하였다. u c (y)= 포함인자 n ( f ) 2 u 2 (x i=1 x i ) (8) i 포함인자 (k) 는합성표준불확도의유효자유도 ( V eff ) 를추정하고, Welch- Satterthwaite 공식 (9) 를이용하여산출하였다. V eff = u c 4 (y) n i=1 [c i u(x i ) 4 ] ν i (9) 확장불확도확장불확도는감응계수와유효자유도를구한후신뢰수준을고려하여 t 분포도에서값을확인하였다. 산출된합성표준불확도에신뢰수준에상당하는포함인자 k 를곱하여확장불확도는식 (10) 을이용하여산출하였다. U =ku c (y) (10) 소급성확인방법 측정기관의소급성유지를위한지침서에의거하여 (KOLAS-R-008:2008) 분석기기및장비에대하여공인교정기관으로부터시험또는교정을받아측정불확도계산에사 용하였으며, 외부공인교정기관의결과를바탕으로, 시험소에서는분석기기및장비에대한내부교정을시행하여실험에사용하였다. 또한, 분석결과에대한신뢰도를국제적으로인정받기위해 (Ting et al., 2006) 영국환경식품부 (Department for Environment Food and Rural Affairs) 의 CSL (Central Science Laboratory) 에서운영하는 FAPAS(Food Analysis Performance Assessment Scheme) 국제비교숙련도프로그램에참여하여카드뮴및납등중금속분석에서우수한결과를얻었다. 결과및고찰 표준용액의무게측정시불확도토마토페이스트의카드뮴및납분석을위하여표준용액 1,000 mg/l를 0.125 g의무게측정시, 저울에대한교정성적서상의불확도, 저울의분해능이불확도요인으로고려되어야한다. 본실험에서는저울의교정성적서상의불확도는 95% 신뢰수준에서 0.0009 g의불확도를가지고있으므로표준불확도는 0.00045(0.0009/2) 가된다. 저울의안정성은분동을이용하여 10회반복측정한값의표준편차 0.0002 g 을불확도로산출하였다. 저울의분해능은 0.0001 g이며, 분해능에대한표준불확도는 0.00007이었다. 저울의합성표준불확도는각표준불확도 (u(w cd,pb)) 에대한제곱합의제곱근으로 0.00024이며, 상대표준불확도 (u(w cd,pb)/w cd,pb) 는 0.00196(0.00024/0.125) g이었다. 표준용액의순도및분자량의불확도표준용액의순도에대한불확도를산출하기위해서시약제조사의규격에서카드뮴및납모두 1,000±2 mg/kg으로성적서상에기재되어있으므로순도에대한표준불확도는 (u(p cd,pb ) 2이고상대표준불확도는 (u(p cd,pb)/p cd,pb) 0.002(2/ 1,000) mg/kg이다. 카드뮴의분자량은 112.4110이고 IUPAC(IUPAC, 1997) 에서발표한불확도는 0.008이므로직사각형분포를가정하여 3으로나누면 0.004618이며, 상대합성표준불확도는 0.000041(0.004618/112.4110) 으로산출되었다. 그리고납의분자량은 207.2이고 IUPAC에서발표한불확도는 0.1 이므로직사각형분포를가정하여 3으로나누면 0.057735이며, 합성표준불확도 0.057735, 상대합성표준불확도는 0.000278 (0.057735/207.2000) 으로산출되었다. 표준용액제조과정의불확도카드뮴및납표준용액조제시, 표준품 0.125 g를 25 ml volumetric flask에정용후 5 mg/l로만든후, 2% HNO 3 로 5, 10, 50 µg/l의표준용액을제조하였다. 표준품제조시부피측정에대한불확도를확인하기위해서플라스크의교정성적서상에나타난불확도, 눈금읽기에대한시험원의재현성에대한불확도, 피펫의편차에대한불확도를합성하여표준불확도를계산하였다.
