Quantitative Analysis CHEM 3000
Weber State University
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Date Created: 10/28/15
Weber State University H CHEM 3000 Quantitative Analysis H Calibration Methods Reading Sections 4 7 to 4 9 amp Chapter 5 Calibration Comparison of a standard or technique with another standard or technique for the purpose of determining and eliminating any systematic error that in uences accuracy Box 31 pg 43 Calibration is the act of determining the relationship between a measured signal and the concentration of the analyte producing the signal A technique is useless for a given analyte unless it can detect the analyte at the levels expected in the sample being investigated The levels of accuracy and precision for an analysis are ultimately dictated by the decisions that are made based upon the result Blank A solution or sample that does not contain the analyte of interest A measured signal from a blank is due to some artifact or interference and is subtracted from the analyte signal The net result is the analyte signal Ideally the blank should contain all components of the prepared samples except for the analyte matrix blank That way any contribution to the analyte signal from the matrix can be appropriately subtracted A method blank contains everything the sample does and it carried through each step of the analysis A reagent blank is a prepared blank close to a method blank but is not carried through each step A eld blank is one that has been exposed to the actual site from which the samples Where taken or prepared Sensitivity This is the magnitude of the signal for a given amount of analyte A more sensitive technique is one that produces a greater signal than another technique for the same amount of analyte Signal Concentration Selectivity It is a measure to which a particular method is free from additive interference a type of interference in which one or more components in the matrix produce a signal that adds to the analyte signal Detection Limit LOD In more quantitative terms it is the concentration or amount of analyte that produces a signal that exceeds the blank signal by an amount equal to 3 times the standard deviation for replicate measurements of the blank Because the standard deviation is dependent upon the number of measurements n the IUPAC recommends n 20 assuming an ideal matrix blank Only 1 of the samples with no analyte will give a signal greater than the detection limit 99 0f the analyte samples at the detection limit will give a signal greater than the blank Measured signal Mean background Signal Sblank Signal probability Illustration above was based upon Fig 18B2 pg 757 of Chemical Analysis by Kenneth A Rubinson 1987 Use reported LODs With caution usually obtained under ideal conditions Optimum instrument performance Clean samples Experienced analyst Controlled settings Procedure for determining LOD 1 Prepare sample l 5x the estimated detection limit of the method 2 Measure signal from n replicate samples n 2 7 3 Compute s of the n measurements 4 Measure signal from n blank samples and determine the average Yum 5 ydl yblank ts Where t is the value of Student s tfor n 1 degrees of freedom and the 98 con dence level IUPAC recommends 20 measurements and t 3 ydl is called the signal LOD 6 Concentration LOD Use calibration curve and determine the slope of the best t line The corrected signal is proportional to the sample concentration ysample yblank m x concentration Calibration curve near detection limit signal s1 gnalblank 0 DL COl lC Limit of Quanti cation LOQ The smallest concentration or amount of analyte that can be reliable quantified Reporting Limit The concentration below which regulatory rules say that an analyte is reported as not detected although it may still be present Different matrices may dictate different reporting levels due to unique difficulties or interferences with a particular matrix Control Charts represent the con dence intervals around a target value and are used to assess the quality of analytical procedures Time Unlikely conditions 1 observation outside action lines 2 out of 3 consecutive measurements between warning and action lines 7 consecutive measurements all above or all below center line 6 consecutive measurements all increasing or all decreasing 14 consecutive points alternating up and down An obvious non random pattern Calibration Methods With two exceptions gravimetric and coulometric methods all analytical methods require calibration Calibration Curve A calibration curve is a plot of a measured signal y as a function of known analyte concentration x L Conc Signal The blanks and standards are measured and their blank corrected values plotted as a function of concentration I I I I I I I I I I I I I I I I I I I I I s v 20 i t xquot m I x I v z I l 0 0 0 Concentratlon M The purpose of the calibration plot is to quantify the response of the instrument or technique to various amounts of analyte We can then measure an unknown and determine Where it falls on our calibration plot always within the range 0fthe standards and determine its corresponding concentration Blank correction is often performed by the instrument In order to quantify the concentration of the unknown based upon the calibration curve the slope and intercept of the bestfitting trend line through the data must be determined 5 The method of least Vertical squares linear 4 deviation regression analysis is zyquot Y utilized for this purpose We assume that