Introductfon

nalytical chemistry deals with methods for de-

termining the chemical composition of samples ofmqtter. A qualitqtive method yields information about

the identity of atomic or molecular species or the func-tional groups in the sample; a quantitative method, in

contrast, provides numerical information as to the rel-

ative amount of one or more of these components.

1,A CLASSIFICATION OF ANALYTICATMETHODS

Analytical methods are often classifled as being eitherclassical or instrumental. This classiflcation is largelyhistorical with classical methods, sometimes called wet-chemical methods, preceding instrumental methods bya century or more.

1A-1 Classical Methods

In the early years of chemistry, most analyses were ca?ried out by separating the components of interest (the

analytes) in a sample by precipitation, extraction, ordistillation. For qualitative analyses, the separated com-ponents were then treated with reagents that yieldedproducts that could be reco gnrzed by their colors, theirboiling or melting points, their solubilities in a series ofsolvents, their odors, their optical activities, or their re-

fractive indexes. For quantitative analyses, the amountof analyte was determined by gravimetric or by titri-metric measurements. In gravimetric measurements,the mass of the analyte or some compound producedfrom the analyte was determined. In titrimetric proce-dures, the volume or mass of a standard reagent re-quired to rcact completely with the analyte wasmeasured.

These classical methods for separating and deter-mining analytes still find use in many laboratories. Theextent of their general application is, however, decreas-ing with the passage of time and with the advent of in-strumental methods to supplant them.

LA-Z Instrumental Methods

Early in the twentieth centur), chemists began to exploitphenomena other than those used for classical methodsfor solving analytical problems. Thus, measurements ofphysical properties of analytes-such as conductivity,electrode potential, light absorption or emission, mass-

to-charge ratio, and fluorescence-began to be used forquantitative analysis of a variety of inorganic, organic,and biochemical analytes. Furthermore, highly efficientchromatographic and electrophoretic techniques beganto replace distillation, extraction, and precipitation forthe separation of components of complex mixtures priorto their qualitative or quantitative determination. Thesenewer methods for separating and determining chemical

Chapter 1 Introduction

species are known collectively as instrumental methodsof analysis.

Many of the phenomena that instrumental methodsare based on have been known for a century or more.Their application by most chemists, however, was de-

layed by lack of reliable and simple instrumentation. Infact, the growth of modern instrumental methods ofanalysis has paralleled the development of the electron-ics and computer industries.

18 TYPES OF INSTRI,]MENTAL METHODS

For this discussion, it is useful to consider chemical andphysical characteristics that are useful for qualitative orquantitative analysis. Table 1-1 lists most of the charac-teristic properties that are cuffently used for instrumen-

TABLE l-L Chemical and Physical Properties Employedin Instrumental Methods

tal analysis. Most of the characteristics listed in thetable require a source of energy to stimulate a measur-able response from the analyte. For example, in atomicemission an increase in the temperature of the analyte is

required to flrst produce gaseous analyte atoms and thento excite the atoms to higher energy states. The excited-state atoms then emit charucteristic electromagnetic ra-diation, which is the quantity measured by the instru-ment. Sources of excitation energy may take the form ofa rapid thermal change as in the previous example, elec-tromagnetic radiation from a selected region of thespectrum, application of one of the electrical quanti-ties-voltage, current, or charge-or perhaps subtlerforms intrinsic to the analyte itself.

Note that the flrst six entries in Table 1- 1 involveinteractions of the analyte with electromagnetic radia-tion. In the flrst property, radiant energy is produced by

Characteristic Properties Instrumental Methods

Emission ofradiation Emission spectroscopy (X-ray, UV, visible, electron, Auger); fluorescence, phosphorescence,

and luminescence (X-ray, UY and visible)

Absorption of radiation Spectrophotometry and photometry (X-ray, UV, visible, IR); photoacoustic spectroscopy;

nuclear magnetic resonance and elecffon spin resonance spectroscopy

Scatteringofradiation Turbidimetry;nephelometry;Ramanspectroscopy

Refraction of radiation Refractometry; interferometry

Diffraction of radiation X-Ray and electron diffraction methods

Rotation ofradiation Polarimetry; optical rotary dispersion; circular dichroism

Electrical potential Potentiometry; chronopotentiomety

Electrical charge Coulometry

Electrical current Amperometry; polarography

Electrical resistance Conductometry

Mass Gravimetry (quartz crystal microbalance)

Mass-to-charge ratio Mass spectrometry

Rate of reaction Kinetic methods

Thermal characteristics Thermal gravimetry and titrimetry; differential scanning colorimetry; differential thermal

analyses; thermal conductometric methods

Radioactivity Activation and isotope dilution methods

the analyte; the next flve properties involve changes inelectromagnetic radiation brought about by its interac-tion with the sample. Four electrical properties then fol-low. Finally, four miscellaneous properties are groupedtogether: mass-to-charge ratio, reaction rate, thermalcharacteristics, and radioactivity.

The second column in Table 1-1 lists the names ofinstrumental methods that are based upon the variousphysical and chemical properties. Be aware that it is notalways easy to select an optimal method from amongavailable instrumental techniques and their classicalcounterparts. Some instrumental techniques ate moresensitive than classical techniques, but others are not.With certain combinations of elements or compounds,an instrumental method may be more selective; withothers, a gravtmetric or volumetric approach may sufferless interference. Generalizatrons on the basis of accu-rac!,, convenience, or expenditure of time are equallydifflcult to draw. Nor is it necessarily true that instru-mental procedures employ more sophisticated or morecostly apparatus; indeed, the modern electronic analyti-cal balance used for gravimetric determinations is a

more complex and reflned instrument than some ofthose used in the other methods listed in Table 1-1.

As noted earlier, in addition to the numerous meth-ods listed in the second column of Table 1-1, there is agroup of instrumental procedures that are used for sepa-

ration and resolution of closely related compounds.Most of these procedures are based upon chromatogra-phy or electrophoresis. One of the characteristics listedin Table 1-1 is.ordinarily used to complete the analysisfollowing chromatographic separations. Thus, for ex-ample, thermal conductivity, ultraviolet and infrared ab-

sorption, refractive index, and electrical conductancehave been used for this purpose.

This text deals with the principles, the applications,and the performance characteristics of the instrumentalmethods listed in Table 1- 1 and of chromatographic and

electrophoretic separation procedures as well. No space

is devoted to the classical methods, the assumption be-ing that the reader will have encountered these tech-niques in earlier studies.

1C INSTRI]MENTS FOR ANALYSIS

An instrument for chemical analysis converts informa-tion stored in the physical or chemical characteristics ofthe analyte to information that may be manipulated and

interpreted by a human. Thus, an analytical instrument

lC Instruments for Analysis

can be viewed as a communication device between thesystem under study and the investigator. To retrieve thedesired information from the analyte, it is necessary toprovide a stimulus, which is usually in the form of elec-tromagnetic, electrical, mechanical, or nuclear energyas illustrated in Figure 1-1. The stimulus elicits a re-sponse from the system under study whose nature and

magnitude are governed by the fundamental laws ofchemistry and physics. The resulting information iscontained in the phenomena that result from the interac-tion of the stimulus with the analyte. A familiar exampleis the passage of a narrow band of wavelengths of visi-ble light through a sample to measure the extent of itsabsorption by the analyte. The intensity of the light isdetermined before and after its interaction with the sam-

ple, and the ratio of these intensities provides a measureof the analyte concentration.