A Study on the Factors Causing Analytical Errors through the Estimation of Uncertainty for Cadmium and Lead Analysis in Tomato Paste183 25 ml volumetric flask의교정성적서상의불확도는 95% 신뢰수준에서 ±0.013 ml로나타났으며, 포함인자 k 의값이 2이므로 2를나누어줌으로써표준불확도는 0.00065 ml가된다. volumetric flask의표선맞추기에따른시험원의불확도를측정하기위하여 10회반복하여측정한결과 25 ml의표준편차는각각 0.0074이므로 A type불확도로계산하면표준불확도는 0.00232(0.0074/ 10) 로나타났으며, 측정횟수가 10이므로자유도는 9이다. 또한실험실온도변화가 ±4 C이고, 물의부피팽창계수는 0.00021/ C이다. 따라서온도변화에따른부피의불확도는직사각형분포로간주하여계산하면 0.02100 ml이며표준불확도는 0.01212 ml가된다. 플라스크의합성표준불확도 (u(std0v)) 는각표준불확도에대한제곱합의제곱근으로 0.01560이된다. 따라서카드뮴및납의표준용액제조에사용된 25 ml volumetric flask에대한상대표준불확도는 ((ustd0v)/std0v) 는 0.0006(0.01560/25) 가된다. 또한, 피펫을사용하여희석조제하였으므로 1 ml, 5 ml 피펫의교정성적서상의불확도는 95% 신뢰수준에서각각 ±0.006, 0.015 ml로나타났으며, 포함인자 k 의값이 2이므로표준불확도 (u(std5.0p)) 는 0.003, 0.0075 ml가된다. 모표준용액 (5.0 mg/l) 으로부터 1 ml 피펫을이용하여 50 µg/l(std1) 을제조하고, 다시희석하여 10 µg/l(std2), 5 µg/l(std3) 의표준용액을제조하였으므로피펫에대한부피팽창및시험원의반복성, 피펫의편차지시값을감안하여 1 ml, 5 ml의합성표준불확도를계산하면각각 0.0030, 0.0090 ml이되므로상대표준불확도는 (u(std1~3v))/std1~3v)) 는 0.003(0.0030/1) ml, 0.0018(0.0090/5) ml이되며, 측정횟수가 10이므로자유도는각각 9이다. 시료전처리시불확도토마토페이스트중카드뮴및납을정량분석하기위하여시료 2.05 g을취하여 HNO 3 7 ml와 H 2O 2 1~2 ml를사용하여 Microwave 분해과정을거쳐서 3차증류수로희석하여최종 28.0742 g으로정용하였다. 앞서표준품무게측정시와같은방법으로시료의무게 (W spl) 와희석용매를넣은최 종무게 (FW spl) 의합성표준불확도 (u(w spl), u(fw spl)) 는시료무게 0.00045 g, 희석한최종시료무게는 0.00045로산출되었으며, 상대표준불확도 ((u(w spl)/w spl, u(fw spl)/ (FW spl)) 은각각 0.00022(0.00045/2.05), 0.000016 (0.00045/ 28.0742) g이된다. 검정곡선불확도검정곡선의비직선성은측정결과값의주요한불확도요인이된다. 본연구에서는검정곡선의불확도측정을위하여검정곡선은모표준용액으로부터희석된 3개의표준용액농도를 3회씩반복하여 ICP/MS로측정하여작성하였으며, 상관성 ( cal) 은카드뮴, 납모두 0.999로높은상관성을나타내었다. 검정곡선은선형최소제곱법을이용하여산출하였으며, 검정곡선의불확도 (u( cal)) 는 (3)~(6) 의식을사용하여불확도를계산하면, 카드뮴은 0.034, 납은 0.012이며, 이때상대표준불확도 (u( cal)/ cal) 는카드뮴 0.034(0.034/0.999), 납 0.012(0.012/0.999) g/100g이되며, 이때자유도는측정횟수가 9회이므로 2를빼면 7로나타났다. 시료측정시불확도 ICP/MS를이용하여시료를 8회반복분석한결과카드뮴및납의평균값 (C spl) 및표준편차는각각 0.0077±0.0006 (mg/kg), 0.0221±0.0006 (mg/kg) 이며, A type의표준오차로산출된표준불확도 (u(c spl)) 는카드뮴 0.00023, 납 0.00061이며상대표준불확도 (u(c spl)/c spl) 는각각 0.0294 (0.00023/0.0077), 0.0099(0.00021/0.0221) mg/kg가되며이때자유도는측정횟수가 8이므로 7이다. 회수율및정밀성의불확도시료의기질에대한불확도는반복측정과회수율불확도의상대불확도를합성하여구하였다. 회수율시험을 10회반복측정한결과카드뮴및납의평균 (R matrix) 및표준편차는각각 102.46±4.76%, 98.65±3.89% 이었으며, 이에대한표준불확도 (u(r matrix)) 는표준편차와같으므로카드뮴 0.049, 납 0.039로나타났다. 