Introductfon

nalytical chemistry deals with methods for de- fractive indexes. For quantitative analyses, the amount
termining the chemical composition of samples of of analyte was determined by gravimetric or by titri-
mqtter. A qualitqtive method yields information about metric measurements. In gravimetric measurements,
the mass of the analyte or some compound produced
the identity of atomic or molecular species or the func-
from the analyte was determined. In titrimetric proce-
tional groups in the sample; a quantitative method, in dures, the volume or mass of a standard reagent re-
contrast, provides numerical information as to the rel- quired to rcact completely with the analyte was
ative amount of one or more of these components. measured.
These classical methods for separating and deter-
mining analytes still find use in many laboratories. The
1,A CLASSIFICATION OF ANALYTICAT extent of their general application is, however, decreas-
METHODS ing with the passage of time and with the advent of in-
strumental methods to supplant them.
Analytical methods are often classifled as being either
classical or instrumental. This classiflcation is largely
LA-Z Instrumental Methods
historical with classical methods, sometimes called wet-
chemical methods, preceding instrumental methods by Early in the twentieth centur), chemists began to exploit
a century or more. phenomena other than those used for classical methods
for solving analytical problems. Thus, measurements of
physical properties of analytes-such as conductivity,
1A-1 Classical Methods
electrode potential, light absorption or emission, mass-
In the early years of chemistry, most analyses were ca? to-charge ratio, and fluorescence-began to be used for
ried out by separating the components of interest (the quantitative analysis of a variety of inorganic, organic,
analytes) in a sample by precipitation, extraction, or and biochemical analytes. Furthermore, highly efficient
distillation. For qualitative analyses, the separated com- chromatographic and electrophoretic techniques began
ponents were then treated with reagents that yielded to replace distillation, extraction, and precipitation for
products that could be reco gnrzed by their colors, their the separation of components of complex mixtures prior
boiling or melting points, their solubilities in a series of to their qualitative or quantitative determination. These
solvents, their odors, their optical activities, or their re- newer methods for separating and determining chemical
 Chapter 1 Introduction

species are known collectively as instrumental methods tal analysis. Most of the characteristics listed in the
of analysis. table require a source of energy to stimulate a measur-
Many of the phenomena that instrumental methods able response from the analyte. For example, in atomic
are based on have been known for a century or more. emission an increase in the temperature of the analyte is
Their application by most chemists, however, was de- required to flrst produce gaseous analyte atoms and then
layed by lack of reliable and simple instrumentation. In to excite the atoms to higher energy states. The excited-
fact, the growth of modern instrumental methods of state atoms then emit charucteristic electromagnetic ra-
analysis has paralleled the development of the electron- diation, which is the quantity measured by the instru-
ics and computer industries. ment. Sources of excitation energy may take the form of
a rapid thermal change as in the previous example, elec-
tromagnetic radiation from a selected region of the
18 TYPES OF INSTRI,]MENTAL METHODS spectrum, application of one of the electrical quanti-
ties-voltage, current, or charge-or perhaps subtler
For this discussion, it is useful to consider chemical and forms intrinsic to the analyte itself.
physical characteristics that are useful for qualitative or Note that the flrst six entries in Table 1- 1 involve
quantitative analysis. Table 1-1 lists most of the charac- interactions of the analyte with electromagnetic radia-
teristic properties that are cuffently used for instrumen- tion. In the flrst property, radiant energy is produced by

TABLE l-L Chemical and Physical Properties Employed

in Instrumental Methods
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-chargeratio 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

 lC Instruments for Analysis

the analyte; the next flve properties involve changes in can be viewed as a communication device between the
electromagnetic radiation brought about by its interac- system under study and the investigator. To retrieve the
tion with the sample. Four electrical properties then fol- desired information from the analyte, it is necessary to
low. Finally, four miscellaneous properties are grouped provide a stimulus, which is usually in the form of elec-
together: mass-to-charge ratio, reaction rate, thermal tromagnetic, electrical, mechanical, or nuclear energy
characteristics, and radioactivity. as illustrated in Figure 1-1. The stimulus elicits a re-
The second column in Table 1-1 lists the names of sponse from the system under study whose nature and
instrumental methods that are based upon the various magnitude are governed by the fundamental laws of
physical and chemical properties. Be aware that it is not chemistry and physics. The resulting information is
always easy to select an optimal method from among contained in the phenomena that result from the interac-
available instrumental techniques and their classical tion of the stimulus with the analyte. A familiar example
counterparts. Some instrumental techniques ate more is the passage of a narrow band of wavelengths of visi-
sensitive than classical techniques, but others are not. ble light through a sample to measure the extent of its
With certain combinations of elements or compounds, absorption by the analyte. The intensity of the light is
an instrumental method may be more selective; with determined before and after its interaction with the sam-
others, a gravtmetric or volumetric approach may suffer ple, and the ratio of these intensities provides a measure
less interference. Generalizatrons on the basis of accu- of the analyte concentration.
rac!,, convenience, or expenditure of time are equally Generally, instruments for chemical analysis com-
difflcult to draw. Nor is it necessarily true that instru- prise just a few basic components, some of which are
mental procedures employ more sophisticated or more listed in Table l-2. To understand the relationships
costly apparatus; indeed, the modern electronic analyti- among these instrument components and the flow of in-
cal balance used for gravimetric determinations is a formation from the characteristics of the analyte
more complex and reflned instrument than some of through the components to the numerical or graphical
those used in the other methods listed in Table 1-1. output produced by the instrument, it is instructive to
As noted earlier, in addition to the numerous meth- explore the concept of data domains.
ods listed in the second column of Table 1-1, there is a
group of instrumental procedures that are used for sepa-
1C-1 Data Domains
ration and resolution of closely related compounds.
Most of these procedures are based upon chromatogra- The measurement process is aided by a wide variety of
phy or electrophoresis. One of the characteristics listed devices that convert information from one form to an-
in Table 1-1 is.ordinarily used to complete the analysis other. In order to investi gate how instruments function,
following chromatographic separations. Thus, for ex- it is important to understand the way in which informa-
ample, thermal conductivity, ultraviolet and infrared ab- tion is encoded, or transformed from one system of in-
sorption, refractive index, and electrical conductance formation to another, as a characteristic of electrical
have been used for this purpose. signals-that is, as voltage, current, charge, or varia-
This text deals with the principles, the applications, tions in these quantities. The various modes of encoding
and the performance characteristics of the instrumental information electrically are called data domains. A
methods listed in Table 1- 1 and of chromatographic and classification scheme has been developed based on this
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

