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CHEM 3440 F09 [3]

Some Experiments

Emission of Radiation Emission spectroscopy (X-ray, UV-visible, IR), Fluorescence,Phosphorescence

Absorption of Radiation Spectrophotometry (X-ray, UV-visible, IR),Photoacoustic spectroscopy, NMR, ESR, EXAFS, NEXAFS

Scattering of Radiation Raman spectroscopy, turbidimetry

Diffraction of Radiation X-ray diffraction (XRD), Electron diffraction

Polarization of Radiation Polarimetry, Optical Rotatory Dispersion (ORD),Circular Dichroism (CD)

Mass Gravimetry, Quartz Crystal Nanobalance

Mass-to-Charge Ratio Mass Spectrometry

Thermal Properties Thermal Gravimetric Analysis, Differential Thermal AnalysisDifferential Scanning Calorimtery (TGA, DTA, DSC)

Electrical Properties Potentiometry, Coulometry, Voltammetry, Differential Capacitance,Polarography

Radioactivity Neutron Activation, Isotope Enrichment

CHEM 3440 F09 [4]

Instruments move data across domains

Controls the applied probe.

Measures the systems response.

The Physical and

Chemical Domain

The Analysts

Domain

Instrument Encodes Data

Transformations

ElectricalDomains

Non-electricalDomains

Physical andChemicalDomain

Scale

Position

Number

ChargeCurrent

VoltagePower

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CHEM 3440 F09 [5]

Domain Conversion

An analyst seeks to measure the physicalor chemicalproperties of asystem. An instrument creates an electrical signal which representsthis

datum. As analytical chemists, we must understand and quantify this

representation (Exact? Interferences? Specificity?)

Data proceeds through the instrument where different transducersconvertthe signal from one domain to another.

As analytical chemists, we must understand these transducersand this conversionprocess (Speed? Sensitivity? Impedance?)

The analysis of an instruments behaviour proceeds by characterizing it

as a sequence of data domain converters which can each be analyzedseparately.

It is possible to construct highly integrated instruments where

this separation is murky or completely lost, but not in CHEM3440

CHEM 3440 F09 [6]

Transducers and sensors

All modern instrumentation employs data conversion between at leastthree domains and often more. Each domain transformation is

accomplished by a transducer, or sensor.

Input Transducer converts data from a non-electrical domainto an electrical domain.

Sensor a species-specific transducer (SHC, page 9)Output Transducer converts data from an electrical domain

to a non-electrical domain.

A thermocouplegenerates a specific voltage at a certain temperature. It is atemperature-to-voltage input transducer.

A glass electrodeproduces a potential (voltage) that is related specifically to

the [H+] in solution. It is a sensor.

A stepper motorrunning a pen on a recorder moves the pen in response to acurrent flow. It is a current-to-position output transducer.

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CHEM 3440 F09 [7]

Example: The Thermocouple

A temperature-to-voltage transducer. Connect two dissimilar metal wires appropriately (A-B)-(B-A).

The thermoelectric effect produces a voltage difference between theends of the wires whose magnitude depends upon the temperaturedifference between the two junctions.

Metal 2Metal 1

V

Treference Tmeasure

In modern instruments, the Reference junction has often beenreplaced by an integrated circuit that provides a voltage that is

constant, thus simulating the effect of a thermocouple junction at afixed temperature (usually 0 oC).

e.g. Analog Devices AD594

As a side note, progress in the physical sciences is often dependentupon progress in the measurement sciences. So the take-homemessage is !

CHEM 3440 F09 [8]

Thermocouples - 1

Voltage magnitude depends upon temperature difference (Tm - Tr). Therelationship is called the transfer function.

Tr is almost always chosen to be 0 C. The transfer function for a thermocouple isoften used from a table. However, it is often useful to automate the conversionwhich requires an analytic function. For a thermocouple, the transfer function isgenerally written as

In most cases for well-chosen materials, B and C are quite small and aresafely ignored, leaving us with a l inear transfer function in a small range ofT. For the chromel/alumel (K-type) thermocouple, A has the value of about4 x 10-5V/ C.

This usually requires the use of a voltage amplifier to get easily measuredvoltages (we will see this later : OpAmps are an analytical chemists friend!)

f Tm Tr( )= A Tm Tr( )+ B Tm Tr( )2+

C

Tm Tr( )

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CHEM 3440 F09 [9]

Thermocouples - 2

A measurement instrument is created when the voltage of the thermocoupletransducer is amplified and turned into a current (or voltage) whichsubsequently turns a meter dial to report the temperature as viewed by theanalysts eye.

