Inappropriate Drug Use in the Elderly-Revised Beer’s Criteria for 2012-Patient Safety Initiative
7. Beer’s Law and It’s Implications for Instrument Construction.
-
Upload
logan-pope -
Category
Documents
-
view
223 -
download
2
Transcript of 7. Beer’s Law and It’s Implications for Instrument Construction.
7. Beer’s Law and It’s Implications for Instrument Construction
dS dn
1. Derive Beer’s Law
ASSUMPTIONS1. No light is emitted
2. dx infinitesimal
3. Monochromatic light uniform on the surface, S
4. dn molecules in a section volume
5. Capture cross sectional area is
M h M kT *
V dx S
dP
P
dn
Sx
xP
P n
0 0
dP
P dn
S0
Photons cap tured
Pho tons im ping ing cap ture area
to ta l area
P dS
S
( ) 0
dS dn
Po P1P2
Consider a large # of boxes
This is an integration
Set up Derivation
ln P
n n
Sx P
P
0
0
dP
P
dn
Sx
xP
P n
0 0
ln lnP Pn
S0
ln
P
P
n
S0
log
.
P
P
n
S0 2 303
AP
PT
n
S
log log
.0 2 303
Substitutions
SV
b n MN
L
cmVa
1
10 3 3
A
P
P
MNL
cmV
V
b
a
log.0
3 3
1
10
2 303
A
NL
cmM b bM
a
1
102 303
3 3
.
A T bM log
What is the absorbance when the light transmitted is 50% of the initialbeam in a 2 cm path length cell for a concentration of 10-3 M?
Deviations
1. Assumed each molecule was independent of the other
When will the assumptions fail?
Molecules not independent when:
Neighbors experience each other
1. High concentrations
2. High electrolyte
3. Large local fields due to large absorption probability (alpha)
Apparent Instrumental Deviations
**polychromatic radiation***
What is the source of polychromatic radiation?
12
AP
PbC
1
1
101
log
Rearrange
P P bC
1 1
10 10
Similarly
AP
PbC
2
2
0 22
log
P P bC
2 2
20 10
Total absorbanceA
P P
P P
P P
P Pmeasured
log log
1
1
2
0 2 0 2
0 2 0 2
2
AP P
P Pmeasured bC bC
log 0 2 0 2
0 0 21
1 210 10
Consider several cases using this equation
AP P
P Pmeasured bC bC
log 0 2 0 2
0 0 21
1 210 10
1. Monochromatic light
1 2
AP P
P Pmeasured bC
log 0 2 0 2
0 0 2110
Ameasured bC
log
1
10
A bCmeasuredbC log 10 Reality check ok
AP P
P Pmeasured bC bC
log 0 2 0 2
0 0 21
1 210 10
2. Case 2
P P Po , , 1 0 2 0
AP P
P Pmeasured bC bC
log 0 0
0 010 101 2
AP
Pmeasured bC bC
log2
10 100
01 2
Ameasured bC bC
log2
10 101 2
Example Calculation
B=1M=0.001Molar absorptivity at 1=2000 at 2 = 200
Ameasured
log2
10 102000 1 10 200 1 103 3
Ameasured
log .
.
2
10 100 494
2 0 2
.494
M
When would this situation apply?
AP P
P Pmeasured bC bC
log 0 2 0 2
0 0 21
1 210 10
3. Stray Light
P P ando , , 1 0 2 2 0
AP P
P Pmeasured bC bC
log 0 1 0 2
0 1 0 2010 101
AP P
P Pmeasured bC
log 0 1 0 2
0 1 0 210 1
What happens when light at 1 is strongly absorbed?
P PbC0 1 0 210 1
AP P
Pmeasured
log 0 1 0 2
0 2
Example Calculation
Stray light is 0.5% of total light
P P0 2 0 10 005 .
AP P
Pmeasured
log
.
.0 1 0 1
0 1
0 005
0 005
Ameasured
log.
..