Generally, instruments for chemical analysis com-prise just a few basic components, some of which are

listed in Table l-2. To understand the relationshipsamong these instrument components and the flow of in-formation from the characteristics of the analytethrough the components to the numerical or graphicaloutput produced by the instrument, it is instructive toexplore the concept of data domains.

1C-1 Data Domains

The measurement process is aided by a wide variety ofdevices that convert information from one form to an-

other. In order to investi gate how instruments function,it is important to understand the way in which informa-tion is encoded, or transformed from one system of in-formation to another, as a characteristic of electricalsignals-that is, as voltage, current, charge, or varia-tions in these quantities. The various modes of encodinginformation electrically are called data domains. Aclassification scheme has been developed based on this

Energy System Analyticalsource under information

study

Figure 1-1 Block diagram showing the overall process ofan instrumental measurement.

Chapter 1 Introduction

TABLE l-2 Some Examples of Instrument Components

Instrument

Photometer

Atomic emission

spectrometer

Coulometer

pH meter

X-Ray powder

diffractometer

Color

comparator

Tungsten lamp,

glass filter

Flame

DC source

Sample/glass

electrode

X-Ray tube,

sample

Sunlight

Attenuated lightbeam

UV or visibleradiation

Cell current

Hydrogen ionactivity

Diffractedradiation

Color

InputTfansducer

Photocell

Photomultipliertube

Electrodes

Glass-calomel

electrodes

Photographic

fi1m

Eye

Electrical

current

Electrical

potential

Electrical

current

Electrical

potential

Latent

lmage

Optic nerve

signal

Meter scale

Amplifler,demodulator,

monochromator

chopper

Amplifier

Amplifler,drgrtrzer

Chemical

developer

Brain

Current

meter

Chart

recorder

Chart

recorder

Digital unit

Blackrmages

on fllm

Visual

color

response

Energy Source Analytical(stimulus) Information

Data Domainof Tlansduced InformationInformation Processor Readout

concept that greatly simplifles the analysis of instru-mental systems and promotes understanding of themeasurement process.l As shown in the data domainsmap of Figure 1 -2, data domains may be broadly classi-fled into nonelectrical domains and electrical domains.

LC-z Nonelectrical Domains

The measurement process begins and ends in nonelectri-cal domains. The physical and chemical characteristicsthat are of interest in a particular experiment reside inthese data domains. Among these characteristics are

length, density, chemical composition, intensity of light,pressure, and others listed in the flrst column of Thble 1- 1 .

It is possible to make a measurement entirely innonelectrical domains. For instance, the determinationof the mass of an object using a mechanical equal-armbalance involves a comparison of the mass of the ob-ject, which is placed on one balance pan, with standardmasses placed on a second pan. The information repre-

Nonelectricatr : domains

Electrical domains

Figure L-2 Data domains map. The upper (shaded) halfof the map comprises nonelectrical domains. The bottomhalf is made up of electrical domains. Note that the digitaldomain spans both electrical and nonelectrical domains.t C. G. Enke, Anal. Chem., 1971, 43, 69A.

senting the mass of the object in standard units is en-

coded directly by the experimenter, who provides infor-mation processing by summing the masses to arriv e at a

number. In certain other mechanical balances, the grav-itational force on a mass is amplifled mechanically bymaking one of the balance arms longer than the other,thus increasing the resolution of the measurement.

The determination of the linear dimensions of an

object with a ruler and the measurement of the volume ofa sample of liquid with a graduated cylinder are other ex-amples of measurements carried out exclusively in non-electrical domains. Such measurements are often associ-ated with classical analytical methods. The advent ofinexpensive electronic signal processors, sensitive trans-ducers, and readout devices has led to the developmentof a host of electronic instruments, which acquire in-formation from nonelectrical domains, process it inelectrical domains, and flnally present it in nonelectricaldomains once again. Electronic devices process infor-mation and transform it from one domain to another inways analogous to the multiplication of mass in mechan-ical balances with unequal arms. As a consequence of theavailability of these electronic devices and their rapidand sophisticated information processing, instrumentsthat rely exclusively on nonelectrical information trans-

lC Instruments for Analysis

fer are rapidly becoming relics of the past. Nonetheless,the information that we seek begins in the properties ofthe analyte and ends in a number, both of which are non-electrical domains. The ultimate objective in all mea-surements is that the flnal numerical result must be insome manner proportional to the relevant chemical orphysical characteristic of the analyte.

1C-3 Electrical Domains

The modes of encoding information as electrical quanti-ties can be subdivided into analog domains, time do-mains, and digital domainr, as illustrated in the bottomhalf of the circular map in Figure 1-2. Note that the dig-ital domain spans three electrrcal domains and one non-electrical domain because numbers presented on anytype of display convey digital information and can alsobe encoded electrically.

Any measurement process can be represented as a

series of interdomain conversions. For example, Figure1-3 illustrates the measurement of the intensity of molec-ular fluorescence of a sample of tonic water containing a

trace of quinine and, in a general way, some of the data-domain conversions that are necessary to arrive at anumber expressing the intensity. The intensity of the flu-

Energy source

Laser

Fluorescenceemlsslon

Phototransducer

Opticalfilter

(b)

Transducer

transferfunction

(c)

Resistor Digital voltmeter

Tonic water(analyte) (a)

Informationflow

Laws ofGoverned by =---.+ chemistry and

physics

Ohm'slaw

V_IR

Metertransferfunction

Figure 1-3 A block diagram of a fluorometer showing (a) a general diagram of the instrument,(b) a diagrammatic representation of the flow of information through various data domains inthe instrument, and (c) the rules governing the data domain transformations during the mea-surement process.

Fluorescenceintensity

of analyte

Electricalcurrent 1

Voltage V

Chapter 1 Introduction

Time --+(c)

Figure 1-5 Time-domain signals. The horizontal dashed

lines represent signal thresholds. When each signal isabove the threshold, the signal is HI, and when it is belowthe threshold, the signal is LO.

Chaptet 4, we shall explore the means for making HI-LO electronic decisions and encoding the informationin the digital domain.

As suggested by the data domains map of FigureI-2, the digital domain spans both electrical and non-electrical domains. In the example just cited, the nuclearevents are accumulated by using an electronic counterand are displayed on a digital readout. When the experi-menter reads and interprets the display, the number thatrepresents the measured quantity is once again in a non-electrical domain. Each piece of HI-LO data that repre-

sents a nuclear event is a bit of information, which is thefundamental unit of information in the digital domain.Bits of information that are transmitted along a singleelectronic channel or wire may be counted by an ob-server or by an electronic device that is monitoring thechannel; such accumulated data is termed count digitaldata, which appears in the data-domains map of FigureI-2. For example, the signal in Figure 1-5a correspondsto the number n - 8 because there are eight complete cy-cles in the signal. The signal in the Figure 1-5b corre-sponds to n _ 5, and the signal in Figure 1-5c corre-sponds to n _ 14. Although effective, this means oftransmitting information is not very efflcient.

