Spektrophotometry Method Characterization
1. Aims
- Determining KmnO4 concentration
- Charakterisation of spectrophotometry method
2. Introduction
2.1.
Spectrophotometer
The overall design
If you pass white light through a coloured substance, some of the light
gets absorbed. A solution containing hydrated copper(II) ions, for
example, looks pale blue because the solution absorbs light from the red
end of the spectrum. The remaining wavelengths in the light combine in
the eye and brain to give the appearance of cyan (pale blue).
Some colourless substances also absorb light - but in the ultra-violet
region. Since we can't see UV light, we don't notice this absorption.
Different substances absorb different wavelengths of light, and this can be
used to help to identify the substance - the presence of particular metal
ions, for example, or of particular functional groups in organic compounds.
The amount of absorption is also dependent on the concentration of the
substance if it is in solution. Measurement of the amount of absorption can
be used to find concentrations of very dilute solutions.
An absorption spectrometer measures the way that the light absorbed by
a compound varies across the UV and visible spectrum.
A simple double beam spectrometer
We'll start with the full diagram, and then explain exactly what is going on
at each stage.
IMPORTANT! The colour-coding of the light beams through the spectrometer is NOT to
show that some light is red or blue or green. The colours are simply to emphasise the two
different paths that light can take through the device.
Where the light is shown as a blue line, this is the path that it will always take. Where it is
shown red or green, it will go either one way or the other - depending on how it strikes the
rotating disc (see below).
The light source
You need a light source which gives the entire visible spectrum plus the
near ultra-violet so that you are covering the range from about 200 nm to
about 800 nm. (This extends slightly into the near infra-red as well.)
Note: "Near UV" and "near IR" simply means the parts of the UV and IR spectra which
are close to the visible spectrum. If you aren't happy about how the various types of
electromagnetic radiation relate to each other, follow this link before you go on. Use the
BACK button on your browser to return here later.
You can't get this range of wavelengths from a single lamp, and so a
combination of two is used - a deuterium lamp for the UV part of the
spectrum, and a tungsten / halogen lamp for the visible part.
Note: A deuterium lamp contains deuterium gas under low pressure subjected to a high
voltage. It produces a continuous spectrum in the part of the UV spectrum we are
interested in.
The combined output of these two bulbs is focussed on to a diffraction
grating.
The diffraction grating and the slit
You are probably familiar with the way that a prism splits light into its
component colours. A diffraction grating does the same job, but more
efficiently.
The blue arrows show the way the various wavelengths of the light are
sent off in different directions. The slit only allows light of a very narrow
range of wavelengths through into the rest of the spectrometer.
By gradually rotating the diffraction grating, you can allow light from the
whole spectrum (a tiny part of the range at a time) through into the rest of
the instrument.
The rotating discs
This is the clever bit! Each disc is made up of a number of different
segments. Those in the machine we are describing have three different
sections - other designs may have a different number.
The light coming from the diffraction grating and slit will hit the rotating
disc and one of three things can happen.
1. If it hits the transparent section, it will go straight through and pass
through the cell containing the sample. It is then bounced by a
mirror onto a second rotating disc.
This disc is rotating such that when the light arrives from the first
disc, it meets the mirrored section of the second disc. That bounces
it onto the detector.
It is following the red path in the diagram:
2. If the original beam of light from the slit hits the mirrored section of
the first rotating disc, it is bounced down along the green path. After
the mirror, it passes through a reference cell (more about that
later).
Finally the light gets to the second disc which is rotating in such a
way that it meets the transparent section. It goes straight through to
the detector.
3. If the light meets the first disc at the black section, it is blocked and for a very short while no light passes through the spectrometer.
This just allows the computer to make allowance for any current
generated by the detector in the absence of any light.
The sample and reference cells
These are small rectangular glass or quartz containers. They are often
designed so that the light beam travels a distance of 1 cm through the
contents.
The sample cell contains a solution of the substance you are testing usually very dilute. The solvent is chosen so that it doesn't absorb any
significant amount of light in the wavelength range we are interested in
(200 - 800 nm).
The reference cell just contains the pure solvent.
The detector and computer
The detector converts the incoming light into a current. The higher the
current, the greater the intensity of the light.
For each wavelength of light passing through the spectrometer, the
intensity of the light passing through the reference cell is measured. This
is usually referred to as Io - that's I for Intensity.
The intensity of the light passing through the sample cell is also measured
for that wavelength - given the symbol, I.
If I is less than Io, then obviously the sample has absorbed some of the
light. A simple bit of maths is then done in the computer to convert this into
something called the absorbance of the sample - given the symbol, A.
For reasons which will become clearer when we do a bit of theory on
another page, the relationship between A and the two intensities is given
by:
On most of the diagrams you will come across, the absorbance ranges
from 0 to 1, but it can go higher than that.
An absorbance of 0 at some wavelength means that no light of that
particular wavelength has been absorbed. The intensities of the sample
and reference beam are both the same, so the ratio Io/I is 1. Log10 of 1 is
zero.
An absorbance of 1 happens when 90% of the light at that wavelength has
been absorbed - which means that the intensity is 10% of what it would
otherwise be.
In that case, Io/I is 100/I0 (=10) and log10 of 10 is 1.
Note: If you don't feel comfortable with logarithms, don't worry about it. Just accept that
an absorbance scale often runs from zero to 1, but could go higher than that in extreme
cases (in other words where more than 90% of a wavelength of light is absorbed).
The chart recorder
Chart recorders usually plot absorbance against wavelength. The output
might look like this:
Spectrometer Specifications:
The following table is an example of spectrometer Specifications
Specifications
Item
Description
Setting wavelength range 190  1100nm
Measurement wavelength 190  900nm (up to 1100nm with special detector)
range
Wavelength accuracy
0.3nm with auto wavelength correction included
Wavelength repeatability
0.1nm
Wavelength scanning
speed
Wavelength slew rate: about 3200nm/min
Wavelength scan rate: about 900  160nm/min
Monitor scan rate: about 2500nm/min
Wavelength setting
At 1nm units for scan start and scan end wavelengths, and 0.1nm units for other
wavelengths
Lamp interchange
wavelength
Auto switching synchronized with wavelength, switching range selectable
between 282  393nm (0.1nm units)
Spectral bandwidth
6-step switching among 0.1/0.2/0.5/1/2/5nm
Response
Optimum response speed automatically set depending on bandwidth, minimum
0.1sec
Resolution
0.1nm
Stray light
UV-2450
UV-2550
Less than 0.015%
Less than 0.0003%
(220nm, NaI 10g/L solution)
Less than 0.015%
Less than 0.0003%
(340nm, UV-39 filter)
Photometric system
Double-beam, direct ratio system with dynode feedback
Photometric modes
Absorbance (Abs.), transmittance (%), reflectance (%), energy (E)
Photometric range
Absorbance: -4  5 Abs
Transmittance, reflectance: 0.0  999.9%
Recording range
Absorbance: -9.999  9.999 Abs
Transmittance, reflectance: -999.9  999.9%
Photometric accuracy
0.002 Abs (0  0.5 Abs)
0.004 Abs (0.5  1.0 Abs)}Tested with NIST 930D standard filter
0.3%T (0  100% T)
* If the detector has been replaced with a near infrared sensitive photomultiplier, the standard optical specifications of the above
instrument will not be satisfied.
Item
Description
Photometric
repeatability
0.001 Abs (0 ~ 0.5 Abs)
0.002 Abs (0.5 ~ 1.0 Abs)
0.1%T
Baseline flatness
0.001 Abs (excluding noise, using 2nm slit, and slow wavelength scanning
speed)
Baseline correction
Auto correction using PC (Stored baseline is automatically loaded when power is
switched on, re-correction is possible)
Drift
0.0004Abs/h (after power is on for 2 hours)
Temperature and
humidity requirements
15 ~ 35°C, 45 ~ 80% (no condensation, less than 70% above 30°C)
Light source
50W halogen lamp (2,000 hours life), deuterium lamp (socket type), light source
auto position adjustment built in
Monochromator
UV-2450
Single monochromator, high-performance blazed holographic grating in aberrationcorrected Czerny-Turner mounting
UV-2550
Grating/Grating type double monochromator, Pre-monochromator: double-blazed
holographic grating Main monochromator: high-performance blazed holographic
grating in aberration-corrected Czerny-Turner mounting
Detector
Photomultiplier R-928
Sample compartment
Internal dimensions: 150W x 260D x 120H (mm)
Distance between light beams: 100mm
Maximum light path length of cell: 100 mm
Power requirements
AC100, 120, 220, 240 V, switch selectable
50/60Hz; 250 VA
Dimensions
570W x 660D x 275H (mm)
Weight
About 36 kg
(PC and printer are not included.)
UVProbe Software Specifications
Operating System
Windows XP Pro/2000 Pro
Instruments
UV-1601 Series, UV-2401/2501 Series
Data Acquisition
Modes
Spectrum, Kinetics and Photometric
General


