5-Quant_and_Qual.pdf

7/29/2019 5-Quant_and_Qual.pdf

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Qualitative & quantitative analysis

We typically think of GC and LC as

quantitative tools.

In general, chromatography is a blind

method. It indicates the presence of asubstance but not what it is.

Even so, qualitative data can be obtained

even with non-discriminating detectors.

Qualitative analysis

Retention data

can be used for some qualitative work.

The tRis characteristic of a substance,

compared to a standard. To be useful, someproblems must be addressed.

Reproducibility of absolute retention datadepends on several experimental conditions.

Is tR, v

R, v

Ror t

Rbest to use?

Retention time - tR- time elapsed from point of

injection to maximum of peak.

Adjusted tR- t

R- time from maximum of unretained

peak to maximum of eluent.

Hold up time - tM- time required for mobile phase

to traverse the column.

Retention volumes

If the flowrate (Fc) is constant and known

then:

Retention volume = VR

= tRFc

Adjusted VR = VR = tR Fc Hold up volume = Vm = tM Fc

Retention relationships

Retention volume or time may be used for

identification.

For a homologous series, VRcan be accurately

determined by:

ln Vn= a + bn

where Vn = adjusted retention volume n = carbon number a, b = fit parametersand V

n= V

n- V

m

Retention

relationships

To determine an unknown carbon number:

This can only be used for straight chain compounds

and the unknown must fall between n1and n

2.

Expressed as integer.

x= n1+ n2- n1] glnVn2- lnVn1

lnVx- lnVn1

where n2> x > n2


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Absolute retention index

To evaluate species that are not members of a

homologous, we calculate an index value like it

was a paraffin. The value does not need to be a

whole number.

n2and n

1are reference paraffins. Other

homologous series could be use but paraffins are

the norm.

IP= n1+ (n2- n1) lnVn2- lnVn1

lnVx- lnVn1

wheren2> x > n1

Kovats retention index

A modification of the absolute index where:

This index has been determined at differenttemperatures for a large number of compounds.Tables are also available.

The value can be used to compare relatedseparations.

Ik= 100IP

Ik= 100n1+ 100 n2- n1] glnVn2- lnVn1

lnVx- lnVn1

Relative retention data

One practical approach for your own data

is the use of relative retention.

This is a common approach. It only

requires a single standard. If the

standard is the last peak to elute then riis called the retention index.

ri=tR std'

tRunk'

=

VR std'

VRunk'

=kstd

kunk

Relative retention dataTo be useful

Standard should be a part of the sampleor added to it - internal standard.

It should be something that:

Elutes near center of an analysis.

Uses a sample size.

Values will remain pretty constantbetween runs - may vary with a newcolumn.

Only for isothermal/isocraticconditions.

Retention time, tR

Retention time data is adequate for simpleassays like process quality control.

! You already know what is there.

! There are only a few components in the

sample (or only a few of interest).

If a true unknown is observed, you cant

do much more than note its presence!

Other methods

Retention plots

Retention values of materialsbelonging to a homologous series canusually be related to physicalcharacteristics.

In many cases, a semi-log plot of tR

vs. carbon number will give a linearrelationship for earlier members of aseries.

This can be used to pick outpotential series members.


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Other methods

Peak shifting in liquid chromatography

Unlike with GC, LC allows forchanging the nature of the mobilephase.

Altering the solvent can be used tochange the elution times and orders.

This, with the addition of standardscan often give a good match.

Post-column methods

! Post-column collection

and analysis using a

separate qualitative

tool.

! Quant/qual detector.

Couple the GC or LC to

a discriminating

detector.

Other methodsQuantitative analysis

All chromatographic detectors produce a signalthat drives a meter, recorder, integrator or A/D

converter.

While the detectors used for GC and LC are notthe same, quantitative methods are identical.

Each detector will produce a response/unitconcentration. This is substance dependent so

standards must always be used.

Peaks

Each quantitativemethod assumes that

you have one or more

reasonably resolved

peaks.

You must be able to

find the beginning and

end of each peak as

well as its maximum.

Peak height

In some cases, you can

assume that peak height is

proportional to

concentration.

Advantages

Simplicity

Rapid calculations

Disadvantages

Height is more variable

than area

Typically used only with

capillary columns


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Peak areaThis is the major approach for establishing

a relationship between peaks and

concentration.

area ! concentration

Area is determined from a large number of

measurements and detectors usually have very

large dynamic ranges.

This results in a very reliable measurement.

If the peak is approximately Gaussian, how do

we accurately measure its area?

Manual Automated Cut & Weigh Integrating recorder Planimeter Digital integrators Triangulation Computer systemsToday, stand alone digital integrators and

computer systems are the norm.

Still good to review earlier approaches.

Peak area

Cut and weigh

With this approach, each peak is cut from the

recording paper and weighted. Weight is then

considered proportional to area.

Planimeter

A device used to

trace the peak. It

produces a number

that is proportional

to peak area.

TriangulationMain manual method.Assumes that each peak approximates a triangle.

Area can be determined by

area = peak height x width

or

area = peak height x 2 W1/2

Create an isosceles

triangle andextrapolate the heightand width.

This is useful forregular shape peaksbut where you mighthave peak overlap.


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Integrating recorders

A special two pen recorder.

The first pen tracks the chromatographic signal.

The second traces a series of zigzags.

Integrating recorders

The larger the peak response gets, the

more rapidly the second pen sweeps back

and forth.

The total number of zigs and zags can then

be related to the peak area.

If the peak gets to large, the second pen

stops moving. You must keep the peak with

in range.

Digital integrators

Relies on A/D conversion of detector response.

