Chapter 2-Fall-2022-2023-C411
Chapter 2-Fall-2022-2023-C411
Chapter 2-Fall-2022-2023-C411
The law relates the fraction of radiation absorbed by an analyte (single or mixture) to its concentration.
𝑃
𝑇= 𝐴 = −log 𝑇
𝑃0
𝑃 Where ,
𝑇=
𝑃0 T: transmittance
P0: incident radiant power or I0: incident intensity
𝐴 = −log 𝑇 P: transmitted radiant power or I : transmitted intensity
𝑃 A: absorbance
𝐴 = −𝑙𝑜𝑔 a: absorptivity (cm-1g-1L)
𝑃0
b: path length of the light through the sample (cm)
𝑃0 c: concentration of the analyte (mol L-1) or (g L-1)
𝐴 = 𝑙𝑜𝑔 : molar absorptivity (cm-1mol-1L)
𝑃
𝑃0 𝑃0
𝐴 = 𝑙𝑜𝑔 =𝑎 𝑏 𝑐 𝐴 = 𝑙𝑜𝑔 =𝑏 𝑐
𝑃 𝑃
Remember :
= 𝑎 x 𝑀𝑤𝑡 𝑤𝑡
number of moles =
𝑀𝑤𝑡
%T = 𝑇 x 100
Have a GO!!:
Derive this math. formula A = 2 − log %𝑇
RRRelation between %T and pathlength
Relation between A and pathelength
Path length /
0 0.2 0.4 0.6 0.8 1.0
cm
Draw the graph of %T vs
pathlength and the graph of A vs %T 100 50 25 12.5 6.25 3.125
pathlength
Absorbance 0 0.3 0.6 0.9 1.2 1.5
eeLinear
eeExponential
Example 2.1
A sample in a 1.0 cm cell is determined with a spectrometer to
transmit 85% light at a certain λ. If the absorptivity of this
substance at this λ is 2.0, what is the concentration of the
substance?
Answer: %T = 𝑇 x 100
Answer:
A = εbc
0.368 = 1.25 x 104cm-1mol-1L x 1.00 cm x c
c = 2.94 x 10-5mol/L
Example 16.3: Amines, RNH2, react with picric acid to form amine
picrates, which absorb strongly at 359 nm ( = 1.25 × 104). An unknown
amine (0.1155 g) is dissolved in water and diluted to 100 mL. A 1-mL
aliquot of this is diluted to 250 mL for measurement. If this final solution
exhibits an absorbance of 0.454 at 359 nm using a 1.00-cm cell, what is
the formula weight of the amine?
Answer: M.wt = 127.2 g/mol
What if the sample is a mixture of absorbing species,
can we still apply Beer Lambert law?
Atotal = A1 + A2 + … An
= 1bc1 + 2bc2 + … + nbcn
Step 2 : from the data of pure solution, calculate the ɛ KMNO4 at the two given λ
The sample and the reference are measured separately (one after the other).
A problem could arise if 1) the two cells are not matched
2) electricity is fluctuating
2) Double beam spectrophotometer
Standard addition must be used whenever the matrix (refers to the components of a
sample other than the analyte ) may change the analytical sensitivity of the method as
example (blood sample). In other words, the slope of the working curve for standards
made with distilled water is different from the same working curve.
Prepare the Standards
The concentration and volume of the stock solution added should be chosen to
increase the concentration of the unknown by about 30% in each succeeding flask.
Slope = (A2-A1)/(C2-C1) = Ax / Cx
Example 2.5: Problem on standard addition method
𝐴=𝑎 𝑏 𝑐
𝐴= 𝑏 𝑐
What are the
types of
deviation from
B- If Beer’s Law is not obeyed: Beer’s law?
The measured absorbance can be either larger or smaller than that predicted
by using Beer’s law:
A- Instrumental Deviations:
1- Fluctuations in the electric current :
cause deviation in single-beam instruments by changing the intensity of the radiation
that is emitted by the EMR source and by changing the response of the detector
(negative deviation or positive deviation)
Give reason: Double beam is
preferred than the single beam
2- Stray radiation:
it can result when EMR is reflected from the walls of the cell and the walls of the cavity
within the instrument into which the cell is placed. Or it is any detected light that is
NOT absorbed by the sample. (Stray light is the most common cause of negative
deviation (why?!))
Stray radiation can be minimized or eliminated by painting the cell compartment with
flat black paint and by carefully sealing the door so that radiation from outside the
compartment is prevented from entering.
3- The use of polychromatic radiation
can be minimized by using narrow bandwidth of radiation and by selecting a wavelength on the
spectral peak using monochromator of suitable resolution power (R)
4- Inaccurate response of the detector, when the intensity of the EMR that strikes the detector is
either very large or very small.
i.e: When the concentration of the absorbing species is large, the intensity of radiation that strikes
the detector is v. small.
When the concentration of the absorbing species is small, the intensity P of the EMR that strikes
the detector is nearly identical to the intensity P0
It can be minimized by restricting absorbance measurements to the concentration range in which
the absorbance (A) varies from about 0.2 to 1.
5- Mismatched cells: non uniform cell thickness can affect a quantitative analysis.
B- Chemical deviations:
1-Association-dissociation reactions:
Neither the copper ion nor the Cl- ions absorb radiation at that wavelength.
p-nitrophenol
G. R. HA H+ + A-
In any system containing a weak acid-base couple, the system should be buffered
3- Polymerization reactions:
The monomeric and polymeric forms of the absorbing species normally do not have
identical spectra e.g. the indicator methylene blue (MeBL):
G. R.
For methylene blue Beer’s law is obeyed only at concentration below about 1 x 10-5M.
At this concentration, the monomer of MeBL is the only form in solution
4- Isobestic point:
A wavelength at which more than one absorbing species have identical absorptivities is
an isobestic point.
To avoid deviations from Beer’s law, we should choose a unique wavelength for the analysis at which all of
the possible absorbing species have the same absorptivity i.e working at the isobestic point.
For example, the different colored forms of an indicator in equilibrium (e.g. the red and yellow forms of
methyl orange) often exhibit an isobestic point, supporting evidence that two two colored species participate
in the equilibrium.
C- Temperature changes:
can cause shifts in chemical equilibria which can alter the absorption at a specific
wavelength. The deviation can be avoided by maintaining the cell at constant
temperature.
E- Solvent effect:
The solvent can affect both the location of an absorbance maximum and the absorptivity of
the compound. (solution: using of double beam instrument where both sample cell and
reference cells contain the same solvent)
Home work:
The problem Type of deviation from solution
Beer’s law
1- Fluctuations in the electric current : …………………………….. ……………………
2-Stray radiation: …………………… ……………………
3- polychromatic radiation …………………… ……………………
4- Inaccurate response of the detector …………………… ……………………
A- high sample concentration
B- very low sample concentration
5- Mismatched cells: …………………… ……………………
A= 2 − log 35 = 0.4559
A=abc
0.4559 = a x 2.0 cm x (15.0 μg/mL x 10-6 g x 103 /L)
= a x M.wt
= 15.197 x 280 = 4.25 x 103 cm-1 mol-1L
Problems on Chapter 2:
(Analytical Chemistry, Gary Christian, 7th edition, 2014 pages 543-544)