따라서회수율및정밀성의상대표준불확도 (u(r matrix)/(r matrix)) 을산출하면카드뮴은 0.0481(0.049/ Table 2. Uncertainty sources of cadmium and lead analysis by ICP/MS Description (Parameter) Weight of cadmium and lead (W cd,pb) Purity of cadmium and lead (P cd,pb) Formular weight of cadmium and lead (F cd,pb) Dilution of cadmium and lead (STD 0~3) Weigh of cadmium and lead (W spl) Final Weight of cadmium and lead (FW spl) Calibration Linearity ( cal) Concentration of sample in the extraction solution (C spl) Recovery and Repeatability of matrix (R matrix) Uncertainty source Calibration Repeatability Resolution Purity Calibration Repeatability Temperature Calibration Repeatability Reproducibility Calibration Repeatability Reproducibility Calibration Repeatability Recovery Repeatability
184 KIM et al. 1.025) g/100g 이며, 납은 0.0399(0.039/0.986) g/100g 이되며, 자유도는측정횟수가 10 회이므로 9 회로산출되었다. 합성표준불확도각불확도요인들의합성상대표준불확도값을불확도전파의법칙에따라제곱합의제곱근으로산출하였다. 즉, Table 3,4와같이각불확도인자들의상대표준불확도들을합성하여상대합성표준불확도 (u(c s)/(c s)) 를계산하면토마토페이스트중카드뮴은 0.067, 납은 0.045으로산정되었다. 따라서시료의희석배수를곱한분석결과는카드뮴 0.106 mg/kg, 납은 0.302 mg/kg으로나타났으므로토마토페이스트의합성표준불확도는카드뮴 0.007(0.106 0.067) mg/kg이납은 0.014(0.302 0.045) mg/kg로산출되었다. 확장불확도확장불확도는합성표준불확도에서계산된값에포함인자 (k) 를곱하여계산되므로포함인자 (k) 를구하기위해서는 Welch-Satterthwaite 공식을이용하여추정하였다. 카드뮴의유효자유도는 20.61, 납의유효자유도는 13.47로 95% 신뢰수준에서포함인자 (k) 의값은카드뮴 2.09, 납 2.16이다. 따 라서확장불확도 (U) 는카드뮴 0.0148, 납 0.0291로최종결과값은각각 0.11±0.01 mg/kg, 0.30±0.03 mg/kg (95% 신뢰도구간 ) 으로표현하였다. EU에서화학적분석에있어서실험결과의확장불확도는표시된범위에포함된다면결과값을수용하도록하였기때문에본연구에서산출된카드뮴및납의확장불확도값은모두 1 mg/kg 이하농도에서계산된값이므로적합하였다 (EU, 2004). 불확도인자의상대기여도토마토페이스트의카드뮴및납을분석결과값과비교할때카드뮴은 13.96%(=0.0148/0.106 100), 납은 9.63%(=0.0291/ 0.302 100) 가불확도인것으로산출되었다. 각요인이전체불확도에끼치는영향은 Table 3, 4와같으며, 각불확도인자의 % 값으로표현하였다. 불확도인자의상대불확도가최종실험결과값에미치는영향을살펴보면카드뮴의경우, 회수율과반복성에따른불확도 (36.2%) > 분석시의검정곡선 (25.6%) > 샘플농도 (22.1%) > 표준용액희석 (12.9%) 순으로나타났고, 납의경우, 회수율과반복성에따른불확도 (47.8%) > 표준품조제과정 (20.6%) > 분석시의검정곡선 (14.4%) > 샘플농도 (11.9%) > 순으로나타났으며, 표준품 Table 3. Uncertainty values of cadmium determination Parameter Value Standard Sensitivitycoefficient Degree of freedom Relative standard Effective degree of freedom Type of (x i) x i u(x i) ci/( c x/ i) v u(x i)/x i % [c iu(x i)] 4 /v i A or B W cd 0.125 0.000 0.85 9 0.00196 1.47 2.1E-16 B P cd 1,000 2.000 0.00-0.00200 1.50 0.0E+00 B F cd 112.41 0.005 0.00-0.00004 0.03 0.0E+00 B STD0 V 25.00 0.016 0.00 9 0.00062 0.47 2.1E-18 B STD1 P 0.25 0.003 0.42 9 0.01216 9.15 3.1E-13 B STD1 V 25.00 0.016 0.00 9 0.00062 0.47 2.1E-18 B STD2 P 5 0.009 0.02 9 0.00181 1.36 1.5E-16 B STD2 V 25.00 0.016 0.00 9 0.00062 0.47 2.1E-18 B STD3 P 12.5 0.009 0.01 9 0.00072 0.54 3.8E-18 B STD3 V 25.00 0.016 0.00 9 0.00062 0.47 2.1E-18 B W spl 2.05 0.000 0.05 9 0.00022 0.17 3.4E-20 