Peak recognition

A peak is initially subjected to A/D

conversion.

This results in a series of discrete

measurements at known time internals.

width of a single

A/D reading

Peak recognition

The sampling rate must

be high enough so that

the number of points

represents the signal

being measured.

This example shows what

can happen if the sampling

rate is too low compared

to variations in the signal.


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Peak recognition

Start of peak.

We can evaluate the change in our data (first

and second derivative) as a way of detecting

the start of a peak.

1st and 2nd

derivative

are zero -

no peak.1st and 2nd

derivative are

positive -

possible peak.

1st and 2nd

derivative

are still

positive

OK - its a peak.

Peak recognition

Top of peak.

We need to know the point of RMAX.

positive

slope

negative

slope

We can look for a change in slope as a way

of detecting the top of a peak.

The true apex can be calculated by using

a quadratic fit of the surrounding points.

Peak recognition

End of peak.

Essentially the reverse

of detecting the start

of a peak.

Typically, a system

will look for a minimum

slope for termination

of a peak.

The maximum peak width

can also be used as a

factor for ending a

peak.


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Digital integrators

Caution!

Peaks are typically process on

the fly.

If a peak is missed, the run

must be repeated.

This can happen even with the

best methods.

Computer systems

Include the same methods of peak detection and

integration as integrators.

Major advantage is that the entire

chromatographic run is stored prior to analysis.

This allows you to test

out various methods of

integration on a single

run and to reanalyze data

if a peak is missed.

(or when your research advisor tells

you what you did wrong!)

Method Time, min Precision, %Planimeter 15 4.1Triangulation 10 2.5 - 4Cut & weigh 20 1.7Int. Recorder 5 1.3Integrator N/A 0.44Computer N/A 0.44

Summary

Quantitative

interpretationOK, now you have all of your peak areas.

Lets assume you knew what you were doing

and all the areas were measured properly.

Big deal!

A relationship between concentration and

area must be established or were just

spinning our wheels.

Determining

concentration

Several approaches can be

used. Use the one that is

most appropriate for your

method.

Methods well cover

Internal normalization

External standard method

Internal standard method


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Internal

normalization

Calculate the total area of

all peaks in a sample and

assume:

Each component produces

a peak

Detector response isnot concentrationdependent

The solvent peak, ifany, is typicallyignored.

Internal normalizationWith these assumptions:

This method is commonly reported as the default

for integrators.

Since most detectors give responses that are

both concentration and substance dependent, themethod only serves to give a ballpark estimateof relative concentrations.

%Ci - % Area=Areatotal

Areai

External standard methodRequirements for proper use:

! Standard solution containing all

eluents to be quantified.

! Standard eluents should be of similar

concentration as unknowns.

! The standard and sample matrix should

be as similar as possible

!Analysis conditions must be identical -stable instrument, same sample size ...

External standard method

You either assume that response is linear over the

entire concentration range or actually measure it.

Then:

This is assuming that the same injection volume

was used for both the unknown and standard.

concunk=areaknown

areaunkconcunk

External standard methodExample - determination of X in MeCl

2

Prepare a standard of X

(20.0 mg in 100 ml MeCl2) - 0.200 g/l

Use an injection volume of 5 l for both thestandard and the unknown.

Measure the areas produced by both the sampleand the unknown.

Area Xstd = 2000 units

Area Xunk = 3830 units

External standard methodNow, determine the concentration of X inyou unknown.

You can now convert to a more appropriateconcentration if required.

concunk= areaknownareaunk concunk

concunk= 20003830

0.200 nlng

concunk= 0.384 nlng


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Overall, the most reliable approach.

BasisA known substance is added at a constantconcentration to all standards andsamples - internal standard.

Since the internal standard is alwayspresent at a constant amount, it can beused to account for variations such asinjection volume during an analysis.


Requirements for an internal standard.

" Must be present at a constant

concentration in all samples and

standards.

" Must be stable and measurable under the

analysis conditions.

" Must not interfere with the analysis or

co-elute with sample components.


Three common approaches are used

Classical method - weighed portions of

the standard and sample are combined

Stock solution - a known volume of the

sample is spiked with a known volume

of the standard

Calibration plot - a series of

standards are run and a curve plotted

based on corrected peak areas.

Internal standard

method

Regardless of the method for introducing

the standard or calibrating, the

calculations are the same.

Our NORM or ISTD substance is now

predetermined and has a fixed value.

Cunk=AISTDunk

AISTDknown

Aknown

AunkCknown


Cunk Amount of unknown

Cknown Amount of known

AISTDknown Area of internal standard in known

AISTDunk Area of internal standard in unknown

Aunk Area of unknown peak

Aknown Area of known peak


It is assumed that variations in the

internal standard area are representativeof the whole analysis from the point

where it is introduced. The earlier, the

better.

Accounts for factors such as:

Sample injection errors or changes

Slow detector variations

Slow column changes

Variations in sample prep


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Examples

Standard

Unknown

Too little

injected

Too much

injected


Example

Prepare a standard that contains 11.3 mg of X and

12.00 mg of ISTD.

Make several 2 l injections and calculate an

average response for each component.

Component Average area X 635 ISTD 1009


Now, inject your unknown.

AreaX = 990

AreaISTD = 1031

CX = (1009/1031) (990/635) x 11.3 mg

= 17.24 mg X in the unknown.

Internal standard plot

method

" Hold the ISTD constant but vary the

amount of the target species in a

series of standards.

" Create a calibration curve using the

corrected areas.

" Useful when the linearity of the

detector is in question.

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5-Quant_and_Qual.pdf