COMPARISON OF ATOMIZERS

Similar documents
ANALYSIS OF ZINC IN HAIR USING FLAME ATOMIC ABSORPTION SPECTROSCOPY

2101 Atomic Spectroscopy

3 - Atomic Absorption Spectroscopy

atomic absorption spectroscopy general can be portable and used in-situ preserves sample simpler and less expensive

Atomic Absorption Spectroscopy and Atomic Emission Spectroscopy

Ch. 9 Atomic Absorption & Atomic Fluorescence Spectrometry

9/13/10. Each spectral line is characteristic of an individual energy transition

Atomic Absorption Spectrophotometry. Presentation by, Mrs. Sangita J. Chandratre Department of Microbiology M. J. college, Jalgaon

Zinc Metal Determination Perkin Elmer Atomic Absorption Spectrometer AAnalyst Procedures

AN INTRODUCTION TO ATOMIC SPECTROSCOPY

Emission spectrum of H

PRINCIPLE OF ICP- AES

ATOMIC SPECROSCOPY (AS)

Optical Atomic Spectroscopy

10/2/2008. hc λ. νλ =c. proportional to frequency. Energy is inversely proportional to wavelength And is directly proportional to wavenumber

Atomic Spectroscopy AA/ICP/ICPMS:

Chemistry 311: Instrumentation Analysis Topic 2: Atomic Spectroscopy. Chemistry 311: Instrumentation Analysis Topic 2: Atomic Spectroscopy

CH. 21 Atomic Spectroscopy

Determination of major, minor and trace elements in rice fl our using the 4200 Microwave Plasma- Atomic Emission Spectrometer (MP-AES) Authors

very high temperature for excitation not necessary generally no plasma/arc/spark AAS

UNIVERSITI SAINS MALAYSIA. Second Semester Examination Academic Session 2004/2005. March KAA 502 Atomic Spectroscopy.

Elemental analysis of river sediment using the Agilent 4200 MP-AES

A Spectrophotometric Analysis of Calcium in Cereal

Determination the elemental composition of soil samples

Atomization. In Flame Emission

FLAME PHOTOMETRY AIM INTRODUCTION

Complete the following. Clearly mark your answers. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT.

A New Cross-Shaped Graphite Furnace with Ballast Body for Reduction of Interferences in Atomic Absorption Spectrometry

Brooklyn College Department of Chemistry

Lecture 7: Atomic Spectroscopy

Chem 434 Instrumental Analysis Test 1

ATOMIC ABSORPTION SPECTROSCOPY (AAS) is an analytical technique that measures the concentrations of elements. It makes use of the absorption of light

Atomic Absorption & Atomic Fluorescence Spectrometry

a. An emission line as close as possible to the analyte resonance line

high temp ( K) Chapter 20: Atomic Spectroscopy

Atomic Emission Spectroscopy

Today s Agilent Solutions for Determining Heavy Metals in Food using Atomic Spectroscopy

Chapter 9. Atomic emission and Atomic Fluorescence Spectrometry Emission spectrophotometric Techniques

Atomic Absorption Spectrometer ZEEnit P series

Chemistry Instrumental Analysis Lecture 18. Chem 4631

Prof. Dr. Biljana Škrbić, Jelena Živančev

Partial Energy Level Diagrams

II. Spectrophotometry (Chapters 17, 19, 20)

ANALYSIS OF LEAD IN SEAWATER

Analysis of high matrix samples using argon gas dilution with the Thermo Scientific icap RQ ICP-MS

Quality Control Procedures for Graphite Furnace AAS using Avanta Software

Analysis of domestic sludge using the Agilent 4200 MP-AES

Combustion. Indian Institute of Science Bangalore

CHAPTER 4: ANALYTICAL INSTRUMENTATION

Determinations by Atomic Absorption Spectroscopy and Inductively Coupled Plasma-Atomic Emission

novaa 800 D Atomic Absorption Spectrometer

Experiment 18 - Absorption Spectroscopy and Beer s Law: Analysis of Cu 2+

Determination of Impurities in Silica Wafers with the NexION 300S/350S ICP-MS

INTRODUCTION TO OPTICAL ATOMIC SPECTROSCOPY (Chapter 8)

HEAVY METALS IN LAKE NAKURU ATOMIC SPECTROSCOPY

EXPERIMENT 7. Determination of Sodium by Flame Atomic-Emission Spectroscopy

The Low-Temperature Evaporative Light-Scattering Detector (LT-ELSD)