Physical and

Chemical

Domain

Scale

Position

Number

ChargeCurrent

VoltagePower

1

2

3 4Amplifier

V - IVI

Scale position

Hmm 37 C

Thermocouple

T-V

CHEM 3440 F09 [10]

Transfer Functions

Each transducer has its own transfer function. The thermocouple has the (almost)linear function described earlier.V = f1(T). Although linear relationships are easyto manipulate, any analytical function can be used.

The amplifiergenerally needs to increase the size of the signal, since it is usually inthe millivolt range. This would be another linear relationship.

I = f2(V) = f2(f1(T))The needle on the meter will deflect a certain amount for a given current the passesthrough the coil. This relationship is another transfer function.

D = f3(I) = f3(f2(f1(T)))

The convolution of these functions, describes how a change in temperature will givea rise to a change in needle deflection.

You coulddefine an overall transfer function that directly relates the deflection, D,as a function of T. In effect, this is what the paper scale on the back of the meterdial does!

When is this a good idea ?When is this a bad idea ?

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CHEM 3440 F09 [11]

Example: The pH Meter

A similar situation arises when we want to monitor and record thehydrogen ion activity (pH) of a solution and how it changes with time.

The first sensoris a pair of electrodes; one at a fixed pH and the othersampling the unknown solution. Together they produce a voltagedifference. This is amplified and turned into a current to drive the pendisplacement motor on a chart recorder, permanently recording thechanges in pH with time.

Amplifier

V - I

pH

VI Recorder

CHEM 3440 F09 [12]

Reference Standards

All measurement devices involve a difference detector and areference standard. The magnitude of the signal generated arisesfrom the difference between the sample under test and the referencestandard.

Quantity to be

measured

Quantity of

reference

standard

Difference

Detector

QmQr

QrQm - Qr

Qo = (Qm - Qr) +Qr= Qm

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CHEM 3440 F09 [13]

Example: Double Pan Balance

Unknown mass to

be measured

System for adjusting a

collection of standardweights

DifferenceDetector

CHEM 3440 F09 [14]

Balances - 1

A collection of reference masses are added to the pan until the needlepoints to zero. This is called a null detector .

The result depends upon how small is the smallest reference mass.This defines the units sensitivity.

Smallest increments also dictate the reproducibility of a measurement.This is called the precision.

Only get a good result if the standard masses are correctly calibratedand are not dirty or worn. This affects the m easurementsaccuracy.

When magnitude of difference in null detector is not considered (onlysign is needed to tell operator which way to adjust reference weights toget closer to the null) then it is called a comparator. We will see thatthis is an often used type of null detector.

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CHEM 3440 F09 [15]

Balance2

Top Loading M echanical Balance: Themechanical balance has a series of precise counterweights that are

used to approximately balance off most of the total mass present onthe pan (ie the sample being weighed). The null detector iscalibrated. A final almost null condition provides a measure of thelast fractional mass needed for balance.

Top Loading Electronic Balance: Thecomplete measurement is made by measuring the deformation of amechanical element (often a piezo-electric ceramic) under theweight of the sample.

Bathroom Scale: Manufacturer has calibrated the springsagainst a set of standard masses to make the entire measurement tobe done by the markings of the off-null detector. The referencestandard is remote, instrument is subject to non-linearities,calibration drifts, and potentially large errors. Especially my scalesat home, which are very wrong, always.

What is the logic behind this two-stepweighing process?

What material science constraints doesthis impose on the balance design?

CHEM 3440 F09 [16]

Signal

Every analytical procedure depends upon a signal which is derivedfrom the output of the difference detector.

Every analytical instrument has a non-zero output, even when nodifference is present at the inputs to the detector. This non-zero outputis called the background or baseline.

This background is often slowly varying in time. This changingbackground is called drift.

The analytical signal is the difference between the outputamplitude and the expected baseline at the same moment intime. Quite often, one of the analytical challenges is to predict

the baseline with sufficient certainty. This is especially true forremote instrumentation (think Mars rovers, or Polar researchstations, or high-altitude weather probes)

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CHEM 3440 F09 [17]

Noise

There are other variations in the output signal level; they can occur atall frequencies and constitute an unwanted random or almost randomtime-dependent changes in the output. These variations arecollectively called noise.