B FW spl 28.07 0.000 0.00 9 0.00002 0.01 9.7E-25 B cal 1.00 0.034 0.11 7 0.03402 25.59 2.4E-11 B C spl 0.01 0.000 13.69 7 0.02942 22.13 2.4E-11 A R matrix 1.02 0.049 0.10 9 0.04808 36.16 7.5E-11 B W cd : weight of cadmium, P cd : purity of cadmium, F cd : formular weight of cadmium, STD : dilution of standard solution, Wspl: weight of sample, FW spl : final weight of sample, cal : linearity of calibration curve, C spl : concentration of sample in the final solution, R matrix : recovery and repeatability of matrix
A Study on the Factors Causing Analytical Errors through the Estimation of Uncertainty for Cadmium and Lead Analysis in Tomato Paste185 Table 4. Uncertainty values of lead determination Parameter Value Standard Sensitivitycoefficient Degree of freedom Relative standard Effective degree of freedom Type of (x i) x i u(x i) c i/( c x/ i) v u(x i)/x i % [c iu(x i)] 4 /v i A or B W pb 0.125 0.000 2.42 9 0.00196 2.34 1.4E-14 B P pb 1,000 2.000 0.00-0.00200 2.39 0.0E+00 B F pb 207.2 0.058 0.00-0.00028 0.33 0.0E+00 B STD0 V 25.00 0.016 0.01 9 0.00062 0.75 5.5E-11 B STD1 P 0.25 0.003 0.30 9 0.01216 14.56 2.0E-19 B STD1 V 25.00 0.016 0.01 9 0.00062 0.75 8.8E-14 B STD2 P 5.00 0.009 0.06 9 0.00181 2.16 1.6E-17 B STD2 V 25.00 0.016 0.01 9 0.00062 0.75 8.8E-14 B STD3 P 12.50 0.009 0.06 9 0.00072 0.86 1.6E-17 B STD3 V 25.00 0.016 0.01 9 0.00062 0.75 3.1E-12 B W spl 2.05 0.000 0.15 9 0.00022 0.27 2.2E-18 B FW spl 28.07 0.000 0.01 9 0.00002 0.02 6.4E-23 B cal 1.00 0.012 0.30 7 0.01206 14.43 2.5E-11 B C spl 0.02 0.001 13.69 7 0.00991 11.86 2.5E-11 A R matrix 0.99 0.039 0.31 9 0.03993 47.79 2.4E-09 B W pb : weight of lead, P pb : purity of lead, F pb : formular weight of lead, STD : dilution of standard solution, W spl : weight of sample, FW spl : final weight of sample, cal : linearity of calibration curve, C spl : concentration of sample in the final solution, R matrix : recovery and repeatability of matrix Fig. 2. Uncertainty contributions in cadmium analysis of Certified Reference Material (CRM). 분자량과시료의무게측정에는영향이적은것으로나타났다 (Fig. 2, 3). 매질에의한불확도는회수율의재현성불확도와회수율의상대불확도를합성한것으로, 매질에따른불확도차이가있을것으로판단되므로실험자는회수율재현성및반복성을높이는데주의를기울여야한다 (Ok et al., 2009). 시험원들은분석과정중불확도가높게산출된항목에대해서좀더주의를기울일필요가있으며, 순도가높은표준품사용, 검증된 Volumetric flask, 저울, 피펫등을사용하여야 하며저울및분석기기의경우불확도가낮고, 분해능이높은분석기기를사용하여야불확도를최소화할수있을것으로판단된다 (Hund et al., 2003). 측정불확도추정시불확도인자의기여도가높은인자는회수율및재현성, 표준용액조제, 검정곡선등으로나타났으며, 이들의결과는본연구결과와유사한결과를나타내었다 (Jun et al., 2004;. Ok et al., 2009; Lee et al., 2008).