Determination of Pb, Cd, Cr and Ni in Grains Based on Four Chinese National Methods via Zeeman GFAAS

PRINCIPLES OF AAS atomization flame furnace atomization absorption

Test Method: CPSC-CH-E

V. LAB REPORT. PART I. ICP-AES (section IVA)

Ch. 8 Introduction to Optical Atomic Spectroscopy

Techniques for the Analysis of Organic Chemicals by Inductively Coupled Plasma Mass Spectrometry (ICP-MS)

Harris: Quantitative Chemical Analysis, Eight Edition CHAPTER 23: GAS CHROMATOGRAPHY

Application note. Determination of exchangeable cations in soil extracts using the Agilent 4100 Microwave Plasma-Atomic Emission Spectrometer

Water Hardness and Softening (Bring a water sample from home) Minneapolis Community and Technical College Principles of Chemistry II, C1152 v.2.

Enhancing the productivity of food sample analysis with the Agilent 7700x ICP-MS

Reacting Gas Mixtures

6.5 Optical-Coating-Deposition Technologies

Basic Digestion Principles

Exam 3 Chem 454 April 25, 2018, Name

A process whereby an electron is either removed from or added to the atom or molecule producing an ion in its ground state.

Gummy Bear Demonstration:

Part II. Cu(OH)2(s) CuO(s)

The Determination of Toxic, Trace, and Essential Elements in Food Matrices using THGA Coupled with Longitudinal Zeeman Background Correction

Atomic Spectra: Energy, Light, and the Electron

Pre-Lab Exercises Lab 3: Chemical Properties

TMT4320 Nanomaterials November 10 th, Thin films by physical/chemical methods (From chapter 24 and 25)

Experiment 7: SIMULTANEOUS EQUILIBRIA

School of Chemistry UNIVERSITY OF KWAZULU-NATAL, WESTVILLE CAMPUS JUNE 2009 EXAMINATION CHEM340: INSTRUMENTAL ANALYSIS.

What are the energies (J) and wavelengths (in nm) for these colors? Color Energy wavelength. Rev. F11 Page 1 of 5

2. Why do the discharge tubes get hot after running for a period of time?

Analytical Performance & Method. Validation

Properties of Alkanes, Alkenes, Aromatic Compounds and an Alcohol

Allotropes (Diamond and Graphite) Revision Pack (C3)

Tap Water Analysis Lockwood 1 TAP WATER ANALYSIS BY ATOMIC ABSORPTION SPECTROSCOPY AND ION CHROMATOGRAPHY. Susan Lockwood

Laboratory 3. Development of an Equation. Objectives. Introduction

Fundamentals of Mass Spectrometry. Fundamentals of Mass Spectrometry. Learning Objective. Proteomics

Lecture 8 Laminar Diffusion Flames: Diffusion Flamelet Theory

Introduction to Plasma

OES - Optical Emission Spectrometer 2000

Ionization Techniques Part IV

Atomic absorption spectroscopy

Investigation of Nutrient Elements in Cucurbita pepo Using Atomic Absorption Spectrometry

6.1- Chemical vs. Physical - Pre-Lab Questions

For simplicity, we ll represent BTB s ionization in a solution by the equilibrium: HBTB = H + + BTB -

Unit 4: Chemical Changes (Higher Content)

1. The range of frequencies that a measurement is sensitive to is called the frequency

Atomic Theory: Spectroscopy and Flame Tests

Transcription:

