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Файл:Optical methods of analysis. Educational aid
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21
out by measuring the absorbance of the analyzed (or standard) solution with
different light filters.
2. Optical density. The absorbance of a solution is influenced by a num-
ber of factors: the nature of the solvent, the pH of the solution, the temperature, the concentration of the electrolyte, and the presence of foreign matter.
It is necessary to choose the analytical conditions so that small changes in
these factors do not significantly change the absorbance. One of the ways is
to measure the optical density relative to the reference solution, which can
be used as a blank sample: a solvent, a sample without coloring reagents,
a solvent with reagents.
The main source of random errors in photometric analysis is the measurement of optical density, i.e. measurement of the intensity of the light flux
after passing through the test solution, as well as through the reference solution. It has been shown that the determination of concentration by photometry
is carried out with an error of 1–2 %, if the concentration of the analyzed substance is such that the value of the optical density is in the range of 0.1–1.0.
This is due to the fact that the error distribution in photometry has the form
shown in Fig. 3.3.
Fig. 3.3. Relative error of photometric determination
3. Choice of cuvettes. A set of cuvettes with different distances between
the inner working faces makes it possible to choose a cuvette of such a working length that the measurements are carried out on the section of the optical
density scale that gives the smallest relative measurement errors. A cuvette
can be considered correctly selected if the value of optical density for
the most concentrated solution does not exceed 0.7–0.8. The working faces
of the cuvette in the cuvette holder are set perpendicular to the light beam.
It should be remembered that on one of the two working plane-parallel faces
of the cuvette there are numbers that indicate the thickness of the light-absorbing layer of the solution in millimeters. When working, these edges must
be clean, free of liquid drops and fingerprints. The solution is poured into
the cuvette a little higher than the risk, which is applied on one of the faces
of the cuvette.
4. The lower limit of detection of a substance by the photometric
method (method sensitivity). The sensitivity of photometric methods is quite
high. The lower detection limit of a substance is calculated by the ratio:
с
min
=A
min
/(εl).
If we take A
= 0.01, l = 5 cm, ε = 103–105, then с
min
= 10-5–10-7 mol/l.
min
22
4 . M E T H O D S F O R D E T E R M I N I N G
C O N C E N T R A T I O N I N O P T I C A L M E T H O D S
OF A N A L Y S I S
4 . 1 . C a l i b r a t i o n c u r v e m e t h o d
Usually, four methods are used to determine the concentration from
the measured value of the optical density of the test solution: the calibration
curve method, the comparison method, the standard addition method, and
the differential photometry method.
In the first three methods, a solvent or a solution prepared with the addition of all reagents, but without the analyte, is used as a reference solution.
In the calibration curve method, a number of standard solutions with
a precisely known concentration are prepared in volumetric flasks, the appropriate reagents (reagents) necessary for the formation of a colored compound are added, the solution volumes are adjusted to the mark with a solvent, and the optical densities of the resulting solutions are measured. According to the measurement data, a dependency graph is built in coordinates:
A – concentration. It should have a linear character when the Bouguer–Lambert–Beer law is fulfilled (Fig. 4.1). Moreover, to build a graph, it is necessary to prepare 5–7 standard solutions with different concentrations and carry
out at least 5 parallel measurements of the optical density of solutions of each
concentration. This will allow, with a minimum error, to build a calibration
graph using the method of mathematical statistics – the method of least
squares (LSM).
Similarly to the preparation of standard solutions, a solution of the investigated (analyzed) solution is prepared, its optical density is measured,
and, using the constructed calibration graph, the content of the substance in
the volume of the analyzed sample is determined. The desired concentration
can be determined by calculation, based on the equation of the obtained
straight line
А = b・с,
where b = tgφ, and φ is the angle of inclination of the straight line.
23
24
Then
с = А/ tgφ = А・k,
where k = сtgφ and is called the sensitivity coefficient.
The formula expression of the calibration dependence allows computer
processing of the measurement results. If the dependence is non-linear,
i.e. the Bouguer–Lambert–Beer law is not fulfilled, to find the concentration
from the optical density value, only the calibration graph is used.
Fig. 4.1. Calibration curve
It is advisable to use the method for a large number of measurements
of the same substance in the absence of interfering components in the analyzed solution.
4 . 2 . C o m p a r i s o n m e t h o d
In the case when a single analysis is carried out, a comparison method
is used. In the comparison method, the obtained value A of the test solution
is compared with the value of the standard solution only if the Bouguer–
Lambert–Beer law is fulfilled. For a standard solution and a solution with an
unknown concentration, the following is true:
А
х
= ε・l・сх and Аst = ε・l・сst.
