Modern Analytical Cheymistry - Chapter 3 ppsx

For our pur-poses it is convenient to divide analytical techniques into two general classes based on whether this signal is proportional to an absolute amount of analyte or a relative am

35

The Language of Analytical Chemistry

specific meaning to other analytical chemists To discuss and learn

analytical chemistry you must first understand its language You are

probably already familiar with some analytical terms, such as

“accuracy” and “precision,” but you may not have placed them in their

appropriate analytical context Other terms, such as “analyte” and

“matrix,” may be less familiar This chapter introduces many important

terms routinely used by analytical chemists Becoming comfortable

with these terms will make the material in the chapters that follow

easier to read and understand.

A process that provides chemical or

physical information about the

constituents in the sample or the sample

itself.

analytes

The constituents of interest in a sample.

matrix

All other constituents in a sample except

for the analytes.

determination

An analysis of a sample to find the

identity, concentration, or properties of

the analyte.

measurement

An experimental determination of an

analyte’s chemical or physical properties.

The first important distinction we will make is among the terms “analysis,”

“deter-mination,” and “measurement.” An analysis provides chemical or physical infor-mation about a sample The components of interest in the sample are called

ana-lytes, and the remainder of the sample is the matrix In an analysis we determine

the identity, concentration, or properties of the analytes To make this

determina-tion we measure one or more of the analyte’s chemical or physical properties.

An example helps clarify the differences among an analysis, a determination,

and a measurement In 1974, the federal government enacted the Safe Drinking

Water Act to ensure the safety of public drinking water supplies To comply with this act municipalities regularly monitor their drinking water supply for potentially harmful substances One such substance is coliform bacteria Municipal water de-partments collect and analyze samples from their water supply To determine the concentration of coliform bacteria, a portion of water is passed through a mem-brane filter The filter is placed in a dish containing a nutrient broth and incu-bated At the end of the incubation period the number of coliform bacterial colonies in the dish is measured by counting (Figure 3.1) Thus, municipal water departments analyze samples of water to determine the concentration of coliform bacteria by measuring the number of bacterial colonies that form during a speci-fied period of incubation

Suppose you are asked to develop a way to determine the concentration of lead in drinking water How would you approach this problem? To answer this question it helps to distinguish among four levels of analytical methodology: techniques, meth-ods, procedures, and protocols.1

A technique is any chemical or physical principle that can be used to study an

analyte Many techniques have been used to determine lead levels.2For example, in graphite furnace atomic absorption spectroscopy lead is atomized, and the ability of the free atoms to absorb light is measured; thus, both a chemical principle (atom-ization) and a physical principle (absorption of light) are used in this technique Chapters 8–13 of this text cover techniques commonly used to analyze samples

A method is the application of a technique for the determination of a specific

analyte in a specific matrix As shown in Figure 3.2, the graphite furnace atomic ab-sorption spectroscopic method for determining lead levels in water is different from that for the determination of lead in soil or blood Choosing a method for deter-mining lead in water depends on how the information is to be used and the estab-lished design criteria (Figure 3.3) For some analytical problems the best method might use graphite furnace atomic absorption spectroscopy, whereas other prob-lems might be more easily solved by using another technique, such as anodic strip-ping voltammetry or potentiometry with a lead ion-selective electrode

A procedure is a set of written directions detailing how to apply a method to a

particular sample, including information on proper sampling, handling of interfer-ents, and validating results A method does not necessarily lead to a single proce-dure, as different analysts or agencies will adapt the method to their specific needs

As shown in Figure 3.2, the American Public Health Agency and the American Soci-ety for Testing Materials publish separate procedures for the determination of lead levels in water

technique

A chemical or physical principle that can

be used to analyze a sample.

method

A means for analyzing a sample for a

specific analyte in a specific matrix.

procedure

Written directions outlining how to

analyze a sample.

Figure 3.1

Membrane filter showing colonies of coliform

bacteria The number of colonies are counted and

reported as colonies/100 mL of sample.

PourRite™ is a trademark of Hach Company/photo

courtesy of Hach Company.