Noise is measured in the same units as the signal. This can becurrent, voltage, or power. Two of the most common measures of

noise are:

Peak-to-Peak

RMS : the root-(of the) mean- (of the) square of the difference betweenthe signal and its average value

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 2 4 6 8 10 12 14 16 18 20

Vp-p

CHEM 3440 F09 [18]

Signal-to-Noise

The determination of the magnitude of the analytical signal levelrequires measuring the difference between the background and thesample signal. This measure is blurred by the presence of noise. Onehas to account for both the signal level and the noise level inarriving at this measure.

Because of this, the important quantity is not the signal level alone noris it the noise level alone; rather it is the ratio of the two that dictatesthe measurability of the signal level. This is the signal-to-noiseratio or simply S/ N .

SN

meanstandard deviation

xs

= =

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CHEM 3440 F09 [19]

Performance Characteristics

Aperformance characteristic is used to describe a general property ofanalytical techniques that permit their comparisons so that a user canevaluate it for its applicability in a given situation.

Precision Accuracy

Sensitivity Detection Limit

Quantitation Limit Linearity Limit

Dynamic Range Selectivity

Precision Accuracy

Sensitivity Detection Limit

Quantitation Limit Linearity Limit

Dynamic Range Selectivity

CHEM 3440 F09 [20]

Figure of Merit

A figure of merit is anumber which has beenderived experimentally for agiven analytical instrumentor technique that permitsan evaluation orcomparison of thetechnique to assess itsapplicability to a particularanalysis problem.

Performance characteristicsare measured in terms offigures of merit.

Some Important Figures of Merit

xxi

N

s2 xi x( )

2N1

s s2

RSDs

x

sms

N

Mean

Variance

Standard

Deviation

Relative Standard Deviation

Standard Deviation of the Mean

The N-1 denominator for the Variance is perhaps confusing. We usethis when we have taken a sample of data from a larger population. Ifwe had the entire set of data values (rare in measurement science)then you could use N, but when using such large data sets, thedifference between N and N-1 is usually negligible.

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CHEM 3440 F09 [21]

Precision

Mutual agreement of replicate measurements.

The standard deviation and the variance arethe most common measurements of a set of datasprecision for a series of replicate measurements.It ispresumedto be the result ofrandom errors.

But what are random errors?

Although it is difficult for us to work with any otherhypothesis, it is often verydifficult for us toprovethat we are truly operating with random errors.

Causal factorsTemporal sequencesHysteresisSpecific noise sources in the environment

For example, consider (1) a quantitative study of the arrival times for students to

CHEM3440 in the morning, and (2) a similar study for the arrival time of theprofessor.

CHEM 3440 F09 [22]

Accuracy

Errors in Accuracy arise from the presence ofdeterminate errors, or non-random errors. This shifts the measured mean value of a set ofmeasurements away from the true value and is referred to as the errorof the mean.

There are (at least) three basic types of such errors:

Instrumental: something wrong with the instrument (batteries low,temperature effects the circuitry, calibration errors, etc.

Personal:judgment errors, reading the meter from the wrong angle,lack of careful technique.

Method: often a result of non-ideal chemical behaviour; slow reactions,

contaminants, instability of reagents, loss of analyte by adsorption. Mustuse guaranteed standards (NIST).

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CHEM 3440 F09 [23]

Parallax of Viewing Angles

CHEM 3440 F09 [24]

Sensitivity

Refers to a techniques ability to detect changes in the signal property.

How much does the signal change for a change in the measured variable?

Two factors dictate a techniques sensitivity:

1. Slope of calibration curve (i.e. the nature of the Transfer Function).2. Precision or reproducibility of measurement (i.e. the properties of the

machine)

High Sensitivity

Low Sensitivity

High Precision = High Sensitivity

Low Precision = Low Sensitivity

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CHEM 3440 F09 [25]

Calibration and Analytical Sensitivity

Slope of calibration curve (most curves are linear or are transformedto a linear form,purely for convenience of the operator).

S = m C + Sblsignal

slopeConcentration, or abundance

Blank signal (y-intercept)

m is the calibration sensitivity (e.g. volts per kg). m is not the best figure of merit as it has no measure of the

precision. To incorporate precision, try

= m/sStandard deviation of measurement

Slope of calibration response

Analytical sensitivity factor

This definition is not affected by amplification. Increases in gain lead toincreases m and s by similar factors, so the ratiois unaffected.