A far more efflcient way to encode information is touse binary numbers to represent numeric and alphabeticdata. To see how this type of encoding may be accom-plished, let us consider the signals in Figure I-6. Thecount digital data of the signal in Figure 1 -6a representthe number n - 5 as before. We monitor the signal and

count the number of complete oscillations. The process

requires a period of time that is proportional to the num-ber of cycles of the signal, or in this case, flve times thelength of a single time interval, as indicated in Figurel-6. Note that the time intervals are numbered consecu-tively beginning with zero.In a binary encoding scheffie,such as the one shown for the signal in Figure 1-6b, we

assign a numertcal value to each successive interval oftime. For example, the zercth time interval represents

20 : 1, the flrst time interval represents 2l : 2, the sec-

ond time interval represents 22 _ 4, and so forth, as

shown in Figure 1-6. During each time interval, we need

only decide whether the signal is HI or LO. If the signalis HI during any given time interval, then the value cor-responding to that interval is added to the total. A11 inter-vals that are LO contribtte zero to the total.

In Figure 1-6b, the signal is HI only in interval 0

and interval 2, so the total value represented is 1 x 20 +0 x 2t + 1 x 22 - 5. Thus, in the space of only three

time intervals, the number n _ 5 has been determined.In the count digital example of the signal in Figure l-6a,flve time intervals were required to determine the same

number. In this limited example, the binary-coded serial

data is nearly twice as efflcient as the count serial data.

A more dramatic example may be seen in the countingof n - 10 oscillations similar to those of the signal inFigure l-6a. In the same ten time intervals, ten HI-LObits of information in the serial binary coding scheme

enable the representation of the binary numbers from 0to 2r0 _ 1024, or 0000000000 to 1111111111. The im-provement in efflciency is 1024110, or about 100-fo1d.

In other words, the count serial scheme requires 1024

time intervals to represent the number 1024, while the

binary coding scheme requires only ten time intervals.As a result of the efflciency of binary coding schemes,

most digital information is encoded, transferred,processed, and decoded in some form of binary.

Data represented by binary coding on a single

transmission line is calle d serial-coded binary data, orsimply serial data. A common example of serial data

transmission is the computer mod€ffi, which is a device

for transmitting data between computers by telephone

over a single conductor (and ground).

EHI.10aLo

Chapter 1 Introduction

orescence is significant in this context because it is pro-portional to the concentration of the quinine in the tonicwater, which is ultimately the information that we desire.

The information begins in the solution of tonic water as

the concentration of quinine. This information is teased

from the sample by applying to it a stimulus in the formof electromagnetic energy from the laser shown in Fig-ure l-3. The radiation interacts with the quinine mole-cules in the tonic water to produce fluorescence emissionin a region of the spectrum characteristic of quinine and

of magnitude proportional to its concentration. Radia-tion, and thus information, that is unrelated to the con-centration of quinine is removed from the beam of lightby an optical fllter, as shown in Figure I-3a. The inten-sity of the fluorescence emission, which is a nonelectri-cal domain, is encoded into an electrical domain by aspecial type of device called an input transducer Theparticular type of transducer used in this experiment is aphototransducer, of which there are nurnerous types,some of which are discussed in Chapter 7 .In this exam-ple, the input transducer converts the fluorescence fromthe tonic water to an electrical current, I, proportional tothe intensity of the radiation. The mathematicalrelation-ship between the electrical output and the input radiantpower impinging on its surface is called the transfer

function of the transducer.The current from the phototransducer is then

passed through a resistor R, which according to Ohm'slaw produces a voltage V that is proportionalto I, whichis in turn proportional to the intensity of the fluores-cence. Finally, V is measured by the digital voltmeter toprovide a readout proportional to the concentration ofthe quinine in the sample.

Voltmeters, alphanumeric displays, electric motors,

computer screens, and many other devices that serve toconvert data from electrical to nonelectrical domains

are called output transducers. The digital voltmeter ofthe fluorometer of Figure I-3a is a rather complex out-put transducer that converts the voltage V to a number

on a liquid crystal display so that it may be read and in-terpreted by the user of the instrument. We shall con-

sider the detailed nature of the digital voltmeter and

various other electrical circuits and signals in Chapters2 through 4.

Analog Domains

Information tn analog domains is encoded as the mag-nitude of one of the electrical quantities-voltage, cur-rent, charge, or power. These quantities are continuous

in both amplitude and time as shown by the typical ana-

log signals of Figure I -4. Magnitudes of analog quanti-ties can be measured continuously or they can be sam-

pled at speciflc points in time dictated by the needs of aparticular experiment or instrumental method as dis-cussed in Chapter 4. Although the data of Figure 1 -4 arcrecorded as a function of time, arly variable such as

wavelength, magnetic fleld strength, or temperaturemay be the independent variable under appropriate cir-cumstances. The correlation of two analog signals thatresult from coffesponding measured physical or chemi-cal properties is important in a wide variety of instru-mental techniques, such as nuclear magnetic resonance

spectroscopy, infrared spectroscopy, and differentialthermal analysis.

Analog signals are especially susceptible to electri-cal noise that results from interactions within measure-ment circuits or from other electrical devices in thevicinity of the measurement system. Such undesirablenoise bears no relationship to the information of inter-est, and methods have been developed to minimize theeffects of this unwanted information. Signals, noise,

and the opttmtzation of instrumental response are dis-

cussed in Chapter 5.

Time Domains

Information is stored in time domains as the time rela-

tionship of signal fluctuations, rather than in the ampli-tudes of the signals. Figure 1-5 illustrates three differ-ent time-domain signals recorded as an afialog quantityversus time. The horizontal dashed lines represent an

arbttrary analog signal threshold that is used to decide

whether a signal is HI (above the threshold) or LO (be-

low the threshold). The time relationships between

transitions of the signal from HI to LO or from LO toHI contain the information of interest. For instruments

that produce periodic signals, the number of cycles

of the signal per unit time is the frequency, and the

time required for each cycle is its period. Two exam-ples of instrumental systems that produce informationencoded in the frequency domain are Raman spec-

troscopy and instrumental neutron actlation analysis.

In these methods, the frequency of arrival of photons

at a detector is directly related to the intensity of the

emission from the analyte, which is proportional to itsconcentration.

The time between successive LO to HI transitionsis called the period, and the time between a LO to HIand a HI to LO transition is called the pulse width. De-

Time

(a)

vices such as voltage-to-frequency converters and

frequency-to-voltage converters may be used to converttime-domain signals to analog-domain signals and viceversa. These and other such data domain converterswill be discussed in Chapters 3 and 4 as a pafi of ourtreatment of electronic devices and will be referred toin other contexts throughout this book.