Graphite furnace atomic absorption spectroscopy

Pb in Soil

Procedures

Techniques

Methods

Protocols

Pb in Blood

Pb in Water

EPA

1 Identify the problem

Determine type of information needed (qualitative, quantitative, or characterization)

Identify context of the problem

2 Design the experimental procedure

Establish design criteria (accuracy, precision, scale of operation, sensitivity, selectivity, cost, speed)

Identify interferents

Select method

Establish validation criteria

Establish sampling strategy

Figure 3.2

Chart showing hierarchical relationship among a technique, methods using that technique,

and procedures and protocols for one method (Abbreviations: APHA = American Public

Health Association, ASTM = American Society for Testing Materials, EPA = Environmental Protection Agency)

Figure 3.3

Subsection of the analytical approach to problem solving (see Figure 1.3), of relevance to the selection of a method and the design of an analytical procedure.

protocol

A set of written guidelines for analyzing

a sample specified by an agency.

signal

An experimental measurement that is

proportional to the amount of analyte (S).

Finally, a protocol is a set of stringent written guidelines detailing the

proce-dure that must be followed if the agency specifying the protocol is to accept the

re-sults of the analysis Protocols are commonly encountered when analytical

chem-istry is used to support or define public policy For purposes of determining lead

levels in water under the Safe Drinking Water Act, labs follow a protocol specified

by the Environmental Protection Agency

There is an obvious order to these four facets of analytical methodology

Ide-ally, a protocol uses a previously validated procedure Before developing and

vali-dating a procedure, a method of analysis must be selected This requires, in turn, an

initial screening of available techniques to determine those that have the potential

for monitoring the analyte We begin by considering a useful way to classify

analyti-cal techniques

Analyzing a sample generates a chemical or physical signal whose magnitude is

pro-portional to the amount of analyte in the sample The signal may be anything we

can measure; common examples are mass, volume, and absorbance For our

pur-poses it is convenient to divide analytical techniques into two general classes based

on whether this signal is proportional to an absolute amount of analyte or a relative

amount of analyte

Consider two graduated cylinders, each containing 0.01 M Cu(NO3)2

(Fig-ure 3.4) Cylinder 1 contains 10 mL, or 0.0001 mol, of Cu2+; cylinder 2 contains

20 mL, or 0.0002 mol, of Cu2+ If a technique responds to the absolute amount of

analyte in the sample, then the signal due to the analyte, SA, can be expressed as

where nAis the moles or grams of analyte in the sample, and k is a proportionality

constant Since cylinder 2 contains twice as many moles of Cu2+as cylinder 1,

an-alyzing the contents of cylinder 2 gives a signal that is twice that of cylinder 1

total analysis techniques

A technique in which the signal is

proportional to the absolute amount of

analyte; also called “classical” techniques.

concentration techniques

A technique in which the signal is

proportional to the analyte’s

concentration; also called “instrumental”

techniques.

Figure 3.4

Graduated cylinders containing 0.01 M

Cu(NO3)2 (a) Cylinder 1 contains 10 mL, or

0.0001 mol, of Cu 2+ (b) Cylinder 2 contains

20 mL, or 0.0002 mol, of Cu 2+

© David Harvey/Marilyn Culler, photographer.

accuracy

A measure of the agreement between an

experimental result and its expected

value.

A second class of analytical techniques are those that respond to the relative amount of analyte; thus

where CAis the concentration of analyte in the sample Since the solutions in both cylinders have the same concentration of Cu2+, their analysis yields identical signals

Techniques responding to the absolute amount of analyte are called total

analysis techniques Historically, most early analytical methods used total analysis

techniques, hence they are often referred to as “classical” techniques Mass, volume, and charge are the most common signals for total analysis techniques, and the cor-responding techniques are gravimetry (Chapter 8), titrimetry (Chapter 9), and coulometry (Chapter 11) With a few exceptions, the signal in a total analysis tech-nique results from one or more chemical reactions involving the analyte These re-actions may involve any combination of precipitation, acid–base, complexation, or redox chemistry The stoichiometry of each reaction, however, must be known to solve equation 3.1 for the moles of analyte