Energy System Analytical
An instrument for chemical analysis converts informa- source under information
study
tion stored in the physical or chemical characteristics of
the analyte to information that may be manipulated and Figure 1-1 Block diagram showing the overall process of
interpreted by a human. Thus, an analytical instrument an instrumental measurement.
 Chapter 1 Introduction

TABLE l-2 Some Examples of Instrument Components

Data Domain
Energy Source Analytical Input of Tlansduced Information
Instrument (stimulus) Information Tfansducer Information Processor Readout

Photometer Tungsten lamp, Attenuated light Photocell Electrical Meter scale Current
glass filter beam current meter

Atomic emission Flame UV or visible Photomultiplier Electrical Amplifler, Chart

spectrometer radiation tube potential demodulator, recorder
monochromator
chopper

Coulometer DC source Cell current Electrodes Electrical Amplifier Chart

current recorder

pH meter Sample/glass Hydrogen ion Glass-calomel Electrical Amplifler, Digital unit

electrode activity electrodes potential drgrtrzer

X-Ray powder X-Ray tube, Diffracted Photographic Latent Chemical Black

diffractometer sample radiation fi1m lmage developer rmages
on fllm

Color Sunlight Color Eye Optic nerve Brain Visual

comparator signal color
response

concept that greatly simplifles the analysis of instru-

mental systems and promotes understanding of the Nonelectricatr domains
:

measurement process.l As shown in the data domains

map 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 characteristics
that are of interest in a particular experiment reside in
these 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 in
nonelectrical domains. For instance, the determination
of the mass of an object using a mechanical equal-arm
balance involves a comparison of the mass of the ob-
ject, which is placed on one balance pan, with standard
masses placed on a second pan. The information repre- Electrical domains

Figure L-2 Data domains map. The upper (shaded) half

of the map comprises nonelectrical domains. The bottom
half is made up of electrical domains. Note that the digital
t C. G. Enke, Anal. Chem., 1971, 43, 69A. domain spans both electrical and nonelectrical domains.
 lC Instruments for Analysis

senting the mass of the object in standard units is en- fer are rapidly becoming relics of the past. Nonetheless,
coded directly by the experimenter, who provides infor- the information that we seek begins in the properties of
mation processing by summing the masses to arriv e at a the analyte and ends in a number, both of which are non-
number. In certain other mechanical balances, the grav- electrical domains. The ultimate objective in all mea-
itational force on a mass is amplifled mechanically by surements is that the flnal numerical result must be in
making one of the balance arms longer than the other, some manner proportional to the relevant chemical or
thus increasing the resolution of the measurement. physical characteristic of the analyte.
The determination of the linear dimensions of an
object with a ruler and the measurement of the volume of
1C-3 Electrical Domains
a sample of liquid with a graduated cylinder are other ex-
amples of measurements carried out exclusively in non- The modes of encoding information as electrical quanti-
electrical domains. Such measurements are often associ- ties can be subdivided into analog domains, time do-
ated with classical analytical methods. The advent of mains, and digital domainr, as illustrated in the bottom
inexpensive electronic signal processors, sensitive trans- half of the circular map in Figure 1-2. Note that the dig-
ducers, and readout devices has led to the development ital domain spans three electrrcal domains and one non-
of a host of electronic instruments, which acquire in- electrical domain because numbers presented on any
formation from nonelectrical domains, process it in type of display convey digital information and can also
electrical domains, and flnally present it in nonelectrical be encoded electrically.
domains once again. Electronic devices process infor- Any measurement process can be represented as a
mation and transform it from one domain to another in series of interdomain conversions. For example, Figure
ways analogous to the multiplication of mass in mechan- 1-3 illustrates the measurement of the intensity of molec-
ical balances with unequal arms. As a consequence of the ular fluorescence of a sample of tonic water containing a
availability of these electronic devices and their rapid trace of quinine and, in a general way, some of the data-
and sophisticated information processing, instruments domain conversions that are necessary to arrive at a
that rely exclusively on nonelectrical information trans- number expressing the intensity. The intensity of the flu-

Phototransducer

Fluorescence
emlsslon
Energy source
Resistor
Optical Digital voltmeter
filter
Laser Tonic water
(analyte) (a)

Fluorescence
Information Electrical
intensity Voltage V
flow current 1
of analyte
(b)

Laws of Transducer Ohm's Meter

Governed by =---.+ chemistry and transfer law transfer
physics function V_IR function
(c)

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 in
the instrument, and (c) the rules governing the data domain transformations during the mea-
surement process.
 Chapter 1 Introduction

A far more efflcient way to encode information is to

use binary numbers to represent numeric and alphabetic
data. To see how this type of encoding may be accom-
plished, let us consider the signals in Figure I-6. The
count digital data of the signal in Figure 1 -6a represent
the number n - 5 as before. We monitor the signal and
EHI count the number of complete oscillations. The process
aLo
.10
requires a period of time that is proportional to the num-
ber of cycles of the signal, or in this case, flve times the
length of a single time interval, as indicated in Figure
l-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 of
time. For example, the zercth time interval represents
Time 20 : 1, the flrst time interval represents 2l : 2, the sec-
--+ ond time interval represents 22 _ 4, and so forth, as
(c)
shown in Figure 1-6. During each time interval, we need
Figure 1-5 Time-domain signals. The horizontal dashed only decide whether the signal is HI or LO. If the signal
lines represent signal thresholds. When each signal is is HI during any given time interval, then the value cor-
above the threshold, the signal is HI, and when it is below
responding to that interval is added to the total. A11 inter-
the threshold, the signal is LO.
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
Chaptet 4, we shall explore the means for making HI- time intervals, the number n _ 5 has been determined.
LO electronic decisions and encoding the information In the count digital example of the signal in Figure l-6a,
in the digital domain. flve time intervals were required to determine the same
As suggested by the data domains map of Figure number. In this limited example, the binary-coded serial
I-2, the digital domain spans both electrical and non- data is nearly twice as efflcient as the count serial data.
electrical domains. In the example just cited, the nuclear A more dramatic example may be seen in the counting
events are accumulated by using an electronic counter of n - 10 oscillations similar to those of the signal in
and are displayed on a digital readout. When the experi- Figure l-6a. In the same ten time intervals, ten HI-LO
menter reads and interprets the display, the number that bits of information in the serial binary coding scheme
represents the measured quantity is once again in a non- enable the representation of the binary numbers from 0
electrical domain. Each piece of HI-LO data that repre- to 2r0 _ 1024, or 0000000000 to 1111111111. The im-
sents a nuclear event is a bit of information, which is the provement in efflciency is 1024110, or about 100-fo1d.
fundamental unit of information in the digital domain. In other words, the count serial scheme requires 1024
Bits of information that are transmitted along a single time intervals to represent the number 1024, while the
electronic channel or wire may be counted by an ob- binary coding scheme requires only ten time intervals.
server or by an electronic device that is monitoring the As a result of the efflciency of binary coding schemes,
channel; such accumulated data is termed count digital most digital information is encoded, transferred,
data, which appears in the data-domains map of Figure processed, and decoded in some form of binary.
I-2. For example, the signal in Figure 1-5a corresponds Data represented by binary coding on a single
to the number n - 8 because there are eight complete cy- transmission line is calle d serial-coded binary data, or
cles in the signal. The signal in the Figure 1-5b corre- simply serial data. A common example of serial data
sponds to n _ 5, and the signal in Figure 1-5c corre- transmission is the computer mod€ffi, which is a device
sponds to n _ 14. Although effective, this means of for transmitting data between computers by telephone
transmitting information is not very efflcient. over a single conductor (and ground).
 Chapter 1 Introduction