Multitasking (Possible to execute data processing while measurement is
being executed.)
Customizable measurement screen layout (wavelengths, data display font
and font size, colors, displayed number of rows)

GLP/GMP compliant (security, history)

Real time concentration display

Spectrum Mode
Comparison of multiple spectra/relative processing

Save all processed data with original data set including a history of all
manipulations

Spectrum enlargement/shrinking, auto scale and Undo/Redo of these
operations

Data Processing in
Spectrum Mode


Photometric
(Quantitation) Mode
Annotation on spectrum screen
Normalization, Point Pick, peak/valley detection, area calculation
Transformations: 1st - 4th derivatives, smoothing, reciprocal, square root,
natural log, logarithm power, Abs. to %T conversion, and exponential, KubelkaMunk conversion

Ensemble averaging, interpolation, data set and constants arithmetic
(between spectra, between spectra and constants)

Single wavelength, multi wavelength (includes 1, 2 or 3 wavelengths),
spectrum quantitation (peak, maximum, minimum, area, etc. for specified
wavelength ranges)

Multi-point, single point, K-factor calibration curves (1st, 2nd, 3rd order
function fits, pass-through-zero specification)


Photometric processing with user-defined functions (+, -, x,
, Log, Exp, etc. functions, including factors)
Weight correction, dilution factor correction, and other corrections using
factors


Averaging of repeat measurement data
Simultaneous display of standard table, unknown table and calibration
curves


Kinetics (Time
Course) Mode
Display of Pass/Fail indications
Comparison/relative data processing of multiple time course data

Single or double wavelength measurement (difference or ratio)

Simultaneous display of time course data, enzyme table and graphs


Enzyme kinetics calculation (for single or multicell)
Michaelis-Menten calculations and graph creation (Michaelis-Menten,
Lineweaver-Burk, Hanes, Woolf, Eadie-Hofstee), Dixon plot, Hill plot

Unitary management of sample information including original data, sample
weight and dilution factors, etc.

Event recording such as addition of reagents during measurement

Time course spectrum data processing (same as in spectrum data
processing)

Report Generator
Preview and print functions for customized formats

Layout and editing of templates

Quick printing using report templates


Multi-page printout support
Insert date, time, text, and drawing objects including lines, circles and
rectangles