Techniques, such as spectroscopy (Chapter 10), potentiometry (Chapter 11), and voltammetry (Chapter 11), in which the signal is proportional to the relative

amount of analyte in a sample are called concentration techniques Since most

concentration techniques rely on measuring an optical or electrical signal, they also are known as “instrumental” techniques For a concentration technique, the rela-tionship between the signal and the analyte is a theoretical function that depends on experimental conditions and the instrumentation used to measure the signal For

this reason the value of k in equation 3.2 must be determined experimentally.

A method is the application of a technique to a specific analyte in a specific matrix Methods for determining the concentration of lead in drinking water can be devel-oped using any of the techniques mentioned in the previous section Insoluble lead salts such as PbSO4and PbCrO4can form the basis for a gravimetric method Lead forms several soluble complexes that can be used in a complexation titrimetric method or, if the complexes are highly absorbing, in a spectrophotometric method Lead in the gaseous free-atom state can be measured by an atomic ab-sorption spectroscopic method Finally, the availability of multiple oxidation states (Pb, Pb2+, Pb4+) makes coulometric, potentiometric, and voltammetric methods feasible

The requirements of the analysis determine the best method In choosing a method, consideration is given to some or all the following design criteria: accuracy, precision, sensitivity, selectivity, robustness, ruggedness, scale of operation, analysis time, availability of equipment, and cost Each of these criteria is considered in more detail in the following sections

Accuracy is a measure of how closely the result of an experiment agrees with the

ex-pected result The difference between the obtained result and the exex-pected result is usually divided by the expected result and reported as a percent relative error

% Error = obtained result – expected result

expected result ×100

Figure 3.5

Two determinations of the concentration of

K + in serum, showing the effect of precision The data in (a) are less scattered and, therefore, more precise than the data in (b).

Analytical methods may be divided into three groups based on the

magnitude of their relative errors.3When an experimental result is

within 1% of the correct result, the analytical method is highly

ac-curate Methods resulting in relative errors between 1% and 5%

are moderately accurate, but methods of low accuracy produce

rel-ative errors greater than 5%

The magnitude of a method’s relative error depends on how

accurately the signal is measured, how accurately the value of k in

equations 3.1 or 3.2 is known, and the ease of handling the sample

without loss or contamination In general, total analysis methods

produce results of high accuracy, and concentration methods range

from high to low accuracy A more detailed discussion of accuracy

is presented in Chapter 4

When a sample is analyzed several times, the individual results are rarely the same

Instead, the results are randomly scattered Precision is a measure of this variability.

The closer the agreement between individual analyses, the more precise the results

For example, in determining the concentration of K+in serum, the results shown in

Figure 3.5(a) are more precise than those in Figure 3.5(b) It is important to realize

that precision does not imply accuracy That the data in Figure 3.5(a) are more

pre-cise does not mean that the first set of results is more accurate In fact, both sets of

results may be very inaccurate

As with accuracy, precision depends on those factors affecting the relationship

between the signal and the analyte (equations 3.1 and 3.2) Of particular

impor-tance are the uncertainty in measuring the signal and the ease of handling samples

reproducibly In most cases the signal for a total analysis method can be measured

with a higher precision than the corresponding signal for a concentration method

Precision is covered in more detail in Chapter 4

The ability to demonstrate that two samples have different amounts of analyte is an

essential part of many analyses A method’s sensitivity is a measure of its ability to

establish that such differences are significant Sensitivity is often confused with a

method’s detection limit.4The detection limit is the smallest amount of analyte

that can be determined with confidence The detection limit, therefore, is a

statisti-cal parameter and is discussed in Chapter 4

Sensitivity is the change in signal per unit change in the amount of analyte and

is equivalent to the proportionality constant, k, in equations 3.1 and 3.2 If ∆SAis

the smallest increment in signal that can be measured, then the smallest difference

in the amount of analyte that can be detected is

Suppose that for a particular total analysis method the signal is a measurement

of mass using a balance whose smallest increment is ±0.0001 g If the method’s

k

k

=

=

total analysis method

concentration method

5.8

(a)

(b)

ppm K +

ppm K +

precision

An indication of the reproducibility of a measurement or result.

sensitivity

A measure of a method’s ability to distinguish between two samples; reported as the change in signal per unit

change in the amount of analyte (k).

detection limit

A statistical statement about the smallest amount of analyte that can be

determined with confidence.