the errors in y are much greater than in x and s for each y value is the same 1 Intercept b I l I 1 2 3 4 5 6 X To determine the best fitting line 2 mx 7 through the data the vertical deviations really the squares of the deviations are minimized From equations 416 417 418 1 12Xiyi inzyi b 2xi22yi 2xiyipixi n2x ltzx1gt2 39 ram w R2 the square of the correlation constant is the statistical parameter used to determine linearity 2 2 2362 xy2 yl R 2ltxv2gt22ltyrtr Uncertainty in m and b The uncertainties are related to the uncertainty in measuring each y value Thus we Will determine the standard deviation of y values estimate of the population standard deviation of all y values 222 2 sin 2 size y n 2 Sin n2ltxi2 2xi2 Sb quot3xi2 3xi2 In Excel use LINESTyrange X range true true Signi cant figures The position decimal place of the rst nonzero digit is the position of the last sig g in the slope or intercept To determine the unknown concentration x just rearrange the above equation and solve for x Uncertainty in x k the number of replicate measurements of the unknown 11 the number of data points on the calibration plot sy the standard deviation uncertainty of y m the slope of the calibration line i the mean value of X points on calibration line y the mean value of y points on calibration line y the measured value of the unknown Use a SpreadSheet Xi the individual values for the points on calibration line One thing that comes from the equation for sx is that the uncertainty in the calculated concentration x is smallest near the center of the calibration line Signal 0 Concentration M Standard Addition This calibration method is utilized when the sample composition matrix is unknown or very complex and in uences the signal from the analyte matrix effect all samples have the exact same matrix Here s what you do Measure the signal SX from a prepared unknown sample with X Prepare another unknown sample but spike it with a known amount of analyte same as unknown Measure the signal S of this prepared solution with X S xs Here s What this looks like graphically g g X S 0 SX SXS O Concentration Note if only one sample solution is prepared and a spike added you must account for any volume changes Graphical Method Prepare multiple solutions one of which contains only the unknown The rest of the solutions contain the same amount of unknown sample plus increasing amounts of known analyte Place 5 mL of unknown in each flask Fill each flask to th Figure 54 Quantitative ChemicalAnulysis Seventh Edition 0 2007 w HFveeman and Company Dif cult to plot a point for a calibration line when the analyte concentration in the sample is unknown So you plot What you know the added standard on the concentration aXis x axis I 5 mL unk 5 mL unk 1 mL stand S1 gnal 5 mL unk 2 mL stand Concentration 5 mL unk 3 mL stand Wki Determine the equation of the best tting straight line through the points and solve for the xintercept The standard deviation uncertainty in the xintercept is calculated by Example An unknown sample of dopamine gave a current of 346 nA in an electrochemical analysis 200 mL of solution containing 00156 M dopamine was mixed with 900 mL of unknown and diluted to a total volume of 1000 mL in a volumetric ask The new signal was 584 nA Calculate the molar dopamine concentration in the unknown Cone of standard Cone of dopamine Solve for dl Another Example Acetylene CZHZ in a gas mixture was measured by mass spectrometry The signal for mass number 26 is proportional to the volume percent of acetylene Gas Signal mV Blank no C2H2 02 Unknown 108 Unknown 0072 vol CZH2 l7l Unknown 0121 vol CZH2 202 Unknown 0200 vol CZH2 300 Unknown 0364 vol CZH2 446 Internal Standard A known amount of a compound different from the analyte is added to analyte samples The signal from the analyte is compared to the signal of the internal standard in order to determine the amount of analyte in the sample Why Internal standards are used to account for loss of analyte during sample prep or to account for variations in analyte concentration during the analysis or from run to run Needle Barrel plunger When small injection volumes are used a seemingly insigni cant l 39 39lli39iquotmi iquot7397 5 7393397 5 7395390 misplacement of the plunger can result in substantial variations in concentration IML Ta Ta 20 w 1njectlon m a Time Time IHJCCUOHI 30 m 4A m M Time Time The overall concentrations may vary but the ratio of the analyte and internal standard signals will remain the same The ratio of the signals is proportional to the ratio of the concentrations The technique or detector may not respond to the internal standard in the same way as the analyte 1 mM analyte may not produce the same signal as 1 mM internal standard Thus a response factor must be determined to quantify the analyte concentration F is the response factor essentially how many times greater or smaller the analyte responds verses the standard Example In a chromatography experiment a mixture containing 800 nM of the analyte iodoacetone and 640 nM of the internal standard p dichlorobenzene gave the relative response An unknown quantity of iodoacetone plus 930 nM pdichlorobenze gave the relative response peak area Iodoacetone 121 peak area p dichlorobenze Calculate the concentration of iodoacetone in the unknown sample S S iodoacetone p dichlorobenzene iodoacetone p dichlorobenzene S S iodoacetone p dichlorobenzene iodoacetone p dichlorobenzene
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