Chemical Analysis

Qualitative Analysis

Quantitative Analysis

Determination

“Analyze” a paint sample for lead

“Determine” lead in a paint sample

Bulk Material

↓

Sample

↓

Analytical Sample

↓

Analytical Matrix

↓

Analyte + Concomitants

BLANK

Same concomitants

No analyte

Difficult if not impossible to acquire a true blank

INSTRUMENTAL ANALYSIS

1) Electroanalytical Chemistry

2) Spectrochemical Analysis

3) Chromatographic Separations

A Typical Instrument

Analytical Sample

Signal Generator Signal

Transducer

Signal Processor

i

Output

V

Types of Signals

1. Emission of Radiation

2. Absorption of Radiation

3. Scattering of Radiation

4. Refraction of Radiation

5. Diffraction of Radiation

6. Rotation of Radiation

7. Electrical Potential

8. Electrical Current

9. Electrical Resistance

10. Mass-to-charge Ratio

11. Reaction Rate

12. Thermal Properties

13. Mass

Signal Sources

1) Analytical Signal

2) Blank Signal

3) Background Signal

4) Dark Signal

Measured Signal: A combination

of these

Analytical Figures of Merit

“Indicate a characteristic of an instrumental technique for a given analyte”

“7”Accuracy, Precision, Signal-to-Noise Ratio

Sensitivity, Limit of Detection

Linearity, Linear Dynamic Range

Accuracy

Indicates how close the measured value is to the true analytical concentration

Requires a Standard Reference Material (SRM) of other official measure

NIST: National Institute of Standards and Technology

Accuracy

Most commonly reported as percent error

│Cm - Ct│

Ct

where:

Cm = measured concentration

Ct = true concentration

x 100%

Precision

Indicates the reproducibility of repetitive measurements of equivalent samples

May be expressed as:

1. Standard Deviation (s or σ)

2. Relative Standard Deviation (RSD)

3. Confidence Limits

Precision

Standard Deviation

For an infinite number of measurements (σ)

For a finite number of measurements (s)

Standard Deviation

Note that both s and σ have the same units as the original values

How many values should be obtained?

Rule of thumb: 16

0

5

10

15

20

25

30

35

40

45

96.0 97.0 98.0 99.0 100.0 101.0 102.0 103.0 104.0

Value

Po

pu

lati

on

Total Population = 1000

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.90%

1.00%

0 5 10 15 20 25 30 35 40 45 50

Number of Samples

Err

or

in M

ea

n

How far is the measured mean from the true value?

0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

0 5 10 15 20 25 30 35 40 45 50

Number of Samples

Err

or

in S

td. D

ev

.

How far is s from σ?

Short Cut: σ ≈ 1/5 (peak-to-peak noise)

Relative Standard Deviation

RSD = σ/mean

Where the mean may be the signal or the analyte concentration. RSD is a unit-less value, so σ must have the same units as

the mean.

RSD is often reported as %RSD, and may be used to compare different techniques.

Confidence Limits

Define an interval that encloses

the true value (Ct) with aspecified level of confidence.

1. Cm ± σ 66.7% Confidence Level

2. Cm ± 2σ 95% Confidence Level

3. Cm ± 3σ 99.0% Confidence Level

Signal to noise Ratio (S/N)

S/N = Sm/σ = 1/RSD

Notes:

1. N = noise (σ)

2. S/N is unitless

3. Always try top maximize S/N

4. S/N is used to compare instruments

5. A plot of S/N versus an instrumental parameter reaches a maximum at the optimum value for that parameter

Sensitivity

Experimental slope of a calibration curve

m = ΔS/ΔC

Sensitivity is almost always specific for one particular instrument.

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12

Concentration (ppm)

Sig

na

l (V

)

m

LOD

LDR

Limit of Detection

The analyte concentration yielding an analytical signal equal to 3 times the standard deviation in the blank signal.

LOD = 3 x σbl / m

By definition, the LOD has just one significant figure!!

Linearity

Measure of how well the observed data follows a straight line.

SA = mC

SA = Analytical Signal

m = calibration sensitivity

Remember SA = Stot - Sbl

Linearity

Plot log(S) versus log(C)

log(SA) = log(m) + log(C)

The slope of this plot should be 1.00

A calibration curve is defined as linear if the

log-log plot has a slope in the range 0.95-1.05

Linear Dynamic Range

The concentration range over which the calibration curve is linear

Lower End → LOD

Upper End

Analyte Concentration where the observed signal falls 5% below the extrapolated line

LDR Units are

“orders of magnitude”

or

“decades”

of analyte concentration

LDR is easiest to observe on log-log plot

If linearity is poor, define an analytically useful range (AUR)

Other figures of merit may be calculated, but these 7 are sufficient.

Selectivity and Resolution may be useful in cases where more than one analyte is

determined in the same sample.