COMPARISON OF ATOMIZERS FOR ATOMIC ABSORPTION SPECTROSCOPY Introduction Atomic spectroscopic methods are all based on the interaction of light and analyte atoms in the gas phase. Thus, a common component of instruments used in atomic spectroscopy is the atomizer, which converts the analyte in the sample to vapor-phase free atoms that can interact with a light beam. The properties and efficiency of the atomizer is crucial in determining the characteristics of a atomic spectroscopic method. In this experiment, you will compare two methods based on atomic absorption in the gas phase: flame atomic absorption spectroscopy (FAAS) and graphite furnace atomic absorption spectroscopy (GFAAS). Specifically, you will compare the detection power (i.e., the ability to detect trace concentrations of analyte), the linear dynamic range and the measurement precision of these two techniques. You will also analyze the copper concentration in the laboratory tap water using both methods. Atomizers Most atomizers require that the sample be in the form of a solution; introduction of the solution into the atomizer is usually accomplished by a nebulizer, which converts the solution into a fine mist of small droplets. Vaporization of the sample requires thermal energy, so that the atomizer is essentially a reservoir where rapid and high-energy collisions occur between gaseous species. The following are the atomizers that have been used most commonly in atomic spectroscopy. combustion flame atomizers, in which a fuel is burned in the presence of an oxidant. The exothermic nature of the combustion reaction supplies the thermal energy needed to vaporize the solution droplets that are introduced by the nebulizer into the flame. Flame atomizers are used for both atomic absorption and emission spectroscopies, although the former application is more common. electrothermal atomizers. In this type of atomizer, the atomizer is a resistive element that is heated by the passage of a large current. The most common electrothermal atomizer by far is the graphite furnace atomizer, in which the heating element is a graphite tube. The sample is introduced directly (usually as a solution) into the graphite tube. Electrothermal atomizers are used almost exclusively for atomic absorption spectroscopy. plasma atomizers. A plasma can be defined simply as a hot gas that contains a significant number of ions. The mechanism of plasma generation varies, and will be discussed in class. The most common plasma atomizer is the inductively coupled plasma, but the direct current plasma and the microwave plasma have also seen some application in atomic spectroscopy. Sample introduction into the plasma is by nebulization of a solution. Plasma atomizers are the most widely used atomizer in atomic emission spectroscopy. Page 1

arc and spark atomizers vaporize the sample through the creation of an electrical discharge between two electrodes. Arcs and sparks have historically been used as atomizers in atomic emission spectroscopy, but have been largely replaced by plasma atomizers. Arcs and sparks can be easily used for the analysis of solid samples, unlike plasmas, and so they still find some limited use for samples that are not conveniently dissolved. The two most common atomizers in atomic absorption spectroscopy are combustion flames and graphite furnaces. We will now discuss in a little more detail the mechanism by which these atomizers work. Combustion Flame Atomizers The following figure gives some idea of the most common type of flame atomizer, complete with the nebulizer and spray chamber. combustion flame fuel spray chamber small droplets oxidant spoilers sample solution auxiliary oxidant drain The fuel and oxidant mix in the spray chamber; small droplets of the sample solution are carried along by this mixture into the combustion region of the flame. The most common fuel is acetylene, C 2 H 2, and the two most common oxidants are air and nitrous oxide, N 2 O. The hottest part of the acetylene-air flame may be about 2200 C, while the temperature of the N 2 O-C 2 H 2 flame can get as hot as 3100 C. It is possible to adjust the temperature of a flame by changing the fuel:oxidant ratio. A stoichiometric flame mixture is one in which, theoretically, neither the fuel nor oxidant are present in excess; stoichiometric flames are generally pretty close to their maximum temperature. A rich (or fuel-rich) flame is one in which the fuel is present in excess, while a lean flame contains an excess of oxidant. Page 2

The mechanism of combustion is not fully understood, but there are many species in a flame: reactive radicals, ions, small molecules, and free electrons. The following figure delineates the main regions of the flame: secondary combustion zone combustion flame interzonal region primary combustion zone fuel/oxidant mix The mixed gases flow rapidly through the burner and are ignited at the top of the burner. The reaction between fuel and oxidant takes place largely in the primary combustion zone; vaporization of solvent and dissociation of analyte species also occurs in this region. By the time the gases reach the interzonal region, the combustion reaction is more or less completed; this is the hottest region of the flame, and the one used for many spectroscopic measurements. The rapidly rising gases entrain the surrounding air, and create a secondary combustion zone on the outside of the flame, a region that is chemically oxidizing in nature. The chemical environment of the flame is complex and, by its very nature, reactive - after all, the thermal energy of the atomizer is sustained by the chemical reaction between the fuel and oxidant. The analyte atoms, after volatilization, can undergo a number of reactions, such as ionization and oxidation. Indeed, some analytes (such as alkali metals) exhibit a significant degree of ionization, while some others (such as Al, Ba and Sn) form very stable oxides, called refractory oxides. Analytes that form species that are difficult to dissociate in the flame are sometimes called refractory elements; these generally benefit from using the hotter N 2 O flames, and/or from fuel-rich flames, which create a more reducing chemical environment. Electrothermal Atomizers An electrothermal atomizer is constructed using a heating element through which a large current is passed. The sample is placed on, or in, the atomizer. The temperature of the element can be set by controlling the current, which is generally increased in a programmed series of steps called a temperature program. There are usually at least four steps: Page 3