Insert spectrum and quantitation data, method and history

Headers and footers easily inserted

2.2.
Specify graph line thickness (as in all modulules), font style and size
The Lamber – Beer Law
A. Equations
Diagram of Beer–Lambert absorption of a beam of light as it travels through a cuvette of
width ℓ.
The law states that there is a logarithmic dependence between the transmission (or
transmissivity), T, of light through a substance and the product of the absorption
coefficient of the substance, α, and the distance the light travels through the material (i.e.
the path length), ℓ. The absorption coefficient can, in turn, be written as a product of
either a molar absorptivity of the absorber, ε, and the concentration c of absorbing species
in the material, or an absorption cross section, σ, and the (number) density N of
absorbers.
For liquids, these relations are usually written as
whereas for gases, and in particular among physicists and for spectroscopy and
spectrophotometry, they are normally written
where I0 and I are the intensity (or power) of the incident light and the transmitted light,
respectively; σ is cross section of light absorption by a single particle and N is the density
(number per unit volume) of absorbing particles. The difference between the use of base
10 and base e is purely conventional, requiring a multiplicative constant to convert
between them.
The transmission (or transmissivity) is expressed in terms of an absorbance which for
liquids is defined as
whereas for gases, it is usually defined as
This implies that the absorbance becomes linear with the concentration (or number
density of absorbers) according to
and
for the two cases, respectively.
Thus, if the path length and the molar absorptivity (or the absorption cross section) are
known and the absorbance is measured, the concentration of the substance (or the number
density of absorbers) can be deduced.
Although several of the expressions above often are used as Beer–Lambert law, the name
should strictly speaking only be associated with the latter two. The reason is that
historically, the Lambert law states that absorption is proportional to the light path length,
whereas the Beer law states that absorption is proportional to the concentration of
absorbing species in the material.[1]
If the concentration is expressed as a mole fraction i.e. a dimensionless fraction, the
molar absorptivity (ε) takes the same dimension as the absorption coefficient, i.e.
reciprocal length (e.g. m−1). However, if the concentration is expressed in moles per unit
volume, the molar absorptivity (ε) is used in L·mol−1·cm−1, or sometimes in converted SI
units of m2·mol−1.
The absorption coefficient α' is one of many ways to describe the absorption of
electromagnetic waves. For the others, and their interrelationships, see the article:
Mathematical descriptions of opacity. For example, α' can be expressed in terms of the
imaginary part of the refractive index, κ, and the wavelength of the light (in free space),
λ0, according to
In molecular absorption spectrometry, the absorption cross section σ is expressed in terms
of a linestrength, S, and an (area-normalized) lineshape function, Φ. The frequency scale
in molecular spectroscopy is often in cm−1, wherefore the lineshape function is expressed
in units of 1/cm−1, which can look funny but is strictly correct. Since N is given as a
number density in units of 1/cm3, the linestrength is often given in units of
cm2cm−1/molecule. A typical linestrength in one of the vibrational overtone bands of
smaller molecules, e.g. around 1.5 μm in CO or CO2, is around 10−23 cm2cm−1, although
it can be larger for species with strong transitions, e.g. C2H2. The linestrengths of various
transitions can be found in large databases, e.g. HITRAN. The lineshape function often
takes a value around a few 1/cm−, up to around 10/cm−1 under low pressure conditions,
when the transition is Doppler broadened, and below this under atmospheric pressure
conditions, when the transition is collision broadened. It has also become commonplace
to express the linestrength in units of cm−2/atm since then the concentration is given in
terms of a pressure in units of atm. A typical linestrength is then often in the order of 10−3
cm−2/atm. Under these conditions, the detectability of a given technique is often quoted in
terms of ppm•m.
The fact that there are two commensurate definitions of absorbance (in base 10 or e)
implies that the absorbance and the absorption coefficient for the cases with gases, A' and
α', are ln 10 (approximately 2.3) times as large as the corresponding values for liquids,
i.e. A and α, respectively. Therefore, care must be taken when interpreting data that the
correct form of the law is used.
The law tends to break down at very high concentrations, especially if the material is
highly scattering. If the light is especially intense, nonlinear optical processes can also
cause variances.
B. Derivation
The derivation is quite simple in concept. There are many details, so think of this first
paragraph as a conceptual overview. Divide the absorbing sample into thin slices that are
perpendicular to the beam of light. The light that emerges from a slice is slightly less
intense than the light that entered because some of the photons have run into molecules in
the sample and did not make it to the other side. For most cases where measurements of
absorption are needed, a vast majority of the light entering the slice leaves without being
absorbed. Because the physical description of the problem is in terms of differences--intensity before and after light passes through the slice---we can easily write an ordinary
differential equation model for absorption. The difference in intensity due to the slice of
absorbing material dI is reduced; leaving the slice, it is a fraction β of the light entering
the slice I. The thickness of the slice is dz, which scales the amount of absorption (thin
slice does not absorb much light but a thick slice absorbs a lot). In symbols, dI = βIdz,
or dI / dz = βI. This conceptual overview uses β to describe how much light is
absorbed. All we can say about the value of this constant is that it will be different for
each material. Also, its values should be constrained between -1 and 0. The following
paragraphs cover the meaning of this constant and the whole derivation in much greater
detail.