Digital Domains

Data are encoded in the digital domain in a two-levelscheme. The information can be represented by thestate of a light bulb, a light-emitting diode, a toggleswitch, or a logic level signal, to cite but a few exam-ples. The characteristic that these devices share is thateach of them must be in one of only two states. For ex-ample, lights and switches may be only ON or OFF andlogic-level signals may be only HI or LO. The deflni-tion of what constitutes ON and OFF for switches and

lC Instruments for Analysis

Time

(b)

lights is understood, but in the case of electrical signals,as in the case of time domain signals , zn arbrtrary sig-nal level must be deflned that distinguishes between HIand LO. Such a definition may depend on the condi-tions of an experiment, or it may depend upon the char-acteristics of the electronic devices in use. For example,the signal represented in Figure 1-5c is a train of pulsesfrom a nuclear detector. The measurement task is tocount the pulses during a flxed period of time to obtaina measure of the intensity of radiation. The dashed linerepresents a signal level that not only is low enough toensure that no pulses are lost but also is sufflcientlyhigh to reject random fluctuations in the signal that are

unrelated to the nuclear phenomena of interest. If thesignal crosses the threshold fourteen times, as in thecase of the signal in Figure 1-5c, then we may be con-fldent that fourteen nuclear events occuffed. After theevents have been counted, the data are then encoded inthe digital domain in the form of the number 14. In

O

U

C)ood

o

Figure 1-4 Analog signals. (a) Instrument response ftom the photometric detection system ofa flow inlection analysis experiment. A stream of reaction mixture containing plugs of redFe(SCN)2+ flows past a monochromatic light source and a phototransducer, which produces achanging voltage as sample concentration changes. (b) The current response of a photomulti-plier tube when the light from a pulsed source falls on the photocathode of the device.

1C Instruments for Analysis

(a) Count

Time interval 4

A still more efflcient method for encoding data inthe digital domain is seen in the signal of Figure I-6c.Here, we use three light bulbs to represent the three bi-nary digits: 20 : l; 2t : 2; and 22 _ 4. However, wecould use switches, wires, light-emitting diodes, or any

of a host of electronic devices to encode the informa-tion. In this scheme, ON : 1 and OFF : 0, so that ournumber is encoded as shown in Figure 1-6 with the flrstand third lights ON and the middle light OFF, whichrepresents 4 + 0 + 1 : 5. This scheme is highly effl-cient because all of the desired information is presented

to us simultaneously, just as all of the digits on the face

of the digital voltmeter in Figure I-3a appear simulta-neously. Data presented in this way are referred to as

parallel dtgttal data. Data arc transmitted within ana-

lytical instruments and computers by parallel datatransmission. Since data usually travel relatively short

distances within these devices, it is economical and ef-flcient to use parallel information transfer. This econ-omy of short distances is in contrast to the situation inwhich data must be transported over long distancesfrom instrument to instrument or from computer tocomputer. In such instances, communication is carriedout serially by using modems or other more sophisti-cated or faster serial data transmission schemes. Wewill consider these ideas in somewhat more detail inChapter 4.

n=4+1=5

LC-4 Detectors, Transducers, and Sensors

The terms detector, transducer, and sensor are oftenused synonymously, but in fact the terms have some-what different meanings. The most general of the threeterms, detector; refers to a mechanical, electrical, orchemical device that identifles, records, or indicates a

change in one of the variables in its environment, such

as pressure, temperature, electrical charge, electromag-netic radiation, nuclear radiation, particulates, or mole-cules. This term has become a catchall to the extent thatentire instruments are often referred to as detectors. Inthe context of instrumental analysis, we shall use theterm detector rn the general sense in which we have justdefined it, and we shall use detection system to refer toentire assemblies that indicate or record physical orchemical quantities. An example is the UV (ultraviolet)detector often used to indi cate and record the presence

of eluted analytes in liquid chromatography.The term transducer refers speciflcally to those de-

vices that convert information in nonelectrical domainsto information in electrical domains and the converse.Examples include photodiodes, photomultipliers, and

other electronic photodetectors that produce culrent orvoltage proportional to the radiant power of electro-magnetic radiation that falls on their surfaces. Other ex-amples include thermistors, strain gauges, and Hall ef-fect magnetic field strength transducers. As suggested

Time +

Figure 1-6 Diagram illustrating three tFpes of digital data: (a) count serial data,(b) binary-coded serial data, and (c) parallel binary data. In all three cases, the data repre-sent the number m : 5.

10 Chapter 1 Introduction

previously, the mathematical relationship between theelectrical output and the input radiant power, tempera-ture, force, or magnetic field strength is called the trans-

fer function of the transducer.The term sensor also has become rather broad, but

in this text we shall reserve the term for the class of an-

alytical devices that are capable of monitoring speciflcchemical species continuously and reversibly. There are

numerous examples of sensors throughout this text, in-cluding the glass electrode and other ion-selective elec-trodes, which are treated in Chapter 23, the Clark oxy-gen electrode, which is described in Chapter 25, and

optrodes, or flber-optic sensors, which appear in Chap-ter 7 . Sensors consist of a transducer coupled with a

chemically selective recognition phase. So, for exam-ple, optrodes consist of a phototransducer coupledwith a flber optic that is coated on the end oppositethe transducer with a substance that responds specifl-cally to a particular physical or chemical characteristicof an analyte.

A sensor that is especially interesting and instruc-tive is the quartz crystal microbalance, or QCM. Thisdevice is based on the piezoelectric characteristics ofqtafiz. When qtartz is mechanically deformed, an elec-trical potential develops across its surface. Furthermore,when a voltage is impressed across the faces of a qtartzcrystal, the crystal deforms. A crystal connected in an

appropriate electrical circuit oscillates at a frequencythat is characteristic of the mass and shape of the crystaland that is arnazingly constant-provided that the mass

of the crystal is constant. This property of some crys-talline materials is called the piezoelectric effect, and

forms the basis for the quafiz-crystal microbalance.Moreover, the characteristic constant frequency of thequartz crystal is the basis for modern high-precisionclocks, time bases, counters, timers, and frequency me-

ters, which in turn have led to many highly accurate andprecise analytical instrumental systems.

If a quartz crystal is coated with a polymer that se-

lectively adsorbs certain molecules, the mass of thecrystal increases if the molecules are present, thus de-

creasing the resonant frequency of the quartz crystal.When the molecules are desorbed from the surface, thecrystal returns to its original frequency. The relationshipbetween the change in frequency of the crystal LF and

the change in mass of the crystal LM is given by

where M rs the mass of the crystal, A is its surface area,

F is the frequency of oscillation of the crystal, and C isa proportionality constant. The relationship above indi-cates that it is possible to measure very small changes inthe mass of the crystal if the frequency of the crystal can

be measured precisely. As it turns out, it is possible tomeasure frequency changes of one part in 107 quite eas-

ily with inexpensive instrumentation. The limit of de-

tection for a prczoelectric sensor of this type is esti-mated to be about 1 pg, or 1\-tz g. These sensors havebeen used to dete ct a variety of gas-phase analytes in-cluding formaldehyde, hydrogen chloride, hydrogensulflde, and benzene. They have also been proposed as

sensors for chemical warfare agents such, as mustardgas and phosgene.