1. a solvent vaporization step; 2. a pretreatment step (sometimes called a charring or ashing step), where organic components of the matrix are oxidized and the more volatile matrix components are lost; 3. an atomization step, where the analyte (and presumably the rest of the sample) is vaporized; and 4. a cleaning step, where the last remains of the sample are (hopefully) removed. The ability to control the temperature of an electrothermal atomizer by regulating the current is a big asset, since we don t have to evaporate the solvent, vaporize the sample matrix and atomize the analyte all at once. By far the most common heating element in electrothermal atomizers is a tube of graphite, into which the sample solution is deposited. The maximum temperature of these graphite furnace atomizers is about 3000 C or so. The following figure gives some indication of how the furnace atomizer is used. argon gas inject sample here water in graphite tube from light source water out sample solution insulator A small volume (20 40 µl, usually) is deposited into the graphite tube, which is constantly bathed with an inert gas such as argon. The purpose of the inert gas is twofold: (a) to protect the graphite from oxidation during atomization, and (b) to provide a chemically inert environment for analyte atomization, greatly reducing the formation of refractory oxides of the analyte. Comparison of Atomizer Characteristics The atomization efficiency is an important property of the atomizer used in atomic spectroscopy. It is defined as the fraction of analyte species in the sample that will be converted to free atoms in the atomizer. An atomization efficiency of 1 (or 100%) means that every analyte species in the sample can be converted into free atoms. The atomization efficiencies of graphite furnaces almost always exceed that of flames for the following reasons: Page 4

sample introduction is far more efficient for furnaces than for flames. The nebulizers used with flame atomizers are quite wasteful: about 95% of the aspirated sample solution goes down the drain, while the fine mist that actually gets carried into the flame only constitutes about 5% of the aspirated solution. Furnace atomizers have no need of a nebulizer. the solution droplets only spend a short amount of time (on the order of milliseconds) in the flame, during which time the flame must evaporate the solvent and dissociate the analyte salt. Less is demanded of the furnace, since the temperature program usually takes about 2 minutes, and occurs in steps, leading to greater efficiency. after formation of free analyte atoms, the residence time of the analyte in the flame is much shorter (milliseconds) than for the furnace (1-2 seconds). This means that the analyte atoms in the furnace can absorb more photons, increasing the absorption signal, than analyte atoms in flames. the relatively inert chemical environment of the furnace is less likely to lead to the formation of stable analyte species than is the case in flame atomizers. The atomization efficiency in any atomizer cannot be any better than the efficiency of introducing the sample into the atomizer, so the maximum atomization efficiencies achievable in flames is about 5-10%, and it is frequently less than this value. Of course, the actual efficiency will depend on the nature of the analyte and on the choice of fuel and oxidant (and, to a lesser extent, on their mixing ratios). Atomization efficiencies from clean aqueous samples can often approach 100% in graphite furnaces; efficiencies for more complicated sample matrices are often considerably less than 100%. In summary, furnaces have a number of advantages over flames for sample atomization in atomic absorption spectroscopy. There are, however, also some disadvantages. Can you think of them? Figures of Merit Analytical figures of merit (FOM s) are commonly used to compare the characteristics different techniques. Imagine that you are out shopping for a new car: you will probably spend a lot of time comparing different makes and models before the actual purchase. In making a final decision, you might be influenced by factors such as price, maintenance, fuel economy, handling, buyer satisfaction, appearance, etc. There may be a number of distinct instrumental methods that can be used in the analysis of any particular chemical species, and many minor variations can exists for each of these methods. Figures of merit characterize an analytical method so that you can make an informed decision in choosing a method for a particular application. They can also be used to evaluate the effects of technique modifications. Three very important characteristics of any analytical method are detection power: the ability of the technique to detect small concentrations of analyte in a sample. dynamic range: the range of concentrations over which the technique is useful. measurement precision, which characterizes the between-measurement variability of the method. Page 5