Assume that particles may be described as having an absorption cross section (i.e. area),
σ, perpendicular to the path of light through a solution, such that a photon of light is
absorbed if it strikes the particle, and is transmitted if it does not.
Define z as an axis parallel to the direction that photons of light are moving, and A and dz
as the area and thickness (along the z axis) of a 3-dimensional slab of space through
which light is passing. We assume that dz is sufficiently small that one particle in the slab
cannot obscure another particle in the slab when viewed along the z direction. The
concentration of particles in the slab is represented by N.
It follows that the fraction of photons absorbed when passing through this slab is equal to
the total opaque area of the particles in the slab, σAN dz, divided by the area of the slab A,
which yields σN dz. Expressing the number of photons absorbed by the slab as dIz, and
the total number of photons incident on the slab as Iz, the fraction of photons absorbed by
the slab is given by
Note that because there are fewer photons which pass through the slab than are incident
on it, dIz is actually negative (It is proportional in magnitude to the number of photons
absorbed).
The solution to this simple differential equation is obtained by integrating both sides to
obtain Iz as a function of z
The difference of intensity for a slab of real thickness ℓ is I0 at z = 0, and I1 at z = ℓ. Using
the previous equation, the difference in intensity can be written as,
rearranging and exponentiating yields,
This implies that
and
The derivation assumes that every absorbing particle behaves independently with respect
to the light and is not affected by other particles. Error is introduced when particles are
lying along the same optical path such that some particles are in the shadow of others.
This occurs in highly concentrated solutions. In practice, when large absorption values
are measured, dilution is required to achieve accurate results. Measurements of
absorption in the range of I1 / I0 = 0.1 to 1 are less affected by shadowing than other
sources of random error. In this range, the ODE model developed above is a good
approximation; measurements of absorption in this range are linearly related to
concentration. At higher absorbances, concentrations will be underestimated due to this
shadow effect unless one employs a more sophisticated model that describes the nonlinear relationship between absorption and concentration.
C. A calibration curve
In analytical chemistry, a calibration curve is a general method for determining the
concentration of a substance in an unknown sample by comparing the unknown to a set
of standard samples of known concentration.[1] A calibration curve is one approach to the
problem of instrument calibration; other approaches may mix the standard into the
unknown, giving an internal standard.
The calibration curve is a plot of how the instrumental response, the so-called analytical
signal, changes with the concentration of the analyte (the substance to be measured). The
operator prepares a series of standards across a range of concentrations near the expected
concentration of analyte in the unknown. The concentrations of the standards must lie
within the working range of the technique (instrumentation) they are using (see figure).[2]
Analyzing each of these standards using the chosen technique will produce a series of
measurements. For most analyses a plot of instrument response vs. analyte concentration
will show a linear relationship. The operator can measure the response of the unknown
and, using the calibration curve, can interpolate to find the concentration of analyte.
The data - the concentrations of the analyte and the instrument response for each standard
- can be fit to a straight line, using linear regression analysis. This yields a model
described by the equation y = mx + y0, where y is the instrument response, m represents
the sensitivity, and y0 is a constant that describes the background. The analyte
concentration (x) of unknown samples may be calculated from this equation.
Many different variables can be used as the analytical signal. For instance, chromium
(III) might be measured using a chemiluminescence method, in an instrument that
contains a photomultiplier tube (PMT) as the detector. The detector converts the light
produced by the sample into a voltage, which increases with intensity of light. The
amount of light measured is the analytical signal.
Most analytical techniques use a calibration curve. There are a number of advantages to
this approach. First, the calibration curve provides a reliable way to calculate the
uncertainty of the concentration calculated from the calibration curve (using the statistics
of the least squares line fit to the data). [3]
Second, the calibration curve provides data on an empirical relationship. The mechanism
for the instrument's response to the analyte may be predicted or understood according to
some theoretical model, but most such models have limited value for real samples.
(Instrumental response is usually highly dependent on the condition of the analyte,
solvents used and impurities it may contain; it could also be affected by external factors
such as pressure and temperature.)
Many theoretical relationships, such as fluorescence, require the determination of an
instrumental constant anyway, by analysis of one or more reference standards; a
calibration curve is a convenient extension of this approach. The calibration curve for a
particular analyte in a particular (type of) sample provides the empirical relationship
needed for those particular measurements.
The chief disadvantages are that the standards require a supply of the analyte material,
preferably of high purity and in known concentration. (Some analytes - e.g., particular
proteins - are extremely difficult to obtain pure in sufficient quantity.)
Figure 1. An example of a calibration curve
D. Error in Calibration Curve Results
As expected, the concentration of the unknown will have some error which can be
calculated from the formula below.[4][5] This formula assumes that a linear relationship is
observed for all the standards. It is important to note that the error in the concentration
will be minimal if the signal from the unknown lies in the middle of the signals of all the
standards (the term
goes to zero if
)









