1、Calibration Methods,Introduction1.) Graphs are critical to understanding quantitative relationships One parameter or observable varies in a predictable manner in relationship to changes in a second parameter 2.) Calibration curve: graph showing the analytical response as a function of the known quan
2、tity of analyte Necessary to interpret response for unknown quantities,Time-dependent measurements of drugs and metabolites in urine samples,Generally desirable to graph data to generate a straight line,Calibration Methods,Finding the “Best” Straight Line1.) Many analytical methods generate calibrat
3、ion curves that are linear or near linear in nature(i) Equation of Line:where: x = independent variabley = dependent variablem = slopeb = y-intercept,Calibration Methods,Finding the “Best” Straight Line2.) Determining the Best fit to the Experimental Data (i) Method of Linear Least Squares is used t
4、o determine the best values for “m” (slope) and “b” (y-intercept) given a set of x and y values Minimize vertical deviation between points and lineUse square of the deviations deviation irrespective of sign,Calibration Methods,Finding the “Best” Straight Line4.) Goodness of the Fit (i) R2: compares
5、the sums of the variations for the y-values to the best-fit line relative to the variations to a horizontal line. R2 x 100: percent of the variation of the y-variable that is explained by the variation of the x-variable. A perfect fit has an R2 = 1; no relationship for R2 0,R2=0.9952,99.5% of the y-
6、variation is due to the x-variation,R2=0.5298,53.0% of the y-variation is due to the x-variation What is the other 47% caused by?,Very weak to no relationship,Strong direct relationship,R2 based on these relative differences Summed for each point,Calibration Methods,Calibration Curve1.) Calibration
7、curve: shows a response of an analytical method to known quantities of analyte,Procedure: Prepare known samples of analyte covering convenient range of concentrations.Measure the response of the analytical procedure.Subtract average response of blank (no analyte).Make graph of corrected response ver
8、sus concentration.Determine best straight line.,Calibration Methods,Calibration Curve2.) Using a Calibration CurvePrefer calibration with a linear response- analytical signal proportional to the quantity of analyteLinear range- analyte concentration range over which the response is proportional to c
9、oncentrationDynamic range- concentration range over which thereis a measurable response to analyte,Additional analyte does not result in an increase in response,Calibration Methods,Calibration Curve3.) Impact of “Bad” Data Points Identification of erroneous data point.- compare points to the best-fi
10、t line- compare value to duplicate measures Omit “bad” points if much larger than average ranges and not reproducible.- “bad” data points can skew the best-fit line and distort the accurate interpretation of data.,Remove “bad” pointImprove fit and accuracy of m and b,y=0.16x + 0.12 R2=0.53261,y=0.09
11、1x + 0.11 R2=0.99518,Calibration Methods,Calibration Curve4.) Determining Unknown Values from Calibration Curves(i) Knowing the values of “m” and “b” allow the value of x to be determined once the experimentally y value is known. (ii) Know the standard deviation of m & b, the uncertainty of the dete
12、rmined x-value can also be calculated,Calibration Methods,Calibration Curve4.) Determining Unknown Values from Calibration Curves (iii) Example:,The amount of protein in a sample is measured by the samples absorbance of light at a given wavelength. Using standards, a best fit line of absorbance vs.
13、mg protein gave the following parameters:m = 0.01630 sm = 0.00022 b = 0.1040 sb = 0.0026An unknown sample has an absorbance of 0.246 0.0059. What is the amount of protein in the sample?,Calibration Methods,Calibration Curve5.) Limitations in a Calibration Curve (iv) Limited application of calibratio
14、n curve to determine an unknown.- Limited to linear range of curve- Limited to range of experimentally determined response for known analyte concentrations,Unreliable determination of analyte concentration,Uncertainty increases further from experimental points,Calibration Methods,Calibration Curve6.
15、) Limitations in a Calibration Curve (v) Detection limit- smallest quantity of an analyte that is significantly different from the blankwhere s is standard deviation- need to correct for blank signal- minimum detectable concentrationWhere c is concentration s standard deviation m slope of calibratio
16、n curve,Signal detection limit:,Corrected signal:,Detection limit:,Calibration Methods,Calibration Curve6.) Limitations in a Calibration Curve (vi) Example:Low concentrations of Ni-EDTA near the detection limit gave the following counts in a mass spectral measurement: 175, 104, 164, 193, 131, 189, 1
17、55, 133, 151, 176. Ten measurements of a blank had a mean of 45 counts. A sample containing 1.00 mM Ni-EDTA gave 1,797 counts. Estimate the detection limit for Ni-EDTA,Calibration Methods,Standard Addition1.) Protocol to Determine the Quantity of an Unknown (i) Known quantities of an analyte are add
18、ed to the unknown- known and unknown are the same analyte- increase in analytical signal is related to the total quantity of the analyte - requires a linear response to analyte(ii) Very useful for complex mixtures- compensates for matrix effect change in analytical signal caused by anything else tha
19、n the analyte of interest.(iii) Procedure:(a) place known volume of unknown sample in multiple flasks,Calibration Methods,Standard Addition1.) Protocol to Determine the Quantity of an Unknown (iii) Procedure:(b) add different (increasing) volume of known standard to each unknown sample(c) fill each
20、flask to a constant, known volume,Calibration Methods,Standard Addition1.) Protocol to Determine the Quantity of an Unknown (iii) Procedure:(d) Measure an analytical response for each sample - signal is directly proportional to analyte concentration,Standard addition equation:,Total volume (V):,X-in
21、tercept (y=0) yields which is used to calculate from:,Calibration Methods,Standard Addition1.) Protocol to Determine the Quantity of an Unknown (iii) Procedure:(f) Plot signals as a function of the added known analyte concentration and determine the best-fit line.,Calibration Methods,Standard Additi
22、on1.) Protocol to Determine the Quantity of an Unknown (iii) Example:,Tooth enamel consists mainly of the mineral calcium hydroxyapatite, Ca10(PO4)6(OH)2. Trace elements in teeth of archaeological specimens provide anthropologists with clues about diet and disease of ancient people. Students at Haml
23、ine University measured strontium in enamel from extracted wisdom teeth by atomic absorption spectroscopy. Solutions with a constant total volume of 10.0 mL contained 0.750 mg of dissolved tooth enamel plus variable concentrations of added Sr. Find the concentration of Sr.,Calibration Methods,Intern
24、al Standards1.) Known amount of a compound, different from analyte, added to the unknown. (i) Signal from unknown analyte is compared against signal from internal standard Relative signal intensity is proportional to concentration of unknown- Valuable for samples/instruments where response varies be
25、tween runs- Calibration curves only accurate under conditions curve obtained - relative response between unknown and standard are constant Widely used in chromatography Useful if sample is lost prior to analysis,Area under curve proportional to concentration of unknown (x) and standard (s),Calibrati
26、on Methods,Internal Standards1.) Example:,A solution containing 3.47 mM X (analyte) and 1.72 mM S (standard) gave peak areas of 3,473 and 10,222, respectively, in a chromatographic analysis. Then 1.00 mL of 8.47 mM S was added to 5.00 mL of unknown X, and the mixture was diluted to 10.0 mL. The solution gave peak areas of 5,428 and 4,431 for X and S, respectivelyCalculate the response factor for the analyte Find the concentration of S (mM) in the 10.0 mL of mixed solution. Find the concentration of X (mM) in the 10.0 mL of mixed solution. Find the concnetration of X in the original unknown.,