The prczoelectric mass sensor presents an excellentexample of a transducer converting a property of the an-

alyte, mass in this case, to a change in an electricalquantity, the resonant frequency of the quartz crystal.This example also illustrates the distinction between atransducer and a sensor. In the quartz-crystal microbal-afice, the transducer is the qtartz crystal, and the selec-

tive second phase is the polymeric coating. The combi-nation of the transducer and the selective phase

constitute the sensor,

1C-5 Readout Devices

A readout device is a transducer that converts informa-tion from an electrical domain to a domain that is un-derstandable by a human observer. Usually, the trans-duced signal takes the form of the alphanumeric orgraphic output of a cathode-ray tube, a series of num-bers on a digital display, the position of a pointer on ameter scale, or, occasionally, the blackening of a photo-graphic plate, or a tracing on a recorder paper. In some

instances, the readout device rnay be arranged to givethe analyte concentration directly.

LC-6 Microprocessors and Cornputersin Instruments

Most modern analytical instruments contain or are at-

tached to one or more sophisticated electronic devicesand data domain converters, such as operational ampli-flers, integrated circuits, analog-to-digital and digital-to-analog converters, counters, microprocessors, and com-puters. In order to appreciate the power and limitationsof such instruments, it is necess ary that the scientist de-

velop at least a qualitative understanding of how these

devices function and what they can do. Chapters 3 and 4provide a brief treatment of these important topics.

1D SELECTING AN ANALYTICALMETHOD

It is evident from column 2 of Table 1-1 that the modernchemist has an enormous array of tools for carrying outanalyses-so many, in fact, that the choice among themis often difflcult. In this section, we describe how such

choices are made.

1D-1 Defining the Problem

In order to select an analytical method intelligently; it isessential to define clearly the nature of the analyticalproblem. Such a deflnition requires answers to the fol-lowing questions:

1. What accuracy is required?2. How much sample is available?3. What is the concentration range of the analyte?4. What components of the sample will cause interfer-

ence?

5. What are the physical and chemical properties of thesample matrix?

6. How many samples are to be analyzed?

The answer to question 1 is of vital importance because

it determines how much time and care will be needed

for the analysis. The answers to questions2 and 3 deter-mine how sensitive the method must be and how wide a

range of concentrations must be accommodated. Theanswer to question 4 determines the selectivity requiredof the method. The answers to question 5 are importantbecause some analytical methods in Table 1-1 are ap-

plicable to solutions (usually aqueous) of the analyte.Other methods are more easily applied to gaseous sam-

ples, while still other methods are suited to the directanalysis of solids.

The number of samples to be analyzed (question 6)is also an important consideration from the economicstandpoint. If this number is large,, considerable timeand money can be spent on instrumentation, method de-

velopment, and calibration. Furthermore, if the numberis large, a method should be chosen that requires theleast operator time per sample. On the other hand, ifonly a few samples are to be analyzed, a simpler but

1D Selecting an Analytical Method 11

more time-consuming method that requires little or nopreliminary work is often the wiser choice.

With answers to the foregoing six questions, a

method can then be chosen, provided that the perfor-mance characteristics of the various instruments shownin Table 1-l are known.

LD-z Performance Characteristicsof Instrumentsl Figures of Merit

Table l-3 lists quantitative performance criteria of in-struments that can be used to decide whether a given in-strumental method is suitable for attacking an analyticalproblem. These characteristics are expressed in numeri-cal terms that are called figures of merit. Figures ofmerit permit us to nalrow the choice of instruments fora given analytical problem to a relatively few. Selectionamong these few can then be based upon the qualitativeperformance criteria listed in Table l-4.

In this section, we define each of the six flgures ofmerit listed in Table l-3. These figures are then used

throughout the remainder of the text in discussing vari-ous instruments and instrumental methods.

TABLE 1-3 Numerical Criteria for SelectingAnalytical Methods

Criterion

1. Precision

2. Bias

3. Sensitivity

4. Detection limit

5. Concentration range

6. Selectivity

Figure of Merit

Absolute standard deviation,

relative standard deviation

coefflcient of variation,

variance

Absolute systematic elror,

relative systematic error

Calibration sensitivity,

analytical sensitivity

Blank plus three times

standard deviation of a blank

Concentration limit ofquantitation (LOQ) toconcentration limit oflinearity (LOL)

Coefflcient of selectivity

12 Chapter 1 Introduction

TABLE 1,.-4 Other Characteristicsto Be Consideredin Method Choice

1. Speed

2. Ease and convenience

3. Skill required of operator

4. Cost and availability of equipment

5. Per-sample cost

Precision

As we show in Section alA,Appendix 1, the precisionof analytical data is the degree of mutual agreementamong data that have been obtained in the same way.Precision provides a measure of the random, or indeter-minate, error of an analysis. Figures of merit for preci-sion include absolute standard deviation, relative stan-dard deviation, cofficient of variation, and variance.These terms are defined in Table 1-5.

Bias

As shown in Section alA-Z, Appendix 1, bias providesa measure of the systematic, or determinate, effor of an

analytical method. Bias is deflned by the equation

bias_p-x1

where Lr, is the population mean for the concentration ofan analyte in a sample that has a true concentration of xr.

Determining bias involves analyzing one or more stan-

dard reference materials whose analyte concentration isknown. Sources of such materials are given in refer-ences 3 and 4 rn Section aIA-2 of Appendix 1. The re-sults from such an analysis will, however, contain bothrandom and systematrc effors; but if a sufflcient numberof analyses are performed, the mean value may be de-

termined with a given level of confldence. As shown inSection alB-2,Appendix 1, the mean of 20 or 30 repli-cate analyses can ordinarily be taken as a good estimateof the population mean p in Equation 1-1. Any differ-ence between this mean and the known value analyteconcentration of the standard reference material can be

attributed to bias.If performing 20 replicate analyses on a standard is

impractical, the probable presence or absence of bias canbe evaluated as shown in Example a1 -7 tnAppendix 1.

TABLE 1-5 Figures of Merit for Precisionof Analytical Methods

*xi: numerical value of the lth measurement.

JZ*,

x : mean of N measurements : LN

Ordinarily in deyeloping an analytical method,every effort is made to identify the source of bias and

eliminate it or coffect for it by the use of blanks and byinstrument calibration.

Sensitivity

There is general agreement that the sensitivity of an in-strument or a method is a measure of its ability to dis-criminate between small differences in analyte concen-tration. Two factors limit sensitivity: the slope of thecalibration curve and the reproducibility or precision ofthe measuring device. Of two methods that have equalprecision, the one that has the steeper calibration curve

will be the more sensitive. A corollary to this statementis that if two methods have calibration curves withequal slopes, the one that exhibits the better precisionwill be the more sensitive.