186 KIM et al. Fig. 3. Uncertainty contributions in lead analysis of Certified Reference Material (CRM). Table 5. Results and of cadmium and lead in tomato paste LOD (μg/kg) LOQ (μg/kg) Certified Value (mg/kg) Analysis result (mg/kg) Cd 0.005 0.017 0.112±0.007 (k = 2.03) 0.106±0.015 (k =2.09) Pb 0.01 0.033 0.316±0.021 (k = 2.01) 0.302±0.029 (k =2.16) 시험결과의소급성시험결과의소급성을위하여시료를인증표준물질 (CRM) 인 ERM-BC084a 토마토페이스트를사용하였으며카드뮴은 0.112±0.007(mg/kg, k=2.03), 납은 0.316±0.021(mg/kg, k=2.01) 의인증결과값을가지고있었으며, 측정불확도추정결과, 토마토페이스트의카드뮴및납모두인증값범위내에포함되었다 (Table 5). 시험결과의소급성유지를위해이들의회수율은카드뮴 102.47%, 납 98.65% 였으며, 모두인증표준물질의유효농도내에속하는값이므로본실험결과의분석방법및실험기기의소급성을확인할수있었다. 또한, FAPAS 07152(Food Analysis Performance Assessment Scheme) 국제비교숙련도프로그램에참가하여 vegetable puree 중카드뮴및납을분석한결과, 모두 Z <2 이하로만족스러운결과를얻었다 (Fig. 4). 측정불확도에대해서시험자가시험할때마다산정하는건사실상불가능하지만, 본연구와같이시험과정중분석오차의발생요인을규명하고, 영향이큰요인들을집중관리하여오차발생요인들을최소화하는방법을모색한다면농산물중중금속등과같이미량원소의경우실험결과에대한오차발생을크게줄일수있을것이다. 요약 본연구에서는국내농산물중중금속의기준규격설정이증가되고있는추세이므로농산물중미량의중금속을분석함에있어발생될수있는측정불확도및오차요인을규명하는것은매우중요한업무이다. 따라서이들을평가하고, 분석방법등을개선하며오차를최소화하여신뢰성있는결과 를얻기위해서는측정불확도의산출이요구된다. 본연구에서는측정불확도인자로표준품의무게, 순도, 분자량, 표준용액제조, 시료무게, 검정곡선, 회수율등을불확도인자로선택하였으며이들은저울및피펫, 부피플라스크의안전성, 분해능, 재현성, 표준품의순도, 분석기기의재현성등이결과에영향을미칠수있었다. 측정불확도산출시 GUM과 EURA- CHEM에근거하여결과를확인하였으며각인자들을 A-type 또는 B-type으로산출된표준불확도값을확인하여합성불확도를산출하였다. 토마토페이스트를분석한결과카드뮴은 0.106±0.015(mg/kg), 납은 0.302±0.029(mg/kg) 로산출되었다. 확장불확도 (U) 는카드뮴 0.015(k=2.09, 신뢰수준 95%), 납 0.029(k=2.16, 신뢰수준 95%) 의결과를나타내었다. 토마토페이스트중중금속을분석함에있어불확도에영향을줄수있는인자는회수율과반복측정, 검량곡선, 샘플농도순으로확인되었으며, 이를통해서시험원들은분석시불확도가높게나오는실험과정에좀더세심한주의가요구된다. 측정불확도결과판단시측정된불확도값과더불어표준시약의소급성유지, 시험기구의교정, 실험자의숙련도향상등을통해실험결과의오차를줄이는노력이필요하며, 측정불확도에영향을미치는요인들이축적된다면오차등을감소시키는자료로활용될수있을것으로판단된다. 감사의글 This study was supported by the grant (No. PJ006446) from RDA, Suwon, Korea.