sy is the standard deviation in the residuals Linear least squares#Residual values
and correlation
m is the slope of the line
b is the y-intercept of the line
n is the number standards
k is the number of replicate unknowns
yunknown is the measurement of the unknown
is the average measurement of the standards
xi are the concentrations of the standards
is the average concentration of the standards
3. Instrumentation Set Up
Spectrometer UV/Vis 1601 PC
KmnO4 Solution
4. PROSEDURE
A. 1. KmnO4 Solution preparations in Molar; 2.10-5, 4.10-5, 6.10-5, 8.10-5, 10.10-5, 15.10-5,
20.10-5 , 25.10-5, 30.10-5 M
2. Blank refernce (only solvent)
3. Sample solution (Given by assistent)
B. Scanning
1. Switch on the spectrometer, follows the intruction manual (laboratory)
2. Use setup repetation to 3 times
3. Scan the respon power of spectrometer from 199 to 1100 nm, follows the instruction
manual (laboratory)
4. Scan each KmnO4 Solutions from 250 up to 700 nm
5. Read out the wavelength of each shown peak
5. Read Absorbance at 2 peaks shown in the spectrograph
6. Scan the sample from instructur wit same previous prosedure
C. Analysis
1. Construct the calibration curves A vs C from the above measured prosedures
2. Determine the concentration of given KmnO4 sample
D. Analysis of Method
1. Plot each peak wavelength, and determine the wavelength reading repeatibility of
spectrometer
2. From the calibration curve, determine:
a. Linierity of curve
b. the zero concentration
c. plot the concentration error vs A (c/C vs A), give comment from your plot