Detection Power The most common FOM used to describe the detection capability of a technique is the limit of detection, LOD, (sometimes called the detection limit) which is defined by IUPAC as LOD = 3s b b 1 where s b is the standard deviation of measurements on the blank, and b 1 is the slope of the (linear) calibration curve (the sensitivity, which is another FOM). The LOD is the concentration that corresponds to a signal that is just detectable above the random noise of the blank measurements. A sample that contains the analyte at exactly the detection limit will have (approximately) a 50% probability of being detected above the blank noise. The LOD is a nice figure of merit, even if it is a little abstract (at least, to those who have no background in statistics - unlike the students of CHM301 at the University of Richmond). There are, however, two problems with it: 1. The detection limit usually gives an overly optimistic idea of the concentrations that can be reliably detected; this is usually because the estimate of the blank noise generally does not include a number of important sources of error, such as sampling error, sample treatment error, and calibration error. 2. IUPAC recommends that 16 measurements of the blank be used to calculate s b ; in fact, to be strictly proper, 16 different blanks should be prepared and analyzed. This process can be quite time-consuming; many people estimate the LOD using fewer blank measurements. In absorption spectroscopy, an alternate measure of detection capability is frequently used: the characteristic concentration 1 (or the characteristic mass, if appropriate). The characteristic concentration is the concentration of analyte in the sample that will cause an absorption of 1% of the incident light (i.e., a transmittance of 0.99). This corresponds to an absorbance value of A = 0.0044, so that the characteristic concentration can be calculated by dividing this value by the sensitivity of the absorption method: characteristic concentration [] char = 0.0044 b 1 where b 1 is the sensitivity (i.e., the slope of the calibration curve). The characteristic concentration is generally significantly larger than the detection limit, and is usually a more realistic assessment of the lower concentrations of analyte that can be analyzed with some degree of precision. It is also fairly easy to obtain, since one usually must construct a calibration curve during the course of an analysis. The principal disadvantage it has as a figure of merit is that it can only be used to describe absorption-based analytical methods. The detection capability of graphite furnace AAS is better described in terms of analyte masses rather than concentrations. The characteristic mass is the analyte mass that, when deposited in the furnace, will give a signal of 0.0044 AU. Since a discrete volume of sample is analyzed in the furnace, and the characteristic concentration will depend on the actual sample volume being used (a disadvantage). The characteristic mass, however, will not depend on the concentration. 1 confusingly, the characteristic concentration is often called the sensitivity, whereas IUPAC defines the sensitivity as the slope of the calibration curve. [1] Page 6

Dynamic Range The dynamic range is the range of concentrations over which there is a measurable change in instrument response. It is advantageous to have a linear calibration curve, and so the linear dynamic range (LDR) is usually of interest. As you might guess, the LDR provides the range of concentrations over which the instrument response is linearly dependent on the analyte concentration. In this experiment, we will consider the characteristic concentration as the lower limit of the LDR, so all that is left is to find the upper limit of the LDR. Commonly, this value is defined as the value at which the instrument response loses 10% of the value that it would have if it were truly linear. The following figure illustrates: signal concentration In the figure, the larger double arrow gives the net response if the calibration curve remains linear. The smaller arrows show the difference between the actual and the projected linear response. When the ratio of the smaller to larger arrows is 10% (i.e., when there is a 10% drop-off from a theoretical linear response), then we have reached the upper limit of the LDR. Measurement Precision The random error in a measurement is characterized by its standard deviation. The relative standard deviation, RSD, is a convenient way to compare the variability in the measurements when using a particular analytical method. Another common method used to compare measurement precision is the signal-to-noise ratio, S/N. As the name might imply, the S/N is simply the inverse of the RSD: S/N = RSD 1 = x/σ x Both S/N and RSD are widely used to indicate the magnitude of measurement precision. Better precision is indicated by a larger S/N or a smaller RSD. The RSD is frequently given as a percentage value. Generally, RSD and S/N will depend on concentration, so it is desirable to specify the concentration (or concentration range) when reporting the measurement precision. Page 7