orescence is significant in this context because it is pro- in both amplitude and time as shown by the typical ana-
portional to the concentration of the quinine in the tonic log signals of Figure I -4. Magnitudes of analog quanti-
water, which is ultimately the information that we desire. ties can be measured continuously or they can be sam-
The information begins in the solution of tonic water as pled at speciflc points in time dictated by the needs of a
the concentration of quinine. This information is teased particular experiment or instrumental method as dis-
from the sample by applying to it a stimulus in the form cussed in Chapter 4. Although the data of Figure 1 -4 arc
of electromagnetic energy from the laser shown in Fig- recorded as a function of time, arly variable such as
ure l-3. The radiation interacts with the quinine mole- wavelength, magnetic fleld strength, or temperature
cules in the tonic water to produce fluorescence emission may be the independent variable under appropriate cir-
in a region of the spectrum characteristic of quinine and cumstances. The correlation of two analog signals that
of magnitude proportional to its concentration. Radia- result from coffesponding measured physical or chemi-
tion, and thus information, that is unrelated to the con- cal properties is important in a wide variety of instru-
centration of quinine is removed from the beam of light mental techniques, such as nuclear magnetic resonance
by an optical fllter, as shown in Figure I-3a. The inten- spectroscopy, infrared spectroscopy, and differential
sity of the fluorescence emission, which is a nonelectri- thermal analysis.
cal domain, is encoded into an electrical domain by a Analog signals are especially susceptible to electri-
special type of device called an input transducer The cal noise that results from interactions within measure-
particular type of transducer used in this experiment is a ment circuits or from other electrical devices in the
phototransducer, of which there are nurnerous types, vicinity of the measurement system. Such undesirable
some of which are discussed in Chapter 7 .In this exam- noise bears no relationship to the information of inter-
ple, the input transducer converts the fluorescence from est, and methods have been developed to minimize the
the tonic water to an electrical current, I, proportional to effects of this unwanted information. Signals, noise,
the intensity of the radiation. The mathematicalrelation- and the opttmtzation of instrumental response are dis-
ship between the electrical output and the input radiant cussed in Chapter 5.
power impinging on its surface is called the transfer
function of the transducer.
The current from the phototransducer is then Time Domains
passed through a resistor R, which according to Ohm's Information is stored in time domains as the time rela-
law produces a voltage V that is proportionalto I, which tionship of signal fluctuations, rather than in the ampli-
is in turn proportional to the intensity of the fluores- tudes of the signals. Figure 1-5 illustrates three differ-
cence. Finally, V is measured by the digital voltmeter to ent time-domain signals recorded as an afialog quantity
provide a readout proportional to the concentration of versus time. The horizontal dashed lines represent an
the quinine in the sample. arbttrary analog signal threshold that is used to decide
Voltmeters, alphanumeric displays, electric motors, whether a signal is HI (above the threshold) or LO (be-
computer screens, and many other devices that serve to low the threshold). The time relationships between
convert data from electrical to nonelectrical domains transitions of the signal from HI to LO or from LO to
are called output transducers. The digital voltmeter of HI contain the information of interest. For instruments
the fluorometer of Figure I-3a is a rather complex out- that produce periodic signals, the number of cycles
put transducer that converts the voltage V to a number of the signal per unit time is the frequency, and the
on a liquid crystal display so that it may be read and in- time required for each cycle is its period. Two exam-
terpreted by the user of the instrument. We shall con- ples of instrumental systems that produce information
sider the detailed nature of the digital voltmeter and encoded in the frequency domain are Raman spec-
various other electrical circuits and signals in Chapters troscopy and instrumental neutron actlation analysis.
2 through 4. 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 its
Analog Domains concentration.
Information tn analog domains is encoded as the mag- The time between successive LO to HI transitions
nitude of one of the electrical quantities-voltage, cur- is called the period, and the time between a LO to HI
rent, charge, or power. These quantities are continuous and a HI to LO transition is called the pulse width. De-
 lC Instruments for Analysis

C)
oo O
d

o
U

Time Time
(a) (b)

Figure 1-4 Analog signals. (a) Instrument response ftom the photometric detection system of
a flow inlection analysis experiment. A stream of reaction mixture containing plugs of red
Fe(SCN)2+ flows past a monochromatic light source and a phototransducer, which produces a
changing 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.