25
Solving the equation for cx, we get:
с
х
= сst Ах/Аst.
The method gives the most accurate results when the ratio of the optical
densities of the studied and standard solutions is close to unity, i.e. for comparison, choose the concentration of the standard solution that is closest to
the one being determined:
А
х/Аst
= 1.
Under this condition, the Bouguer–Lambert–Beer law is satisfied with
a higher probability, i.e. there is a directly proportional dependence of Ast on
cst and Ax on cx.
To achieve this, 3–4 standard solutions are prepared, their optical densities are measured and the most suitable Ast value is selected from them for
calculating cx.
4 . 3 . S t a n d a r d a d d i t i o n m e t h o d
If there are components in the test solution that contribute to the value
of optical density, the calibration curve method becomes unsuitable, since
the conditions for measuring the optical density of standard solutions without
impurities and the test solution with interfering components are different.
To eliminate the error in determining the concentration in this case,
the method of standard additions is used.
In the standard addition method, equal volumes of the test solution are
placed in a series of volumetric flasks (usually 4). Then, they do not add to
the first flask, but add various volumes of the standard solution to the rest,
add the appropriate reagents (reagents), bring the volume of the solution to
the mark with a solvent, and measure the optical densities of the resulting
colored solutions. It is nessesary build a graph of the dependence of optical
density on the amount of additive. This is a calibration graph obtained against
the background of the analyzed solution with interfering components.
The concentration of the test solution (the amount of substance in the sample)
is determined according to the graph (Fig. 4.2), where c1, c2, c3 are the concentrations of the added standard solution, mg in the volume of the flask; Ax,
26
A
x+1
, A
x+2
, A
x+3
are the optical densities of the test solution and the test solution with additives. The segment 0 - Cx expresses the desired concentration
(amount) of the analyte in the volume (sample) of the solution.
The concentration of the test solution can also be determined by comparing the optical density of the test solution and the solution with the smallest additive. We get two equations based on the Bouguer–Lambert–Beer law:
А
х
= ε・l・сх ,
А
х + n
= ε l・ с
х + n
= ε・l・(сх + сn),
where cn is the concentration of the additive in the analyzed solution.
Further, these equations are solved with respect to cx.
Fig. 4.2. Determination of the concentration of the solution by the method
of standard additions
The advantage of the addition method is that this method eliminates
the systematic error introduced into the determination of concentration by
the influence of impurities, since it creates the same conditions for photometry of the test solution and solutions with a standard additive. In this regard,
it is particularly suitable for the determination of traces of analytes in
the presence of large amounts of foreign components.
4 . 4 . D i f f e r e n t i a l p h o t o m e t r y m e t h o d
The differential photometry method is mainly used to determine large
concentrations when the optical density value exceeds unity. In this method,
27
a series of standard solutions are prepared and their optical density is measured relative to a reference solution, which is the standard solution with
the lowest concentration from a series of given ones. The amount of the analyte is determined either according to the calibration curve A = f (c)
(Fig. 4.3), or by calculation using the comparison method:
cх = с
comp
+ F・Ах,
where F is the conversion factor; Aх and Ast are the optical densities of
the test and standard solutions, measured relative to the reference solution;
cst is the concentration of the substance in the standard solution; c
comp
is
the concentration of the substance in the reference solution.
The method of differential photometry makes it possible to expand
the range of concentrations determined using photometry and to carry out
measurements with high accuracy.
Fig. 4.3. Calibration curve in the method of differential photometry
In some cases, extraction-photometric analysis is used to eliminate
the influence of interfering components and increase the sensitivity of the determination. In this method, the microcomponent to be determined is converted into a water-soluble colored compound, extracted with a suitable solvent, and the extract is photometrically measured. The content of the component is determined by the methods discussed above, and the standard solutions
are carried out through all stages of the analysis. The concentration of the microcomponent in the solvent phase and the separation of interfering components occur during extraction. This method is used, for example, in the analysis of anionic surfactants in water, in the determination of metals in water in
the form of dithizonates in an organic solvent that is added to the analyzed
solution.
28
5 . L A B O R A T O R Y W O R K
ON S P E C T R O P H O T O M E T R Y A N D P H O T O M E T R Y
5 . 1 . L a b o r a t o r y w o r k o n p h o t o m e t r y
The purpose of photometric determination: calculation of the amount
of a component from the value of the optical density of the solution.
Relationship equation: A = f (C).
Applied methods – calibration curve methods, additive method, calculation method.