A measure of a method’s freedom from

interferences as defined by the method’s

selectivity coefficient.

selectivity coefficient

A measure of a method’s sensitivity for

an interferent relative to that for the

analyte (KA,I ).

sensitivity is 0.200, then the method can conceivably detect a difference of as little as

in the absolute amount of analyte in two samples For methods with the same ∆SA, the method with the greatest sensitivity is best able to discriminate among smaller amounts of analyte

An analytical method is selective if its signal is a function of only the amount of an-alyte present in the sample In the presence of an interferent, equations 3.1 and 3.2 can be expanded to include a term corresponding to the interferent’s contribution

to the signal, SI,

Ssamp= SA+ SI= kAnA+ kInI (total analysis method) 3.3

Ssamp= SA+ SI= kACA+ kICI (concentration method) 3.4

where Ssampis the total signal due to constituents in the sample; kAand kIare the

sensitivities for the analyte and the interferent, respectively; and nIand CIare the moles (or grams) and concentration of the interferent in the sample

The selectivity of the method for the interferent relative to the analyte is

de-fined by a selectivity coefficient, KA,I

3.5

which may be positive or negative depending on whether the interferent’s effect on the signal is opposite that of the analyte.* A selectivity coefficient greater than +1 or less than –1 indicates that the method is more selective for the interferent than for

the analyte Solving equation 3.5 for kI

substituting into equations 3.3 and 3.4, and simplifying gives

Ssamp= kA(nA+ KA,I×nI) (total analysis method) 3.7

Ssamp= kA(CA+ KA,I×CI) (concentration method) 3.8

The selectivity coefficient is easy to calculate if kAand kIcan be independently

determined It is also possible to calculate KA,Iby measuring Ssampin the presence and absence of known amounts of analyte and interferent

EXAMPLE 3.1

A method for the analysis of Ca2+in water suffers from an interference in the presence of Zn2+ When the concentration of Ca2+is 100 times greater than that of Zn2+, an analysis for Ca2+gives a relative error of +0.5% What is the selectivity coefficient for this method?

k

A,I A

= I

∆nA = 0.0001 g

0.200 0.0005 g

*Although kAand kI are usually positive, they also may be negative For example, some analytical methods work by measuring the concentration of a species that reacts with the analyte As the analyte’s concentration increases, the concentration of the species producing the signal decreases, and the signal becomes smaller If the signal in the absence

Since only relative concentrations are reported, we can arbitrarily assign

absolute concentrations To make the calculations easy, let CCa= 100 (arbitrary

units) and CZn= 1 A relative error of +0.5% means that the signal in the

presence of Zn2+is 0.5% greater than the signal in the absence of zinc Again,

we can assign values to make the calculation easier If the signal in the absence

of zinc is 100 (arbitrary units), then the signal in the presence of zinc is 100.5

The value of kCais determined using equation 3.2

In the presence of zinc the signal is

Ssamp= 100.5 = kCaCCa+ kZnCZn= (1)(100) + kZn(1)

Solving for kZngives a value of 0.5 The selectivity coefficient, therefore, is

Knowing the selectivity coefficient provides a useful way to evaluate an

inter-ferent’s potential effect on an analysis An interferent will not pose a problem as

long as the term KA,I×nIin equation 3.7 is significantly smaller than nA, or KA,I×CI

in equation 3.8 is significantly smaller than CA.