vices such as voltage-to-frequency converters and lights is understood, but in the case of electrical signals,
frequency-to-voltage converters may be used to convert as in the case of time domain signals , zn arbrtrary sig-
time-domain signals to analog-domain signals and vice nal level must be deflned that distinguishes between HI
versa. These and other such data domain converters and LO. Such a definition may depend on the condi-
will be discussed in Chapters 3 and 4 as a pafi of our tions of an experiment, or it may depend upon the char-
treatment of electronic devices and will be referred to acteristics of the electronic devices in use. For example,
in other contexts throughout this book. the signal represented in Figure 1-5c is a train of pulses
from a nuclear detector. The measurement task is to
count the pulses during a flxed period of time to obtain
Digital Domains a measure of the intensity of radiation. The dashed line
Data are encoded in the digital domain in a two-level represents a signal level that not only is low enough to
scheme. The information can be represented by the ensure that no pulses are lost but also is sufflciently
state of a light bulb, a light-emitting diode, a toggle high to reject random fluctuations in the signal that are
switch, or a logic level signal, to cite but a few exam- unrelated to the nuclear phenomena of interest. If the
ples. The characteristic that these devices share is that signal crosses the threshold fourteen times, as in the
each of them must be in one of only two states. For ex- case of the signal in Figure 1-5c, then we may be con-
ample, lights and switches may be only ON or OFF and fldent that fourteen nuclear events occuffed. After the
logic-level signals may be only HI or LO. The deflni- events have been counted, the data are then encoded in
tion of what constitutes ON and OFF for switches and the digital domain in the form of the number 14. In
 1C Instruments for Analysis

(a) Count

Time interval 4

Time +

n=4+1=5

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. :

LC-4 Detectors, Transducers, and Sensors

A still more efflcient method for encoding data in
the digital domain is seen in the signal of Figure I-6c. The terms detector, transducer, and sensor are often
Here, we use three light bulbs to represent the three bi- used synonymously, but in fact the terms have some-
nary digits: 20 : l; 2t : 2; and 22 _ 4. However, we what different meanings. The most general of the three
could use switches, wires, light-emitting diodes, or any terms, detector; refers to a mechanical, electrical, or
of a host of electronic devices to encode the informa- chemical device that identifles, records, or indicates a
tion. In this scheme, ON : 1 and OFF : 0, so that our change in one of the variables in its environment, such
number is encoded as shown in Figure 1-6 with the flrst as pressure, temperature, electrical charge, electromag-
and third lights ON and the middle light OFF, which netic radiation, nuclear radiation, particulates, or mole-
represents 4 + 0 + 1 : 5. This scheme is highly effl- cules. This term has become a catchall to the extent that
cient because all of the desired information is presented entire instruments are often referred to as detectors. In
to us simultaneously, just as all of the digits on the face the context of instrumental analysis, we shall use the
of the digital voltmeter in Figure I-3a appear simulta- term detector rn the general sense in which we have just
neously. Data presented in this way are referred to as defined it, and we shall use detection system to refer to
parallel dtgttal data. Data arc transmitted within ana- entire assemblies that indicate or record physical or
lytical instruments and computers by parallel data chemical quantities. An example is the UV (ultraviolet)
transmission. Since data usually travel relatively short detector often used to indi cate and record the presence
distances within these devices, it is economical and ef- of eluted analytes in liquid chromatography.
flcient to use parallel information transfer. This econ- The term transducer refers speciflcally to those de-
omy of short distances is in contrast to the situation in vices that convert information in nonelectrical domains
which data must be transported over long distances to information in electrical domains and the converse.
from instrument to instrument or from computer to Examples include photodiodes, photomultipliers, and
computer. In such instances, communication is carried other electronic photodetectors that produce culrent or
out serially by using modems or other more sophisti- voltage proportional to the radiant power of electro-
cated or faster serial data transmission schemes. We magnetic radiation that falls on their surfaces. Other ex-
will consider these ideas in somewhat more detail in amples include thermistors, strain gauges, and Hall ef-
Chapter 4. fect magnetic field strength transducers. As suggested
10 Chapter 1 Introduction

previously, the mathematical relationship between the where M rs the mass of the crystal, A is its surface area,
electrical output and the input radiant power, tempera- F is the frequency of oscillation of the crystal, and C is
ture, force, or magnetic field strength is called the trans- a proportionality constant. The relationship above indi-
fer function of the transducer. cates that it is possible to measure very small changes in
The term sensor also has become rather broad, but the mass of the crystal if the frequency of the crystal can
in this text we shall reserve the term for the class of an- be measured precisely. As it turns out, it is possible to
alytical devices that are capable of monitoring speciflc measure frequency changes of one part in 107 quite eas-
chemical species continuously and reversibly. There are ily with inexpensive instrumentation. The limit of de-
numerous examples of sensors throughout this text, in- tection for a prczoelectric sensor of this type is esti-
cluding the glass electrode and other ion-selective elec- mated to be about 1 pg, or 1\-tz g. These sensors have
trodes, which are treated in Chapter 23, the Clark oxy- been used to dete ct a variety of gas-phase analytes in-
gen electrode, which is described in Chapter 25, and cluding formaldehyde, hydrogen chloride, hydrogen
optrodes, or flber-optic sensors, which appear in Chap- sulflde, and benzene. They have also been proposed as
ter 7 . Sensors consist of a transducer coupled with a sensors for chemical warfare agents such, as mustard
chemically selective recognition phase. So, for exam- gas and phosgene.
ple, optrodes consist of a phototransducer coupled The prczoelectric mass sensor presents an excellent
with a flber optic that is coated on the end opposite example of a transducer converting a property of the an-
the transducer with a substance that responds specifl- alyte, mass in this case, to a change in an electrical
cally to a particular physical or chemical characteristic quantity, the resonant frequency of the quartz crystal.
of an analyte. This example also illustrates the distinction between a
A sensor that is especially interesting and instruc- transducer and a sensor. In the quartz-crystal microbal-
tive is the quartz crystal microbalance, or QCM. This afice, the transducer is the qtartz crystal, and the selec-
device is based on the piezoelectric characteristics of tive second phase is the polymeric coating. The combi-
qtafiz. When qtartz is mechanically deformed, an elec- nation of the transducer and the selective phase
trical potential develops across its surface. Furthermore, constitute the sensor,
when a voltage is impressed across the faces of a qtartz
crystal, the crystal deforms. A crystal connected in an
1C-5 Readout Devices
appropriate electrical circuit oscillates at a frequency
that is characteristic of the mass and shape of the crystal A readout device is a transducer that converts informa-
and that is arnazingly constant-provided that the mass tion from an electrical domain to a domain that is un-
of the crystal is constant. This property of some crys- derstandable by a human observer. Usually, the trans-
talline materials is called the piezoelectric effect, and duced signal takes the form of the alphanumeric or
forms the basis for the quafiz-crystal microbalance. graphic output of a cathode-ray tube, a series of num-
Moreover, the characteristic constant frequency of the bers on a digital display, the position of a pointer on a
quartz crystal is the basis for modern high-precision meter scale, or, occasionally, the blackening of a photo-
clocks, time bases, counters, timers, and frequency me- graphic plate, or a tracing on a recorder paper. In some
ters, which in turn have led to many highly accurate and instances, the readout device rnay be arranged to give
precise analytical instrumental systems. the analyte concentration directly.
If a quartz crystal is coated with a polymer that se-
lectively adsorbs certain molecules, the mass of the
LC-6 Microprocessors and Cornputers
crystal increases if the molecules are present, thus de-
creasing the resonant frequency of the quartz crystal.
in Instruments
When the molecules are desorbed from the surface, the Most modern analytical instruments contain or are at-
crystal returns to its original frequency. The relationship tached to one or more sophisticated electronic devices
between the change in frequency of the crystal LF and and data domain converters, such as operational ampli-
the change in mass of the crystal LM is given by flers, integrated circuits, analog-to-digital and digital-to-
analog converters, counters, microprocessors, and com-
puters. In order to appreciate the power and limitations
of such instruments, it is necess ary that the scientist de-
 1D Selecting an Analytical Method 11