5 . 1 . 1 . C h o i c e o f o p t i m a l c o n d i t i o n s f o r p h o t o m e t r i c
det e r m i n a t i o n s
As follows from the basic law of absorption, the optical density A of a solution of a component with concentration C will be determined by the values of
ε
λ
and l, which depend on the conditions of the study. Since monochromatic
radiation is not used in photometry, the absorption value will be determined by
the characteristic of the light flux that has passed through the filter.
The choice of a light filter is made in such a way that the transmitted
light flux is absorbed as fully as possible by the component to be determined.
This is achieved when the minimum in the absorption spectrum of the optical
filter coincides with the maximum of the absorption band of the component.
It is also possible to select a light filter according to the principle of
complementary color to the color of the component. The optimal light filter
(from those available in the device) can be selected by comparing the optical
density of the analyzed solution obtained with different filters. Solutions are
poured into cuvettes (30 mm), and in one – a reference solution, in the other –
one of the reference solutions of the component under study. Next, determine
the optical density of the solution with all the filters available in the device.
Choose such a light filter, using which the optical density will be the highest.
29
Cuvette selection. Relative errors of photometric determinations will be
minimal when the optical density of solutions is 0.4–0.5. Therefore, they try
to choose a cuvette with such a working length that the optical density of
the reference solution with the highest concentration of the substance does
not exceed 1.0.
In the future, the construction of a calibration curve and
the measurement of the concentration of the test solution are carried out using
the selected cuvettes and light filters.
5 . 1 . 2 . P h o t o m e t r i c d e t e r m i n a t i o n o f c o p p e r
The absorption value of solutions containing the Cu2+ ion is insufficient
to determine low concentrations of copper. The colored ammonia complex
of copper absorbs much more intensively in the visible part of the spectrum.
The determined copper ion is converted into this complex:
Cu2+ + 4NH3·H2O = [Cu(NH3)4]2+ + 4H2O.
The optical density of the copper ammonia solution will be proportional
to the concentration of copper. Determination of copper can interfere with
cations, which also form colored ammonia (Co2+, Ni2+ and others).
Equipment and reagents:
1. Photometer with a set of cuvettes, 50 ml volumetric flasks, 5 ml vol-
umetric cylinder.
2. Copper salt standard solution with a known concentration (Cst) of
about 10-3 g/ml.
3. Solution NH3·H2O (1:1).
Construction of a calibration graph:
1. Prepare 5 copper ammonia standard solutions using volumes Vst of
1.00; 3.00; 5.00; 8.00; 10.00 ml of standard copper salt solution. First, a solution with the highest concentration is prepared, with the help of which
a light filter and a cuvette are selected. If there are not enough volumetric
flasks, then the flask must be thoroughly washed before preparing the next
solution.
A certain volume of a standard copper salt solution is introduced into
a 50 ml volumetric flask using a burette, 5 ml of ammonia solution is added
30
and the volume is adjusted to the mark with distilled water to prepare a reference solution. Stopper the volumetric flask and mix the resulting solution
thoroughly.
2. Calculate the concentration of copper in the prepared standard solu-
tions (C
Cu
2+
).
When constructing a calibration graph, the concentration of the С
ref
so-
lution can be expressed as a titer T (g/ml) or mg/ml.
The calculation method uses molar concentrations of solutions. Therefore, it is necessary to find the concentrations of standard solutions in other
units (mol/l). The recalculation is carried out according to the formula:
С
ref
(mol/l) = С
ref
(g/ml)
.
The calculated concentrations are entered in the table.
3. The reference solution is prepared as follows: 5 ml of ammonia solution is placed in a 50 ml volumetric flask and adjusted with distilled water
to the mark. In this case, it is acceptable to use distilled water as a comparison
solution.
4. Using the standard solution with the highest concentration of copper,
choose a filter and a cuvette with the optimal working length according to
the method described in subsection 5.1.1.
5. Under the chosen conditions, measure the optical density A of
the reference solutions, starting from the minimum concentration. Each determination is repeated 3 times (A1, A2, A3) finding the average values of Ā
for each solution.
6. Calculate the value of ε for each solution.
7. The values, obtained during measurements and the calculated values
entered in the Table 5.1.
Table 5.1
Results of determinations
№
standard
V
orig
,
ml
С
Cu
2+
,
g/ml
С
Cu
2+
,
mol/l
А1
А2
А3
Ā
ε
General
terms
t = l = С =
Light filter
8. Build a calibration graph in the coordinates Ā – СCu, g/ml.
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