EXAMPLE 3.2

Barnett and colleagues5 developed a new method for determining the

concentration of codeine during its extraction from poppy plants As part of

their study they determined the method’s response to codeine relative to that

for several potential interferents For example, the authors found that the

method’s signal for 6-methoxycodeine was 6 (arbitrary units) when that for an

equimolar solution of codeine was 40

(a) What is the value for the selectivity coefficient KA,Iwhen

6-methoxycodeine is the interferent and codeine is the analyte?

(b) If the concentration of codeine is to be determined with an

accuracy of ±0.50%, what is the maximum relative concentration

of 6-methoxycodeine (i.e., [6-methoxycodeine]/[codeine]) that can be present?

SOLUTION

(a) The signals due to the analyte, SA,and the interferent, SI, are

SA= kACA SI= kICI

Solving these two expressions for kAand kIand substituting into equation 3.6 gives

S C

A I , I I

/ /

=

k

Ca Zn / = Zn = . = 0.5

Ca

0 5 1

C

Ca Ca Ca

= = 100 =

100 1

Since equimolar concentrations of analyte and interferent were used

(CA= CI), we have

(b) To achieve an accuracy of better than ±0.50% the term KA,I×CIin

equation 3.8 must be less than 0.50% of CA;thus

0.0050×CA≥KA,I×CI

Solving this inequality for the ratio CI/CAand substituting the value for

KA,Idetermined in part (a) gives

Therefore, the concentration of 6-methoxycodeine cannot exceed 3.3% of codeine’s concentration

Not surprisingly, methods whose signals depend on chemical reactivity are often less selective and, therefore, more susceptible to interferences Problems with selec-tivity become even greater when the analyte is present at a very low concentration.6

For a method to be useful it must provide reliable results Unfortunately, methods are subject to a variety of chemical and physical interferences that contribute uncer-tainty to the analysis When a method is relatively free from chemical interferences,

it can be applied to the determination of analytes in a wide variety of sample

matri-ces Such methods are considered robust.

Random variations in experimental conditions also introduce uncertainty If a method’s sensitivity is highly dependent on experimental conditions, such as tem-perature, acidity, or reaction time, then slight changes in those conditions may lead

to significantly different results A rugged method is relatively insensitive to changes

in experimental conditions

Another way to narrow the choice of methods is to consider the scale on which the analysis must be conducted Three limitations of particular importance are the amount of sample available for the analysis, the concentration of analyte in the sample, and the absolute amount of analyte needed to obtain a measurable signal The first and second limitations define the scale of operations shown in Figure 3.6; the last limitation positions a method within the scale of operations.7

The scale of operations in Figure 3.6 shows the analyte’s concentration in

weight percent on the y-axis and the sample’s size on the x-axis For convenience,

we divide analytes into major (>1% w/w), minor (0.01% w/w – 1% w/w), trace (10–7% w/w – 0.01% w/w) and ultratrace (<10–7% w/w) components, and we divide samples into macro (>0.1 g), meso (10 mg – 100 mg), micro (0.1 mg –

10 mg) and ultramicro (<0.1 mg) sample sizes Note that both the x-axis and the

y-axis use a logarithmic scale The analyte’s concentration and the amount of

C

I

A A I

≤ 0 0050 = 0 0050 =

0 15 0 033

.

,

S

A I I A , = = 6 =

40 0 15

rugged

A method that is insensitive to changes

in experimental conditions is considered

rugged.

robust

A method that can be applied to analytes

in a wide variety of matrices is

considered robust.

Figure 3.6

Scale of operation for analytical methods.

Adapted from references 7a and 7b.

sample used provide a characteristic description for an analysis For example,

samples in a macro–major analysis weigh more than 0.1 g and contain more than

1% analyte

Diagonal lines connecting the two axes show combinations of sample size and

concentration of analyte containing the same absolute amount of analyte As shown

in Figure 3.6, for example, a 1-g sample containing 1% analyte has the same

amount of analyte (0.010 g) as a 100-mg sample containing 10% analyte or a 10-mg

sample containing 100% analyte

Since total analysis methods respond to the absolute amount of analyte in a

sample, the diagonal lines provide an easy way to define their limitations Consider,