velop at least a qualitative understanding of how these more time-consuming method that requires little or no
devices function and what they can do. Chapters 3 and 4 preliminary work is often the wiser choice.
provide a brief treatment of these important topics. With answers to the foregoing six questions, a
method can then be chosen, provided that the perfor-
mance characteristics of the various instruments shown
1D SELECTING AN ANALYTICAL in Table 1-l are known.
METHOD
LD-z Performance Characteristics
It is evident from column 2 of Table 1-1 that the modern
chemist has an enormous array of tools for carrying out
of Instrumentsl Figures of Merit
analyses-so many, in fact, that the choice among them Table l-3 lists quantitative performance criteria of in-
is often difflcult. In this section, we describe how such struments that can be used to decide whether a given in-
choices are made. strumental method is suitable for attacking an analytical
problem. These characteristics are expressed in numeri-
cal terms that are called figures of merit. Figures of
1D-1 Defining the Problem
merit permit us to nalrow the choice of instruments for
In order to select an analytical method intelligently; it is a given analytical problem to a relatively few. Selection
essential to define clearly the nature of the analytical among these few can then be based upon the qualitative
problem. Such a deflnition requires answers to the fol- performance criteria listed in Table l-4.
lowing questions: In this section, we define each of the six flgures of
merit listed in Table l-3. These figures are then used
1. What accuracy is required?
throughout the remainder of the text in discussing vari-
2. How much sample is available?
ous instruments and instrumental methods.
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 the
sample matrix? TABLE 1-3 Numerical Criteria for Selecting
6. How many samples are to be analyzed? Analytical Methods
The answer to question 1 is of vital importance because Criterion Figure of Merit
it determines how much time and care will be needed
for the analysis. The answers to questions2 and 3 deter- 1. Precision Absolute standard deviation,
mine how sensitive the method must be and how wide a relative standard deviation
range of concentrations must be accommodated. The coefflcient of variation,
answer to question 4 determines the selectivity required variance
of the method. The answers to question 5 are important
2. Bias Absolute systematic elror,
because some analytical methods in Table 1-1 are ap-
relative systematic error
plicable to solutions (usually aqueous) of the analyte.
Other methods are more easily applied to gaseous sam- 3. Sensitivity Calibration sensitivity,
ples, while still other methods are suited to the direct analytical sensitivity
analysis of solids.
4. Detection limit Blank plus three times
The number of samples to be analyzed (question 6)
standard deviation of a blank
is also an important consideration from the economic
standpoint. If this number is large,, considerable time 5. Concentration range Concentration limit of
and money can be spent on instrumentation, method de- quantitation (LOQ) to
velopment, and calibration. Furthermore, if the number concentration limit of
is large, a method should be chosen that requires the linearity (LOL)
least operator time per sample. On the other hand, if
6. Selectivity Coefflcient of selectivity
only a few samples are to be analyzed, a simpler but
12 Chapter 1 Introduction

TABLE 1,.-4 Other Characteristics TABLE 1-5 Figures of Merit for Precision
to Be Considered of Analytical Methods
in Method Choice
Terms Definition*
1. Speed
N
2. Ease and convenience
\t*, - i)2
i:l
Absolute standard deviation, s
3. Skill required of operator N-1
4. Cost and availability of equipment s
Relative standard deviation RSD
5. Per-sample cost (RSD)
,
Standard deviation of the sm : st{w
mean, sm

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

Precision x

As we show in Section alA,Appendix 1, the precision Variance s2

of analytical data is the degree of mutual agreement *xi: numerical value of the lth measurement.
among data that have been obtained in the same way. J
Precision provides a measure of the random, or indeter- Z*,
x : mean of N measurements : L
minate, error of an analysis. Figures of merit for preci- N
sion include absolute standard deviation, relative stan-
dard deviation, cofficient of variation, and variance.
These terms are defined in Table 1-5.
Ordinarily in deyeloping an analytical method,
Bias every effort is made to identify the source of bias and
As shown in Section alA-Z, Appendix 1, bias provides eliminate it or coffect for it by the use of blanks and by
a measure of the systematic, or determinate, effor of an instrument calibration.
analytical method. Bias is deflned by the equation

bias_p-x1 (1-1) Sensitivity

There is general agreement that the sensitivity of an in-
where Lr, is the population mean for the concentration of
strument or a method is a measure of its ability to dis-
an analyte in a sample that has a true concentration of xr.
criminate between small differences in analyte concen-
Determining bias involves analyzing one or more stan-
tration. Two factors limit sensitivity: the slope of the
dard reference materials whose analyte concentration is
calibration curve and the reproducibility or precision of
known. Sources of such materials are given in refer-
the measuring device. Of two methods that have equal
ences 3 and 4 rn Section aIA-2 of Appendix 1. The re-
precision, the one that has the steeper calibration curve
sults from such an analysis will, however, contain both
will be the more sensitive. A corollary to this statement
random and systematrc effors; but if a sufflcient number
is that if two methods have calibration curves with
of analyses are performed, the mean value may be de- equal slopes, the one that exhibits the better precision
termined with a given level of confldence. As shown in
will be the more sensitive.
Section alB-2,Appendix 1, the mean of 20 or 30 repli-
The quantitative deflnition of sensitivity that is ac-
cate analyses can ordinarily be taken as a good estimate
cepted by the International Union of Pure and Applied
of the population mean p in Equation 1-1. Any differ-
Chemists (IUPAC) is calibration sensitivity, which is
ence between this mean and the known value analyte
the slope of the calibration curve at the concentration of
concentration of the standard reference material can be
interest. Most calibration curves that are used in analyt-
attributed to bias.
ical chemistry arc linear and may be represented by the
If performing 20 replicate analyses on a standard is
equation
impractical, the probable presence or absence of bias can
be evaluated as shown in Example a1 -7 tnAppendix 1. S - mc + Sur Q-2)
 lD Selecting an Analytical Method 13