The quantitative deflnition of sensitivity that is ac-

cepted by the International Union of Pure and AppliedChemists (IUPAC) is calibration sensitivity, which isthe slope of the calibration curve at the concentration ofinterest. Most calibration curves that are used in analyt-ical chemistry arc linear and may be represented by theequation

(1-1)

Terms Definition*

N

\t*, - i)2i:l

N-1Absolute standard deviation, s

Relative standard deviation RSD(RSD)

Standard deviation of the sm :mean, sm

Coefflcient of variation, CV CV : ' x IOO{zox

Variance s2

s

,

st{w

S - mc + Sur Q-2)

where S is the measured signal, c is the concentration ofthe analyte, 561 is the instrumental signal for a blank,and m rs the slope of the straight line. The quantity Sur

should be the y-intercept of the straight line. With such

curves, the calibration sensitivity is independent of theconcentration c and is equal to m. The calibration sensi-

tivity as a flgure of merit suffers from its failure to takeinto account the precision of individual measurements.

Mandel and Stiehler2 recognrzed the need to in-clude precision in a meaningful mathematical statementof sensitivity and proposed the following deflnition foranalytical s ensitivity, ^y :

T _ mls5

lD Selecting an Analytical Method 13

S* : Sur + ksur (1-4)

Experimentally, S* can be determined by perform-ing 20 to 30 blank measurements, preferably over an

extended period of time. The resulting data are thentreated statistically to obtain Sur and sur. Finally, theslope from Equation I-2 is used to convert S* to cm,

which is deflned as the detection limit. That is, the de-

tection limit is given by

( 1-s)

Here, m LS agaLn the slope of the calibration curve, and

s5 is the standard deviation of the measurement.The analytical sensitivity offers the advantage of

being relatively insensitive to amplification factors. Forexample, increasing the gain of an instrument by a fac-tor of flve will produce a flvefold increas e Lfi m. Ordi-narily, however, this increase will be accompanied by acoffesponding increase in s5, thus leaving the analyticalsensitivity more or less constant. A second advantage ofanalytical sensitivity is that it is independent of themeasurement units for S.

A disadvantage of analytical sensitivity is that it isoften concentration dependent since s5 may yary withconcentratron.

Detection LimitThe most generally accepted qualitative deflnition ofdetection limit is that it is the minimum concentrationor mass of analyte that can be detected at a known con-fldence level. This limit depends upon the ratio of themagnitude of the analytical signal to the size of the sta-

tistical fluctuations in the blank signal. That is, unlessthe analytical signal is larger than the blank by some

multiple k of the variation in the blank owing to randomelrors, it is impossible to detect the analytical signalwith certainty. Thus, as the limit of detection is ap-

proached, the analytical signal and its standard devia-tion approach the blank signal 561 and its standard devi-ation sur. The minimum distinguishable analyticalsignal S- is then taken as the sum of the mean blank sig-nal S51 plus a multiple k of the standard deviation of theblank. That is,

As pointed out by Ingle,3 numerous alternatives,based correctly or incorrectly on / and e statistics (Sec-

tion alB-2,Appendix 1), have been used to determine a

value for k in Equation l-4. Kaiser4 argues that a rea-sonable value for the constant is k _ 3. He points outthat it is wrong to assume a strictly nornal distributionof results from blank measurements and that whenk - 3, the confidence level of detection will be 95Vo rnmost cases. He further argues that little is to be gainedby usin g a larger value of k-and thus a greater confi-dence level. Long and Winefordner,s in a discussion ofdetection limits, also recommend the use of k - 3.

; ;T jT'r*

;

*

; T ;

* ri i Eirs: tixu r:i'i||:i::;' ri:ii:::::: r'iiii:ir:i: I:;ii:iii;i'r ri:ii:iiriiri ri'i';ii|'ii ti:ir:ii:i':' lir+ EI,JI rn

A least-squares analysis of calibration data for the de-

termination of lead based upon its flame emissionspectrum yielded the equation

S - l.l2 cyo + 0.312

where cp6 is the lead concentration in parts per mil-lion and S is a measure of the relative intensity of thelead emission line. The following replicate data werethen obtained:

Concn, ppm PbNo. of Mean

Replications Value of S s

( 1-3)

E.

E

H

E.

E

H

E

ffi'

E

Ei

E.

E.

E'

E

E

E.

E

E.

E.

E.

E

El

E

E.

E

E:

10.0

1.00

0.000

10

10

24

t1.62 0.15

t.Iz 0.0250.0296 0.0082

3 J. D. Ing1e ft., I. Chem. Educ,, 1970, 42,+ H. Kaisel Anal. Chem., 198.7, 42, 53A.s G. L. Long and J. D. Winefordneg Anal.

100.

Chem., L983, 55, 712A.2 1. Mandel and R. D. Stiehler, l. Res. Natl. Bur. Std., 1964, A53, 155.

E

E

E

E

E

E

E

E

E

E

E

H

E

E

E

E

E

E

E

E

E

14 Chapter 1 Introduction

Calculate (a) the calibration sensitivity, (b) theanalytical sensitivity at I and 10 ppm of Pb, and (c)

the detection limit.

(a) By deflnition, the calibration sensitivity m isthe slope of the straight line. Thus, m - 1.12.

(b) At 10 ppm Pb, T : mlss: l.l2l0.l5 :7.5.At 1 ppm Pb, T : 1.1210.025 : 45.

(c) Applying Equation I-4,

To be very useful, an analytical method shouldhave a dynamic range of at least two orders of magni-tude. Some methods have applicable concentrationranges of five to six orders of magnitude.

Selectivity

Selectivity of an analytical method refers to the degree

to which the method is free from interference by otherspecies contained in the sample matrix. Unfortunately,no analytical method is totally free from interferencefrom other species, and frequently steps must be takento minimize the effects of these interferences.

Consider, for example, a sample containing an ana-

lyte A as well as potential interfering species B and C. Ifc A, cB, and cg aira the concentrations of the three species

and ffiA, ffi8, and ms zta their calibration sensitivities,then the total instrument signal will be given by a mod-ified version of Equation l-3. That is,

S - rfitct + rfiBcB + mccc + Sur (1-6)

Let us now define the selectivity coefficient for Awith respect to B as

kB,A: mglm6

S* : 0.0296 + 3 X 0.0082 - 0.054

Substituting into Equation 1-5 gives

0.054 0.0296cm : lJ,

_ 0.022 ppm Pb.

Dynamic Range

Figure l-7 illustrates the deflnition of the dynamicrange of an analytical method, which extends from thelowest concentration at which quantitative measure-ments can be made (limit of quantitation, or LOQ) tothe concentration at which the calibration curve departsfrom linearity (limit of linearity, or LOL). The lowerlimit of quantitative measurements is generally taken tobe equal to ten times the standard deviation of repetitivemeasurements on a blank, or 10sur.At this point, the rel-ative standard deviation is about 307o and decreases

rapidly as concentrations become larger. At the limit ofdetection, the relative standard deviation is 100Vo.

LOL /Z

cmLoQ

/l Dynamic range

I

Concentration

Figure 1-7 Useful range of an analytical method. LOq -limit of quantitative measurement; LOL - limit of linearresponse.

The selectivity coefflcient then gives the relativeresponse of the method to species B as compared withA. A similar coefficient for A with respect to C is

kC,A: mglm6

(r-7)

( 1-8)

a)U)

oaa0)

C)

(n

Substituting these relationships into Equation l-4leads to

S - m6(cs * kB,AcB + kc,xcc) + Sur (1-9)

Selectivity coefflcients can range from zero (no in-terference) to values a good deal greater than unity.Note that a coefflcient is negative when the interferencecauses a reduction in the intensity of the output signalof the analyte. For example, if the presence of interfer-ant B causes a reduction in S in Equation I-7, ms wlllcarry a negative sign, as will kB,A.