for example, a hypothetical total analysis method for which the minimum

de-tectable signal requires 100 mg of analyte Using Figure 3.6, the diagonal line

repre-senting 100 mg suggests that this method is best suited for macro samples and

major analytes Applying the method to a minor analyte with a concentration of

0.1% w/w requires a sample of at least 100 g Working with a sample of this size is

rarely practical, however, due to the complications of carrying such a large amount

of material through the analysis Alternatively, the minimum amount of required

analyte can be decreased by improving the limitations associated with measuring

the signal For example, if the signal is a measurement of mass, a decrease in

the minimum amount of analyte can be accomplished by switching from a

con-ventional analytical balance, which weighs samples to ±0.1 mg, to a semimicro

(±0.01 mg) or microbalance (±0.001 mg)

Ultratrace

Trace

Minor

g mg

µ g ng

1 g sample, 1% analyte ppm

ppb

100 mg10 mg

1 mg100

µg 10 µg 1 µg

0.1 g sample, 10% analyte

0.01 g sample, 100% analyte

Macro

Micro Meso

Ultramicro Major

10 –10 %

10 –9 %

10 –8 %

10 –7 %

10 –6 %

10 –5 %

10 –4 %

10 –3 %

10 –2 %

0.1%

1%

10%

100%

–log(Weight of sample)

1 0.1 0.01

0.1 0.01

0.1 0.01

100 10 1

100

100

10

10 1

1

Concentration methods frequently have both lower and upper limits for the amount of analyte that can be determined The lower limit is dictated by the small-est concentration of analyte producing a useful signal and typically is in the parts per million or parts per billion concentration range Upper concentration limits exist when the sensitivity of the analysis decreases at higher concentrations

An upper concentration level is important because it determines how a sam-ple with a high concentration of analyte must be treated before the analysis Con-sider, for example, a method with an upper concentration limit of 1 ppm (micro-grams per milliliter) If the method requires a sample of 1 mL, then the upper limit on the amount of analyte that can be handled is 1 µg Using Figure 3.6, and following the diagonal line for 1 µg of analyte, we find that the analysis of an ana-lyte present at a concentration of 10% w/w requires a sample of only 10 µg! Ex-tending such an analysis to a major analyte, therefore, requires the ability to ob-tain and work with very small samples or the ability to dilute the original sample accurately Using this example, analyzing a sample for an analyte whose concen-tration is 10% w/w requires a 10,000-fold dilution Not surprisingly, concentra-tion methods are most commonly used for minor, trace, and ultratrace analytes,

in macro and meso samples

Finally, analytical methods can be compared in terms of their need for equipment, the time required to complete an analysis, and the cost per sample Methods relying

on instrumentation are equipment-intensive and may require significant operator training For example, the graphite furnace atomic absorption spectroscopic method for determining lead levels in water requires a significant capital investment

in the instrument and an experienced operator to obtain reliable results Other methods, such as titrimetry, require only simple equipment and reagents and can be learned quickly

The time needed to complete an analysis for a single sample is often fairly simi-lar from method to method This is somewhat misleading, however, because much

of this time is spent preparing the solutions and equipment needed for the analysis Once the solutions and equipment are in place, the number of samples that can be analyzed per hour differs substantially from method to method This is a significant factor in selecting a method for laboratories that handle a high volume of samples The cost of an analysis is determined by many factors, including the cost of necessary equipment and reagents, the cost of hiring analysts, and the number of samples that can be processed per hour In general, methods relying on instruments cost more per sample than other methods

Unfortunately, the design criteria discussed earlier are not mutually independent.8

Working with smaller amounts of analyte or sample, or improving selectivity, often comes at the expense of precision Attempts to minimize cost and analysis time may decrease accuracy Selecting a specific method requires a careful balance among these design criteria Usually, the most important design criterion is accuracy, and the best method is that capable of producing the most accurate results When the need for results is urgent, as is often the case in clinical labs, analysis time may be-come the critical factor

The best method is often dictated by the sample’s properties Analyzing a sam-ple with a comsam-plex matrix may require a method with excellent selectivity to avoid