where S is the measured signal, c is the concentration of S* : Sur + ksur (1-4)

the analyte, is the instrumental signal for a blank,
561
and m rs the slope of the straight line. The quantity Sur Experimentally, S* can be determined by perform-
should be the y-intercept of the straight line. With such ing 20 to 30 blank measurements, preferably over an
curves, the calibration sensitivity is independent of the extended period of time. The resulting data are then
concentration c and is equal to m. The calibration sensi- treated statistically to obtain Sur and sur. Finally, the
tivity as a flgure of merit suffers from its failure to take slope from Equation I-2 is used to convert S* to cm,
into account the precision of individual measurements. which is deflned as the detection limit. That is, the de-
Mandel and Stiehler2 recognrzed the need to in- tection limit is given by
clude precision in a meaningful mathematical statement
of sensitivity and proposed the following deflnition for ( 1-s)
analytical s ensitivity, ^y :

As pointed out by Ingle,3 numerous alternatives,

T_ mls5 ( 1-3)
based correctly or incorrectly on / and e statistics (Sec-
Here, m LS agaLn the slope of the calibration curve, and tion alB-2,Appendix 1), have been used to determine a
s5 is the standard deviation of the measurement. value for k in Equation l-4. Kaiser4 argues that a rea-
The analytical sensitivity offers the advantage of sonable value for the constant is k _ 3. He points out
being relatively insensitive to amplification factors. For that it is wrong to assume a strictly nornal distribution
example, increasing the gain of an instrument by a fac- of results from blank measurements and that when
tor of flve will produce a flvefold increas e Lfi m. Ordi- k - 3, the confidence level of detection will be 95Vo rn
narily, however, this increase will be accompanied by a most cases. He further argues that little is to be gained
coffesponding increase in s5, thus leaving the analytical by usin g a larger value of k-and thus a greater confi-
sensitivity more or less constant. A second advantage of dence level. Long and Winefordner,s in a discussion of
analytical sensitivity is that it is independent of the detection limits, also recommend the use of k - 3.
measurement units for S.
A disadvantage of analytical sensitivity is that it is
often concentration dependent since s5 may yary with * * 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

jT'r*
concentratron. E. ; ;T ; ; T ;
E
H
A least-squares analysis of calibration data for the de-
Detection Limit E.

E termination of lead based upon its flame emission

The most generally accepted qualitative deflnition of H
spectrum yielded the equation
E
detection limit is that it is the minimum concentration
or mass of analyte that can be detected at a known con-
ffi'

E
S - l.l2 cyo + 0.312
Ei
fldence level. This limit depends upon the ratio of the E. where cp6 is the lead concentration in parts per mil-
magnitude of the analytical signal to the size of the sta- E.
lion and S is a measure of the relative intensity of the
tistical fluctuations in the blank signal. That is, unless E'

E lead emission line. The following replicate data were

the analytical signal is larger than the blank by some E then obtained:
multiple k of the variation in the blank owing to random E.

E
elrors, it is impossible to detect the analytical signal E.

No. of Mean
with certainty. Thus, as the limit of detection is ap- E.

E. Concn, ppm Pb Replications Value of S s

proached, the analytical signal and its standard devia- E

tion approach the blank signal 561 and its standard devi- El

E 10.0 10 t1.62 0.15

ation sur. The minimum distinguishable analytical E. 1.00 10 t.Iz 0.025
signal S- is then taken as the sum of the mean blank sig- E
E:
0.000 24 0.0296 0.0082
nal S51 plus a multiple k of the standard deviation of the
blank. That is,

3
J. D. Ing1e ft., I. Chem. Educ,, 1970, 42, 100.
+ H. Kaisel Anal. Chem., 198.7, 42, 53A.
s G. L. Long and
2
1. Mandel and R. D. Stiehler, l. Res. Natl. Bur. Std., 1964, A53, 155. J. D. Winefordneg Anal. Chem., L983, 55, 712A.
14 Chapter 1 Introduction

E
Calculate (a) the calibration sensitivity, (b) the To be very useful, an analytical method should
E
E analytical sensitivity at I and 10 ppm of Pb, and (c) have a dynamic range of at least two orders of magni-
E
the detection limit. tude. Some methods have applicable concentration
E
ranges of five to six orders of magnitude.
E
E
(a) By deflnition, the calibration sensitivity m is
E the slope of the straight line. Thus, m - 1.12.
E
(b) At 10 ppm Pb, T : mlss: l.l2l0.l5 :7.5. Selectivity
At 1 ppm Pb, T : 1.1210.025 : 45.
E
E
Selectivity of an analytical method refers to the degree
H
(c) Applying Equation I-4,
E to which the method is free from interference by other
E
E
S* : 0.0296 + 3 X 0.0082 - 0.054 species contained in the sample matrix. Unfortunately,
E no analytical method is totally free from interference
E Substituting into Equation 1-5 gives
E
from other species, and frequently steps must be taken
E
cm : 0.054 0.0296 _ 0.022 ppm Pb.
to minimize the effects of these interferences.
E
E lJ, Consider, for example, a sample containing an ana-
lyte A as well as potential interfering species B and C. If
c A, cB, and cg aira the concentrations of the three species

and ffiA, ffi8, and ms zta their calibration sensitivities,

Dynamic Range
then the total instrument signal will be given by a mod-
Figure l-7 illustrates the deflnition of the dynamic ified version of Equation l-3. That is,
range of an analytical method, which extends from the
lowest concentration at which quantitative measure- S - rfitct + rfiBcB + mccc + Sur (1-6)
ments can be made (limit of quantitation, or LOQ) to
the concentration at which the calibration curve departs
Let us now define the selectivity coefficient for A
from linearity (limit of linearity, or LOL). The lower with respect to B as
limit of quantitative measurements is generally taken to kB,A: mglm6 (r-7)
be equal to ten times the standard deviation of repetitive
measurements on a blank, or 10sur.At this point, the rel- The selectivity coefflcient then gives the relative
ative standard deviation is about 307o and decreases response of the method to species B as compared with
rapidly as concentrations become larger. At the limit of A. A similar coefficient for A with respect to C is
detection, the relative standard deviation is 100Vo.
kC,A: mglm6 ( 1-8)