Selectivity coefflcients are useful figures of meritfor describing the selectivity of analytical methods. Un-fortunately, they are not widely used except to charac-tetrze the performance of ion-selective electrodes(Chapter 23). Example l-2 tllustrates the use of selec-

tivity coefflcients when they are available.

The selectivity coefflcient for an ion-selective elec-rode for K+ with respect to Na+ is reported to be

0.052. Calculate the relative effor in the determina-tion of K+ in a solution that has a K+ concentrationof 3.00 x 10-3 M if the Na+ concentration isra) 2.00 x l0-2 M; (b) 2.00 x 10-3 M; (c) 2.00 xl0-4 M. Assume that 561 for a series of blanks was

approximately zero.

(a) Substituting into Equation 1-9 yields

S - tntK+(cr* + kNu*,K*cNa+) + 0

stms*

=

,^Z|X i3_;

+ 0.0s2 x 2.00 x 10-2

If Na+ were not present

Slms*:3'00X10-3

The relative effor in c6* will be identical tothe relative effor in Slms* (see Section a1B-5,Appendix 1). Therefore,

4.04 x 10-3 3.00 x 10-3

lE Calibration of Instrumental Methods 15

1E-1 Calibration Curves

To use the calibration curve technique, several stan-

dards containing exactly known concentrations of theanalyte are introduced into the instrument, and the in-strumental response is recorded. Ordinarily, this re-sponse is corrected for the instrument output obtainedwith a blank. Ideally, the blank contains all of the com-ponents of the original sample except for the analyte.The resulting data are then plotted to give a graph ofcorrected instrument response versus analyte concen-tration.

Figure 1-8 shows a typical calibration culve (also

called a working culye or an analytical cwrve). Plots,

such as this, that are linear over a significant concentra-tion range (the dynamic range) are often obtained and

are desirable because they are less subject to effor thanare nonlinear curves. Not uncommonly, however, non-linear plots are observed, which require alarger numberof calibration data to establish accurately the relation-ship between the instrument response and concentra-tion. Usually, an equation is developed for the calibra-tion curve by a least-squares technique (Appendix a1C)so that sample concentrations can be computed directly.

The success of the calibration curve method is crit-ically dependent upon how accurately the analyte con-centrations of the standards are known and how closelythe matrixT of the standards resemble that of the sam-

ples to be analyzed. Unfortunately, matching the matrixof complex samples is often difflcult or impossible, and

matrix effects lead to interference errors. To minimizematrix effects, it is often necessary to separate the ana-

lyte from the interferent before measuring the instru-ment response.

LF,-z Standard Addition Methods

Standard addition methods are particularly useful foranalyzing complex samples in which the likelihood ofmatrix effects is substantial. A standard addition methodcan take several forms.S One of the most commonforms involves adding one or more increments of a

standard solution to sample aliquots of the same size.

7 The term matrix refers to the collection of all of the various con-stituents making up an analytical sample. In addition to the analyte,the sample matrix includes all of the other constituents of the sam-ple, which are sometimes referred to as the concomitants.8 See M. Badeg l. Chem. Educ., L980, 57,703.

3.00 x 10-3X 1007o

_ 35Vo

Proceeding in the same way we find(b) Eret - 3.57o

(c) Er"t - 0.357o

lE CALIBRATION OF INSTRUMENTALMETHODS

With two exceptions, all types of analytical methodsrequire calibration, a process that relates the mea-sured analytical signal to the concentration of analyte.6

The three most common calibration methods includethe preparation and use of a calibration curve, the stan-

dard addition method, and the internal standardmethod.

6 The two exceptions are gravimetric and coulometric methods. Inboth of these cases, the relationship between the quantity measuredand the concentration of analyte can be computed from accuratelyknown physical constants.

16 Chapter 1 Introduction

(.)o

_o

5 06(t)

-oC€

ca 04

-10.0 0.0 10.0 20.0V5, mL

Figure 1-8 Linear calibration plot for the method of standard additions. The con-centration of the unknown solution may be calculated from the slop e m and the in-tercept b, or it may be determined by extrapolation as explained in the text.

This process is often called spiking the sample. Each so-

lution is then diluted to a flxed volume before measure-ment. It should be noted that when the amount of sam-

ple is limited, standard additions can be carried out bysuccessive introductions of increments of the standardto a single measured volume of the unknown. Measure-ments are made on the original sample and on the sam-

ple plus the standard after each addition. In most ver-sions of the standard addition method, the samplematrix is nearly identical after each addition, the onlydifference being the concentration of the analyte or, incases involving the addition of an excess of an analyti-cal reagent, the concentration of the reagent. A1l otherconstituents of the reaction mixture should be identicalbecause the standards are prepared in aliquots of thesample.

Assume that several identical aliquots V, of the un-known solution with a concentratiofl cx are transferredto volumetric flasks having a volume Vt. To each ofthese flasks is added a variable volume V, mL of a

standard solution of the analyte having a known con-centration cs. Suitable reagents are then added, and

each solution is diluted to volume. Instrumental mea-surements are then made on each of these solutions toyietrd an instrument response S. If the instrument re-sponse is proportional to concentration, as it must be ifthe standard addition method is to be applicable, wemay write

o_ kVrc, , kV*c*rrvt'v,

where k is a proportionality constant. A plotfunction of % is a straight line of the form

S - mV, + b

where the slope m and the intercept b are given by

kc,m-vt

and

b- kV*c*

vt

Just such a plot is depicted in Figure 1-8.

A least-squares analysis (Section alC,Appendix 1)

can be used to determLfie m and b; cx cafl then be ob-

tained from the ratio of these two quantities and theknown values of co Vo and Vr. Thus,

b kV*c*lV1 V*c*

m kcrlVs cs

(1- 10)

ofSas a

( 1- 11)

A r alue for the standard deviation in cx can then be ob-

=ned by assuming that the uncertainties in c' V' andi,-- are negligible with respect to those rn m and b. Then,-:e relative variance of the result (srlc*)z is assumed tore the sum of the relative variances of m and b. That is,

,a here sm is the standard deviation of the slope and-'n here s6 is the standard deviation of the intercept. Tak-rnq the square root of this equation gives

sc:cx (t-r2)

-\lternatively, a manual plot of the data may be con-srmcted, and the linear portion of the plot may be extrap-olated to the left of the origin, as shown by the dashed

line of Figure 1-8. The difference between the volume ofthe standard added at the origin (zero) and the value ofthe volume at the intersection of the straight line with the

-r-axis, or the x-intercept (V*)0, is the volume of standardreagent equivalent to the amount of analyte in the sam-

ple. In addition, the x-intercept corresponds to zero in-strument response, so that we may write