A Study on the Factors Causing Analytical Errors through the Estimation of Uncertainty for Cadmium and Lead Analysis in Tomato Paste187 Cd Pb Fig. 4. Proficiency testing results of vegetable puree for cadmium and lead. 참고문헌 AOAC, 2000. Official Methods of Analysis of AOAC Int. Association of Official Analytical Communities, Gaithersbug, MD, USA. 17th ed. Ch 50, 17-18. Chen T., Liu X., Li X., Zhao K., Zhang J., XY J., Shi J., and Dahlgreen R.A. (2009) Heavy metal sources identification and sampling analysis in a field-scale vegetable soil of hangzou, China, Environ. pollut. 157, 1003-1010. Codex Alimentarius Commission, 2011. Codex committee on methods of analysis and sampling, CX/MAS 11/32/1, Budapest, Hungary. Ellison S.L.R., Roesslein M.l., Williams A. (2000) Quantifying Uncertainty in Analytical Measurement, EURACHEM, London, UK. 32-94. EU, 2004. Report on the relationship between analytical results, measurement, recovery factors and the provisions of EU food and feed legislation, with particular reference to community legislation concerning. Brussels, Belgium. Huang S., Liao Q., Hua M., Wu X., Bi K., Yan C.,
188 KIM et al. Chen B., and Zhang X. (2007) Survey of heavy metal pollution and assessment of agricultural soil in Yangzhong district, Jiangsu Province, China, Chemosphere, 67(11), 2148-2155. Hund E., Luc Massart D., and Smeyers Verbeke J. (2003) Comparison of different approaches to estimate the of a liquid chromatographic assay, Anal. Chem. 480, 39-52. ISO, 1995. Guide to the Expression of Uncertainty in Measurement. International Organization for standardization, Geneva, Switz-erland. IUPAC, 1997. Commission on atomic weight an isotopic abundances. J.Pure Appl.Chem. 69. 2471-2473. Jun J.Y., Kwak B.M., Ahn J.H., and Kong U.Y. (2004) Quantifying of calcium determination in infant formula by AAS and ICP-AES, Korean J. Food Sci. Technol. 36(5), 701-710. Jun J.Y., Kwak B.M., Ahn J.H., and Kong U.Y. (2005) Quantifying of vitamin C determination in infant formula by indophenol titration method. Korean J. Food Sci. Technol. 37(3), 352-359. KFDA, 2010. Analytical methods of heavy metals in foods, Korea Food and Drug Administration (KFDA), Seoul, Korea. 1177-1181. Kim B.J., Kim D.H., Choi J.O., and So H.Y. (1999) Quantitative analysis of trace pp'-dde in corn oil by isotope dilution mass spectrometry: evaluations. Bull. Korean Chem. Soc. 20, 910-916. Kim Y.J., and Kim H.W. (2003) Estimation of Measurement Uncertainty in Vitamin C Analysis from vegetable and fruit juice. Korean J. Food Sci. Technol. 35(6), 1053-1059. KOLAS, 2000. Guideline for quantifying and expressing the in measurement results. Korea Laboratory Accreditation Scheme, Daejon, Korea. Lee H.M., Kwak B.M., Ahn J.H., and Jeon T.H. (2008) A comparative study on quantifying of vitamin A determination in infant formula by HPLC. Korean J. Food Sci. Technol. 40(2), 152-159. Lee J.O., Sho Y.S., Oh K.S., Kang K.M., Shu J.H., Lee E.J., Lee Y.B., Park S.S., Kim H.Y., and Woo G.Z. (2005) Heavy metal survey of agricultural products in Korean circulation market, The Annual Report of KFDA, 9, 953. Lee T.J., Kim K.C., Shin I.C., Han K.S., SHim T.H., Ryu M.J., and Lee J.K. (1996) Survey on the trace heavy metals in agricultural products Gangwondo. Rep. Inst. Health Environ. 7, 75-87. NIST, 1993. Guidelines for Evaluating and Expressing the of NIST Measurement Results. NIST Technical Note 1297, NIST, KOREA. Ok H.E., Chang H.J., Ahn J.H., Cho J.Y., and Chun H.S. (2009) Estimation of Measurement Uncertainty for the HPLC Analysis of Deoxynivalenol in Wheat. Korean J. Food Sci. Technol. 41(3), 258-264. Suh Y.S., Mun H.H., Kim I.K., Kim H.Y., Jun S.H., Ji D.H. (1982) A study on the natural contents of heavy metals in soil. Rep. Natl. Inst. Environ. Res. Korea. 4, 189-198 Ting T.L., Sin D.W.M., Ho C. (2006) The role of chemical metrology in the upholding of public health and food safety in Hong Kong. International Symposium on Metrology in Chemistry, Beijing, People's Republic of China. Accreditation and Quality Assurance. 11, 172-174.