Independent ofmeasurement unitsbut may depend upon concentrationsince s can vary with concentration.

CHEM 3440 F09 [26]

Limits of Detection and Quantification

LOD : This is the smallest amount of analyte that can be reliably detected; itsimply determines if the analyte is present or not. Depends upon signal/ noise ratio. Analysis signal must be larger than blank signal. How much larger? Whatdoes rel iably really mean?

Sd = Sblank+ k sblank

Minimum distinguishable

analytical signalMean blank signal

Standard deviation

on blank signal

Usually taken to be 3

LOQ : To determineHow much of the analyte is present?requires a largersignal than the LOD.

The widely accepted level at which the analyte can be quantified is TEN times thestandard deviation.

Sq = Sblank+ 10 sblank

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CHEM 3440 F09 [29]

Dynamic Range

This is the region between the Quantitation Limit (LOQ -Limit ofQuantitation) and the Linearity Limit (LOL - Limit of Linearity). This isthe range over which the technique is useful.

To be viewed as a worthwhile, a technique should have a dynamicrange of at least two orders of magnitude (SHC). Many techniques havea dynamic range of five to six orders of magnitude.

Two orders of magnitudeappears to be quite an arbitrary Figure of Merit.

To be useful, a technique has to perform as required over the required sampleand instrument conditions.

CHEM 3440 F09 [30]

Selectivity

In mostanalyses, we look for a signal that comes from aspecific analyte or class of analytes.

In everyanalysis, we obtain a signal that has a contributionfrom everything that is present in the sample.

We need to minimize contributions from other species and becertain that they are negligible, or else account for theircontribution by determining their selectivity coefficient.

Stotal = R ai + R kij aj(i/j)

Total SignalSignal of Analyte

species i

Signal of other

species j when

in the presence of

species i

Selectivity Coefficient for

the detection j when trying

to detect I.

Activity of

each species

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CHEM 3440 F09 [31]

Calibration Curves: What do they tell us?

Consider the analysis of, for instance, the UV/Vis spectra of an acqueous Co2+

sample (strong absorption band at ~500 nm).

0.014151.01621.71

0.012950.71515.33

0.010350.50310.29

0.010850.2685.63

0.009150.1112.13

0.0037250.03630.00

Standard

Deviation

ReplicantsAverage SignalConcentration

(ppm)

CHEM 3440 F09 [32]

Calibration Curve - 1

1. Use a Least Squares approach to find the parameters for this curveand plot the curve.

2. Use Excel (or similar) spreadsheet.

1. Trendline

2. LINEST function

y = 0.0456x + 0.0231

R2

= 0.9992

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Concentration (ppm)

m = 0.0456

b = 0.0231

m is slope of line and encodeshow the instrument responds tosample concentration.

b is the y-intercept. It is themagnitude of the blank that willbe subtracted from every

measurement.

m =xi yi

xi yiN

xi2

xi( )2

N

b =yi

N m

xiN

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CHEM 3440 F09 [33]


What is the standarddeviation for b and m?

Part of the output fromLINEST in Excel or

Use the following equations.

sr =

yi2

yi( )2

N

xi yi xi yiN

2

xi2

xi( )2

N

N 2

sm = sr1

xi2

xi( )2

N

sb = srxi

2N xi

2

xi( )2

CHEM 3440 F09 [34]


What is the calibration sensitivity for the transfer function?

This is simply m, the slope of the least squares fit: m=0.0456

What is the analytical sensitivity?

This value changes withconcentration so we obtain a value ofg for each data point in the plot.

3.221.71

3.515.33

4.410.29

4.25.63

5.02.13

Analytical SensitivityConcentration

i =m

si

What is the LOD (Limit of Detection)?

L.O.D. =3 sblank

m=

3 0.00370.0456

= 0.24 ppm

What is the LOQ (Limit of Quantitation)?

L.O.Q. =10 sblank

m=

10 0.00370.0456

= 0.81 ppm

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CHEM 3440 F09 [35]


What is the concentration of an unknow n sample when the mean

signal measured for 5 replicated measurments is 0.447?