S_ kVrc, + kV*c*:0Vt Vt

By solving Equation 1-13 for c*, we obtain

EXAMPLE 1.3Ten-millimeter aliquots of a natural water samplewere pipetted into 50.00-mL volumetric flasks. Ex-actly 0.00, 5.00, 10.00, 15.00, and 20.00 mL of astandard solution containing 11.1 ppm of Fe3+ wereadded to each, followed by an excess of thiocyanateion to give the red complex Fe(SCN;z+. After dilu-tion to voluffie, the instrument response S for each ofthe flve solutions, measured with a colorimeter, was

found ro be 0.240,0.437,0.621, 0.809, and 1.009, re-spectively. (a) What was the concentration of Fe3+ inthe water sample? (b) Calculate a standard deviationof the slope and of the intercept and the standard de-

viation for the concentration of Fe3 +.

lE Cqlibrqtion of Instrutmental Methods 17

In this problem, cs: 11.1 ppm, V,: 10.00 mL,and Vt : 50.00 mL. A plot of the data, shown inFigure 1-8, demonstrates that there is a linear re-lationship between the instrument response and

the iron concentration.To obtain the equation for the line in Figure

1-8 (S _ mV, + b), we follow the procedure il-lustrated in Example al-12 in Appendix 1. Theresult ts m: 0.03820 and b - 0.2412 and thus

s - 0.03820 v, + 0.2412

Substituting into Equation 1-11 gives

0.2412 x 11.1 : 7 .0I ppm Fe3+

(a)

(;)': (*)' + (+)'

cx:

L

0.03820 x 10.00

This value may be determined by graphical ex-trapolation as illustrated in the flgure as well. Theextrapolated value represents the volume ofreagent corresponding to zero instrument re-sponse, which in this case is -6.31 mL. The un-known concentration of the analyte in the origi-nal solution is then calculated as follows:

6.31 mL x 11.1 ppm

10.00 mL_ I .01 ppm Fe3+

(b) Equations al-35 and aI-36 give the standard de-

viation of the intercept and the slope. That is,ss: 3.8 X 10-3 and sm: 3.1 X I0-4.

Substituting into Equation 1 -12 gives

sc:7'ott\ az+n )+t ,rr, /

- 0.I2 ppm Fe3+

In the interest of saving time or sample, it is possi-ble to perform a standard addition analysis by usingonly two increments of sample. Hera, z single additionof % mL of standard would be added to one of the twosamples, and we can write

kV*c*

( 1- 13)

vt

,1 kV*c* kV rc,J2_ V, T V,

where 51 and 52 are the analytical signals resulting fromthe diluted sample and the diluted sample plus stand ard,

18 Chapter 1 Introduction

respectively. Dividing the second equation by the flrstgives upon reaffangement

? Src'%Lx - (sz sr)%

1E-3 The Internal Standard Method

An internal standard is a substance that is added in a

constant amount to all samples, blanks, and calibrationstandards in an analysis. Alternatively, it may be a ma-jor constituent of samples and standards that is presentin a large enough amount that its concentration can beassumed to be the same in all cases. Calibration then in-volves plotting the ratio of the analyte signal to the in-ternal standard signal as a function of the analyte con-centration of the standards. This ratio for the samples isthen used to obtain their analyte concentrations from a

calibration curve.An internal standard, if properly chosen and used,

can compensate for several types of both random and

systematic effors. Thus, if the analyte and internal stan-

dard signals respond proportionally to random instru-mental and method fluctuations, the ratio of these sig-nals is independent of these fluctuations. If the twosignals are influenced in the same way by matrix ef-fects, compensation of these effects also occurs. Inthose instances where the internal standard is a majorconstituent of samples and standards, compensation forerrors that arise in sample preparation, solution, and

cleanup may also occur.

A major difflculty in applying the internal standardmethod is that of finding a suitable substance to serve as

the internal standard and of introducing that substance

into both samples and standards in a reproducible way.The internal standard should provide a signal that issimilar to the analyte signal in most ways but suffi-ciently different so that the two signals are readily dis-tinguishable by the instrument. The internal standardmust be known to be absent from the sample matrix so

that the only source of the standard is the added amount.For example, lithium is a good internal standard for thedetermination of sodium or potassium in blood serumbecause the chemical behavior of lithium is similar toboth analytes, but it does not occur naturally in blood.

As an example, the internal standard method is of-ten used in the determination of trace elements in met-als by emission spectroscopy. Thus, in determiningparts per million of antimony and tin in lead to be used

for the manufacture of storage batteries, the relative in-tensity of a strong line for each of the minor con-stituents might be compared with the intensity of a

weak line for lead. Ordinarily, these ratios would be less

affected by variables that arise in causing the samples toemit radiation. In the development of any new internalstandard method, we inust verify that changes in con-centration of analyte do not affect the signal intensitythat results from the internal standard. In order for such

a procedure to be successful, a good deal of time and ef-fort would need to be expended in preparing a set ofpure lead samples that contains exactly known concen-trations of antimony and tin.

lF QUESTTONS AND PROBLEMS

1-1 What is a transducer in an analytical instrument?

1-2 What is the information processor in an instrument for measuring the color of a solutionvisually?

1-3 What is the detector in a spectrograph in which spectral lines are recorded photograph-ically?

1-4 What is the transducer in a smoke detector?

1-5 What is a data domain?

1-6 What are analog domains? How is information encoded in analog domains?

1-7 List four output ffansducers and describe how they are used.

1-8 What is a figure of merit?

lF Question and hoblems L9

1-9 The following calibration data were obtained by an instrumental method for the deter-mination of the species X in aqueous solution.

Concn X, C1 No. Replications, Mean Analytical Standardppm N Signal, S Deviation, ppm

0.00

2.00

6.00

10.00

14.00

18.00

25

5

5

5

5

5

0.031

0.r730,422

0.702

0.956

r.248

0.0079

0.00940.00840.00840.0085

0.0110

(a) Calculate the calibration sensitivity.(b) Calculate the analytical sensitivity at each concentration.(c) Calculate the coefficient of variation for the mean for each of the replicate sets.

(d) What is the detection limit for the method?

1-10 A 25.}-mI- sample containing Cu2+ gave an instrument signal of 23.6 units (corrected

for a blank). When exactly 0.500 mL of 0.0287 M Cu(NO3)2 was added to the solution,the signal increased to 37 .9 units. Calculate the molar concenffation of Cu2+ assumingthat the signal was direcfly proportional to the analyte concentration.

1-11 Exactly 5.00-mL aliquots of a solution containing phenobarbital were measured into50.00-mL volumetric flasks and made basic with KOH. The following volumes of astandard solution of irhenobarbital containing2.OOO lLgknl, of phenobarbital were thenintroduced into each flask and the mixture was diluted to volume: 0.000, 0.500, 1.00,

1.50, and 2.00 mL. A fluorometer reading for each of these solutions was 3.26,4.80,6.4I, 8.02, and 9.56, respectively.(a) Plot the data.(b) Using the plot from (a), calculate the concentration of phenobarbital in the un-

known.(c) Derive a least-squares equation for the data.(d) Compute the concenffation of phenobarbital from the equation in (c).(e) Calculate a standard deviation for the concentration obtained in (d).