References Skoog 8-9 (esp 8B & 9A) Harris 22 (esp 22.2) Page 8

ATOMIZER COMPARISON: PROCEDURE Part I: Graphite Furnace Atomic Absorption Check that the furnace atomizer unit is installed on the Perkin Elmer atomic absorption instrument (ask your lab instructor or TA). You will need to prepare eight calibration standards of the following concentrations: 5, 20, 35, 50, 100, 150, 200, and 250 ppb copper. Use deionized water for your blank and in all dilutions. In addition, you should collect a small sample of tap water in a clean beaker. Important: before actually performing the dilutions, have your instructor check your calculations. The furnace can be damaged if the standards are too concentrated. Once you have made your solutions, you will use the autosampler to measure the standards. You will need to ask your instructor for help in operating the instrument. You should obtain three measurements for each standard, and you are to inject 30 µl volumes into the furnace. Part II: Flame Atomic Absorption For this portion of the experiment, you will be using an air-acetylene flame atomizer. Prepare 100 ml standards of the following concentrations: 5, 10, 15, 20, 30, 40, 50, 60 ppm copper. You will obtain one measurement on each of these using flame atomic absorption spectroscopy; ask your instructor to show you how this is done on the Perkin-Elmer instrument. You should also attempt to determine the copper content of the tap water sample using the flame AA method. Page 9

ATOMIZER COMPARISON: DATA SHEET In addition to filling out the following table, turn in copies of all printouts collected during the experiment. Don t forget to show your calculations on a separate sheet of paper. Name: sample blank std 1 std 2 std 3 std 4 std 5 std 6 std 7 std 8 tap water Furnace Atomizer conc (ppb) peak area (Avs) 0 Flame Atomizer conc (ppm) absorbance 0 characteristic conc, ppb (95% CI) characteristic mass, pg (95% CI) upper limit of LDR, ppb measurement RSD, % 95% CI for [Cu] in tap water, ppb: Results characteristic conc, ppm (95% CI) upper limit of LDR, ppm 95% CI for [Cu] in tap water, ppb measurement RSD, %

ATOMIZER COMPARISON: DATA TREATMENT You will need to fill in the results section in the DATA SHEET. Take special note of those values for which confidence intervals (CI s) are asked: the characteristic concentrations, the characteristic mass, and the concentration of copper in tap water. You do not need to calculate a confidence interval for the upper limit of the LDR or for the measurement RSD. Looking at your results, you should ponder the questions such as the following: which method is more sensitive? (The answer to this question should be fairly obvious.) which method has the largest linear dynamic range? Can you think of any reasons why? which method has the best measurement precision? What are the main sources of random error for each method? Is the difference between measurement RSD statistically significant? what are the advantages and disadvantages associated with each method? When would you prefer to use the FAAS method, and when would you want to use GFAAS? Estimate of Copper Concentration in Tap Water In constructing your calibration curve, average the measurements for each standard, and for the tap water (watch for outliers). Your calibration data should be curved (after all, one of the goals of the experiment is to compare the linear dynamic ranges). A second-order polynomial linear regression should give a reasonable fit for the data: y = 2 x 2 + 1 x + 0 You should use this equation to obtain a confidence interval for the copper concentration in tap water using the GFAAS method. To obtain a point estimate, you will need to solve a quadratic equation. The standard deviation of this estimate can be approximated by s(x u ) l s res 1 + 1 2b 2 x u + b 1 n + (x u x) 2 S xx where b 2 and b 1 are the least-squares estimates of β 2 and β 1. To learn more about using polynomial calibration curves for quantitative analysis, refer to the web-based Tutorial. Characteristic Concentration Calculate the point estimates of the characteristic concentrations using the equation given in the BACKGROUND section. You can use propagation of error in order to determine the standard error in your calculated value; if you assume a normal distribution for the estimate (a somewhat dubious assumption), you may calculate a confidence interval for the characteristic concentration using t-tables. To calculate the characteristic mass of the GFAAS method, you will need to know the volume of solution sample that is analyzed (ask your instructor for more detail).

Linear Dynamic Range The upper range of the LDR is when there is a 10% decrease from a hypothetical linear response. Using a second-order polynomial fit, the upper range of the LDR, x upper, is thus x upper = 0.1 b 1 b 2 The negative sign is necessary because b 2 should be negative (if it isn t, come see me with your data). Measurement Precision The RSD indicates the precision with which the method can determine the analyte concentration of a sample. Calculate the RSD using the following equation: RSD = s res y where s res is the standard deviation of the residuals and y is the average of the y-values (i.e., the signals) in your calibration data set. The RSD calculated in this manner includes the effects of both measurement and calibration error. If you wish, you may compare the RSD values for each method using an F-test, since the ratio of squared RSD values should follow an F-distribution.