1 005
0 0052 303
The maximum absorbance the Instrument is capable of measuring is2.303
Comparison of InstrumentsInstrument %stray light maxASpect 20 0.5 2.3McPherson 0.1 3McPherson +filter 0.01 4Double monochromator 0.001 5
Physical Dimensions: 89.1 mm x 63.3 mm x 34.4 mm
Weight: 190 grams
Detector: Sony ILX511 linear silicon CCD array
Detector range: 200-1100 nm
Pixels: 2048 pixels
Pixel size: 14 μm x 200 μm
Pixel well depth: ~62,500 electrons
Sensitivity: 75 photons/count at 400 nm; 41 photons/count at 600 nm
Design: f/4, Symmetrical crossed Czerny-Turner
Focal length: 42 mm input; 68 mm output
Entrance aperture: 5, 10, 25, 50, 100 or 200 µm wide slits or fiber (no slit)
Grating options: 14 different gratings, UV through Shortwave NIR
Detector collection lens option: Yes, L2
OFLV filter options: OFLV-200-850; OFLV-350-1000
Other bench filter options: Longpass OF-1 filters
Collimating and focusing mirrors: Standard or SAG+
UV enhanced window: Yes, UV2
Fiber optic connector: SMA 905 to 0.22 numerical aperture single-strand optical fiber
Spectroscopic Wavelength range: Grating dependent
Optical resolution: ~0.3-10.0 nm FWHM
Signal-to-noise ratio: 250:1 (at full signal)
A/D resolution: 12 bit
Dark noise: 3.2 RMS counts
Dynamic range: 2 x 10^8 (system); 1300:1 for a single acquisition
Integration time: 3 ms to 65 seconds
Stray light: <0.05% at 600 nm; <0.10% at 435 nm
Corrected linearity: >99.8%
Electronics Power consumption: 90 mA @ 5 VDC
Data transfer speed: Full scans to memory every 13 ms with USB 2.0 or 1.1 port, 300 ms with serial port
Czerny-Turnerconstruction
What would be The maximumA this could measure?
What is the maximum amount of absorbance you can measure if the stray light in an instrument is 8%?
If it is 0.05% at 600 nm as for the Ocean Optics?
1. Where does stray light come from?
2. Is stray light likely to be more important for 200 or for 900 nm light?
3. Is stray light likely to be more or less important near a region where solvent interferes?
Double Dispersion Reduces the Stray Light
Comparison of Instruments
Name $ ∆ range Ps/Po%
Spect 20 2-4k 2-8 190-1000 0.5Double Beam 4-15k 195-850 0.1PE-57 >5k 0.2 190-750 <0.1Double dispersive 0.07 185-3125 0.0008Multichannel Array 7-9k 200-920
Beer’s Law and Standard Additions
QUANTITATION
1. Wide chromophore range (universality)-extended by color forming reactionsfor example complexation
2. Good sensitivity
3. Selectivity
4. Accuracy
5. Ease
1. Standard CurvesChoose a wavelength where the molar absorptivity does not change
where would this be?why choose this wavelength region?
Need clear cells and no greasy fingers. Why?
Need to control: temperature; pH; electrolyte/solvent. Why?
2. Standard addition method is useful when matrix (the solution containing the sample analyte) effects complicate matters
Overcoming Matrix Effects in Calibration Curves
Ppm Metal
SignalSolvent
MatrixExample: FlameAtomic Absorption forPb in SeaWater, PbCl2 Is lost lowering the signal
Matrix EffectIf we don’t have a Clear idea whatThe matrix effect isThen we drasticallyMisjudge the concOf the sample fromThe measured signal
Our standardsSuggest this Sample conc.
Standards madeUp in the matrix ofThe sample wouldSuggest this sampleConc.
Matrix
SampleSignal
A bto ta l m oles
to ta l vo lum emeasured
A bn n
V Vnew m easuredunknown added
sam ple o f unknown added,
A bV M V M
V Vmeasuredunkown unknown stam dard s dard
unkown s dard
tan
tan
A bV M V M
Vmeasuredunkown unknown stam dard s dard
to ta l
tan
A bV M
Vb
M
VVmeasured
unkown unknown
to ta l
s dard
to ta lstam dard
tan
Overcoming Matrix Effects in Calibration Curves
50
40
30
20
10
0
A bV M
Vb
M
VVmeasured
unkown unknown
to ta l
s dard
to ta lstam dard
tan
xslopeintercept
y
slope bM
Vs dard
to ta l
tan
in t ercep t bV M
Vunkown unknown
to ta l
in t
tan tan
ercep t
slope
bV M
V
bM
V
V M
M
unkown unknown
to ta l
s dard
to ta l
unkown unknown
s dard
in t tanercep t
slope
M
VMs dard
unkownunknown
M=slope=0.03912
B=intercept=0.2422
Vunknown= 10 ml
Mstandard=11.1ppm
in t tanercep t
slope
M
VMs dard
unkownunknown
0 2422
0 03812
11 1
107 01
.
.
..
ppmppm
A bto ta l m oles
to ta l vo lum emeasured
You did standard addition for the flame lead analysis. You found:
Your unknown volume is 10 mL and the standard you added is 20 ppb.
What is the unknown concentration?
A ppb 00 0521 0 433. . ( )
Two Component Spectra
A bC bCM M N N1 1 1
A bC bCM M N N2 2 2
Must be known
measure
Result is two equations in two unknowns – can be solved