Substituting these relationships into Equation l-4

LOL /
Z leads to

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

o
a
a
Selectivity coefflcients can range from zero (no in-
terference) to values a good deal greater than unity.
0)

C) Note that a coefflcient is negative when the interference

cmLoQ causes a reduction in the intensity of the output signal
(n

of the analyte. For example, if the presence of interfer-

ant B causes a reduction in S in Equation I-7, ms wlll
Dynamic range
/l I
carry a negative sign, as will kB,A.
Selectivity coefflcients are useful figures of merit
Concentration for describing the selectivity of analytical methods. Un-
fortunately, they are not widely used except to charac-
Figure 1-7 Useful range of an analytical method. LOq - tetrze the performance of ion-selective electrodes
limit of quantitative measurement; LOL - limit of linear (Chapter 23). Example l-2 tllustrates the use of selec-
response. tivity coefflcients when they are available.
 lE Calibration of Instrumental Methods 15

1E-1 Calibration Curves

To use the calibration curve technique, several stan-
The selectivity coefflcient for an ion-selective elec- dards containing exactly known concentrations of the
rode for K+ with respect to Na+ is reported to be analyte are introduced into the instrument, and the in-
0.052. Calculate the relative effor in the determina- strumental response is recorded. Ordinarily, this re-
tion of K+ in a solution that has a K+ concentration sponse is corrected for the instrument output obtained
of 3.00 x 10-3 M if the Na+ concentration is with a blank. Ideally, the blank contains all of the com-
ra) 2.00 x l0-2 M; (b) 2.00 x 10-3 M; (c) 2.00 x ponents of the original sample except for the analyte.
l0-4 M. Assume that 561 for a series of blanks was The resulting data are then plotted to give a graph of
approximately zero. corrected instrument response versus analyte concen-
(a) Substituting into Equation 1-9 yields tration.
Figure 1-8 shows a typical calibration culve (also
S - tntK+(cr* + kNu*,K*cNa+) + 0 called a working culye or an analytical cwrve). Plots,
such as this, that are linear over a significant concentra-
stms* ,^Z|X + 0.0s2 x 2.00 x 10-2
tion range (the dynamic range) are often obtained and
i3_;
are desirable because they are less subject to effor than
=
If Na+ were not present are nonlinear curves. Not uncommonly, however, non-
linear plots are observed, which require alarger number
Slms*:3'00X10-3
of calibration data to establish accurately the relation-
The relative effor in c6* will be identical to ship between the instrument response and concentra-
the relative effor in Slms* (see Section a1B-5, tion. Usually, an equation is developed for the calibra-
Appendix 1). Therefore, tion curve by a least-squares technique (Appendix a1C)
so that sample concentrations can be computed directly.
4.04 x 10-3 3.00 x 10-3
X 1007o The success of the calibration curve method is crit-
3.00 x 10-3
ically dependent upon how accurately the analyte con-
_ 35Vo centrations of the standards are known and how closely
Proceeding in the same way we find the matrixT of the standards resemble that of the sam-
(b) Eret - 3.57o ples to be analyzed. Unfortunately, matching the matrix
(c) Er"t - 0.357o of complex samples is often difflcult or impossible, and
matrix effects lead to interference errors. To minimize
matrix effects, it is often necessary to separate the ana-
lyte from the interferent before measuring the instru-
lE CALIBRATION OF INSTRUMENTAL ment response.
METHODS

With two exceptions, all types of analytical methods LF,-z Standard Addition Methods
require calibration, a process that relates the mea- Standard addition methods are particularly useful for
sured analytical signal to the concentration of analyte.6 analyzing complex samples in which the likelihood of
The three most common calibration methods include matrix effects is substantial. A standard addition method
the preparation and use of a calibration curve, the stan- can take several forms.S One of the most common
dard addition method, and the internal standard forms involves adding one or more increments of a
method. standard solution to sample aliquots of the same size.

7 The term matrix refers to the collection of all of the various con-
6 The two exceptions are gravimetric and coulometric methods. In stituents making up an analytical sample. In addition to the analyte,
both of these cases, the relationship between the quantity measured the sample matrix includes all of the other constituents of the sam-
and the concentration of analyte can be computed from accurately ple, which are sometimes referred to as the concomitants.
known physical constants. 8 See M. Badeg l. Chem. Educ., L980, 57,703.
16 Chapter 1 Introduction

(.)
o
_o
5
(t)
06
-o
C€

ca 04

-10.0 0.0 10.0 20.0

V5, 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- o_ kVrc, ,
rrvt'v,
kV*c*
(1- 10)
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 by where k is a proportionality constant. A plot ofSas a

successive introductions of increments of the standard function of % is a straight line of the form
to a single measured volume of the unknown. Measure- +
ments are made on the original sample and on the sam-
S - mV, b

ple plus the standard after each addition. In most ver- where the slope m and the intercept b are given by
sions of the standard addition method, the sample
kc,
matrix is nearly identical after each addition, the only m-
difference being the concentration of the analyte or, in vt
cases involving the addition of an excess of an analyti-
and
cal reagent, the concentration of the reagent. A1l other
constituents of the reaction mixture should be identical kV*c*
because the standards are prepared in aliquots of the
b-
vt
sample.
Assume that several identical aliquots V, of the un- Just such a plot is depicted in Figure 1-8.
known solution with a concentratiofl cx are transferred A least-squares analysis (Section alC,Appendix 1)
to volumetric flasks having a volume Vt. To each of can be used to determLfie m and b; cx cafl then be ob-
these flasks is added a variable volume V, mL of a tained from the ratio of these two quantities and the
standard solution of the analyte having a known con- known values of co Vo and Vr. Thus,
centration cs. Suitable reagents are then added, and
b kV*c*lV1 V*c*
each solution is diluted to volume. Instrumental mea-
surements are then made on each of these solutions to
m kcrlVs cs
yietrd an instrument response S. If the instrument re-
it must be if
sponse is proportional to concentration, as
the standard addition method is to be applicable, we ( 1- 11)
may write
 lE Cqlibrqtion of Instrutmental Methods 17