What is the standard deviation of this measurement? (M = 5).

cx =0.447 b

m=

0.447 0.02310.0456

= 9.3 ppm

sx =sr

m

1

M+

1

N+

cx y( )2

m2

xi2 xi( )

2

N

= 0.16 ppm

What are the 95% confidence limits for this measurement?

recall that we made 5 measurements for this unknown. From Students t-

table, t = 2.78 for this number of measurements at this confidence level.t s

N=

2.78( ) 0.16( )5

= 0.20 ppm

Cx = 9.3 0.2 ppm with 95% confidence

CHEM 3440 F09 [36]

Standard Addition

Most samples are not clean; there are a many other components to thematrix that may interfere either chemically or physically. Recreating theexact environment to use the calibration curve method can be difficult andeven impossible. Standard Addition method is a good attempt aroundthat.

1. Take an aliquot of the sample into a volumetric flask, add any neededadditional components (pH buffer, complexing agent, etc.), and dilute tothe final volume.

Take another volumetric flask and introduce an identical aliquot and sametreatments. However, in addition, introduce a volume of a known

standard solution of the analyte. Then dilute to volume.

1

2

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CHEM 3440 F09 [37]

Standard Addition - 2

Measure the signal (S1 and S2) for both. The signal depends upon theconcentration of the target analyte, which is simply diluted to the finalvolume, Vt. The experiment has some response factor k that relates theconcentration to the signal amplitude. We can write

From these two measurements, we can solve for the unknownconcentration, and obtain the expression

S1 = kVx

Vtcx S2 = k

Vx

Vtcx +

Vs

Vtcs

cx =S1

S2

S1

( )Vs

Vx

cs

CHEM 3440 F09 [38]


The previous scheme only required two measurements. Better results aremade by spiking several samples with varying volumes of addedstandard.

1. Form one sample with the unknown as before.

2. Form a series of samples with unknown and increasing volumes ofadded standard (perhaps 5 total samples).

These 5 samples are measured, each giving its own signal Si. These datacan be graphed as signal against added standard volume.

The slope and intercept can be determined and used to calculate theunknown concentration.

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CHEM 3440 F09 [39]


Consider the following data. The volume of the unknown and each

standard increment is 5.00 mL. The standard has a concentration of 8.7ppm.

1.12125.00

0.95720.00

0.78515.00

0.61710.00

0.4225.00

0.2510.00

Signal (arbitrary)Added Volume

(mL)

Standard Addition Method

y = 0.035x + 0.2548

R2 = 0.9994

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25

Volume of Added Standard (mL)

CHEM 3440 F09 [40]


A least squares analysis gives the slope and intercept (m and b) for thisstraight line. The equations solve to give an expression for the unknownconcentration as

With the equations given previously, we can find the error in m and b andassuming that those errors dominate, we can find the error in our result as

Use Students t-table for 95% and 5 samples. We would report the finalanswer as

cx = 12.7 0.20 ppm at 95% confidence

cx =b

m Vxcs =

0.2548

0.035( ) 5.00( )8.7 = 12.7 ppm

sc = cxsm

m

2

+sb

b

2

= cx0.00045

0.03498

2

+0.00018

0.2548

2

= 12.7 0.0129 = 0.16 ppm

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CHEM 3440 F09 [41]


A graphical solution can be easily obtained. Extrapolate the curve back to

the x-axis (in the negative-x region). This x-intercept represents thevolume of standard solution which has the same amount ofanalyte as the unknow n solution.

Standard Addition Method

y = 0.035x + 0.2548

R2= 0.9994

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-10 -5 0 5 10 15 20 25

Volume of Added Standard (ml)

V0,s = -7.28 ml

-V0,s cs = Vx cx

cx = -(V0,s/Vx) cs

= -(-7.28/5.00) 8.7 ppm

=12.7 ppm

CHEM 3440 F09 [42]

Internal Standard

In this experiment, a substance different from the analyte is added inequal amounts to all unknowns and calibration standards. We measureboth the analyte signal and internal standard signal for all samples andcalculates the ratio of analyte signal to int ernal standard signaland plots this ratio against the standard analyte concentration, forming acalibration curve.

The rest proceeds as with any calibration curve.

This procedure can correct for many matrix interferences.

The major problem is finding the right internal standard and adding itin a reproducible manner for all standards and unknowns.

Best procedure is when internal standard is an isotope of the analyte.Then all interfering chemistry is identical. But must not occur naturallyand the two species must be measurable and distinguishable.

chem3440 overview 20090820

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