A r alue for the standard deviation in cx can then be ob- (a) In this problem, cs: 11.1 ppm, V,: 10.00 mL,
=ned by assuming that the uncertainties in c' V' and and Vt : 50.00 mL. A plot of the data, shown in
i,-- are negligible with respect to those rn m and b. Then,
Figure 1-8, demonstrates that there is a linear re-
-:e relative variance of the result (srlc*)z is assumed to
lationship between the instrument response and
re the sum of the relative variances of m and b. That is, 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. The
,ahere sm is the standard deviation of the slope and result ts m: 0.03820 and b - 0.2412 and thus
here s6 is the standard deviation of the intercept. Tak-
-'n

rnq the square root of this equation gives

s - 0.03820 v, + 0.2412
Substituting into Equation 1-11 gives
sc:cx (t-r2) x 11.1 :
0.2412
cx: 7 .0I ppm Fe3+
0.03820 x 10.00
-\lternatively, a manual plot of the data may be con-
srmcted, and the linear portion of the plot may be extrap- This value may be determined by graphical ex-
olated to the left of the origin, as shown by the dashed trapolation as illustrated in the flgure as well. The
line of Figure 1-8. The difference between the volume of extrapolated value represents the volume of
the standard added at the origin (zero) and the value of reagent corresponding to zero instrument re-
the volume at the intersection of the straight line with the sponse, which in this case is -6.31 mL. The un-
-r-axis, or the x-intercept (V*)0, is the volume of standard known concentration of the analyte in the origi-
reagent equivalent to the amount of analyte in the sam- nal solution is then calculated as follows:
ple. In addition, the x-intercept corresponds to zero in-
strument response, so that we may write
6.31 mL x 11.1 ppm
10.00 mL
kVrc, kV*c*:0 _ I .01 ppm Fe3+
S_ + ( 1- 13)
Vt Vt
(b) Equations al-35 and aI-36 give the standard de-
By solving Equation 1-13 for c*, we obtain 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+
L
EXAMPLE 1.3
Ten-millimeter aliquots of a natural water sample
were pipetted into 50.00-mL volumetric flasks. Ex- In the interest of saving time or sample, it is possi-
actly 0.00, 5.00, 10.00, 15.00, and 20.00 mL of a ble to perform a standard addition analysis by using
standard solution containing 11.1 ppm of Fe3+ were only two increments of sample. Hera, z single addition
added to each, followed by an excess of thiocyanate of % mL of standard would be added to one of the two
ion to give the red complex Fe(SCN;z+. After dilu- samples, and we can write
tion to voluffie, the instrument response S for each of kV*c*
the flve solutions, measured with a colorimeter, was
vt
found ro be 0.240,0.437,0.621, 0.809, and 1.009, re-
spectively. (a) What was the concentration of Fe3+ in ,1 kV*c*T kV rc,
J2_
the water sample? (b) Calculate a standard deviation V, V,
of the slope and of the intercept and the standard de-
where 51 and 52 are the analytical signals resulting from
viation for the concentration of Fe3 +.
the diluted sample and the diluted sample plus stand ard,
18 Chapter 1 Introduction

respectively. Dividing the second equation by the flrst A major difflculty in applying the internal standard
gives upon reaffangement method is that of finding a suitable substance to serve as
the internal standard and of introducing that substance
? Src'%
Lx - (sz into both samples and standards in a reproducible way.
sr)% The internal standard should provide a signal that is
similar to the analyte signal in most ways but suffi-
ciently different so that the two signals are readily dis-
1E-3 The Internal Standard Method
tinguishable by the instrument. The internal standard
An internal standard is a substance that is added in a must be known to be absent from the sample matrix so
constant amount to all samples, blanks, and calibration that the only source of the standard is the added amount.
standards in an analysis. Alternatively, it may be a ma- For example, lithium is a good internal standard for the
jor constituent of samples and standards that is present determination of sodium or potassium in blood serum
in a large enough amount that its concentration can be because the chemical behavior of lithium is similar to
assumed to be the same in all cases. Calibration then in- both analytes, but it does not occur naturally in blood.
volves plotting the ratio of the analyte signal to the in- As an example, the internal standard method is of-
ternal standard signal as a function of the analyte con- ten used in the determination of trace elements in met-
centration of the standards. This ratio for the samples is als by emission spectroscopy. Thus, in determining
then used to obtain their analyte concentrations from a parts per million of antimony and tin in lead to be used
calibration curve. for the manufacture of storage batteries, the relative in-
An internal standard, if properly chosen and used, tensity of a strong line for each of the minor con-
can compensate for several types of both random and stituents might be compared with the intensity of a
systematic effors. Thus, if the analyte and internal stan- weak line for lead. Ordinarily, these ratios would be less
dard signals respond proportionally to random instru- affected by variables that arise in causing the samples to
mental and method fluctuations, the ratio of these sig- emit radiation. In the development of any new internal
nals is independent of these fluctuations. If the two standard method, we inust verify that changes in con-
signals are influenced in the same way by matrix ef- centration of analyte do not affect the signal intensity
fects, compensation of these effects also occurs. In that results from the internal standard. In order for such
those instances where the internal standard is a major a procedure to be successful, a good deal of time and ef-
constituent of samples and standards, compensation for fort would need to be expended in preparing a set of
errors that arise in sample preparation, solution, and pure lead samples that contains exactly known concen-
cleanup may also occur. 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 solution
visually?
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.

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

0.00 25 0.031 0.0079

2.00 5 0.r73 0.0094
6.00 5 0,422 0.0084
10.00 5 0.702 0.0084
14.00 5 0.956 0.0085
18.00 5 r.248 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+ assuming
that the signal was direcfly proportional to the analyte concentration.

1-11 Exactly 5.00-mL aliquots of a solution containing phenobarbital were measured into
50.00-mL volumetric flasks and made basic with KOH. The following volumes of a
standard solution of irhenobarbital containing2.OOO lLgknl, of phenobarbital were then
introduced 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).