4D Estimation of Detection Limits

EA-ACLecture W7 February 19, 2003

Today’s topics include:

Molecular Spectroscopy

Absorption spectroscopy

Spectrophotometer design and use

First let’s connect light abosrption to molecular structure. One method to determine nitrate ion concentration is by uv absorption spectroscopy. What is the chemical formula for nitrate? NO3- What does a Lewis electron dot structure for the nitrate ion look like?

In terms of molecular orbitals, how do we describe the bonding between the nitrogen atom and the oxygen atoms? 3 sigma bonds and one pi bond.

What hydridization state would we say the nitrogen is in? sp2 oxygens? Also sp2

What about the 16 electrons in oxygen lone pairs? Does anyone know how they are designated in terms of molecular orbitals? They are called n electrons. You can look at the example for formaldehyde on page 419.

In constructing a MO diagram for nitrate we first consider the stable sigma bonds. They will be of low energy. Next we have the pi bonding orbital and probably the nonbonding oxygen n orbitals.

Finally there are the unfilled antibonding orbitals. Usually the anitibonding  orbital is lower in energy than the antibonding  orbitals. So we have a diagram that looks something like this. XXXXX

______antibonding  orbitals (*)

____ antibonding  orbital (*)

_↓_ bonding  orbital

_↓__↓__↓_ etc. nonbonding oxygen n orbitals

_↓_ bonding  orbital

Next there is the concept of the highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO.

When a molecule absorbs light at its longest wavelength (lowest energy), an electron is excited from itsHOMO to its LUMO.

The absorption of light by nitrate ions probably involves a * transition although it is possibly an n * transition.

The point is that in the visible and uv spectral regions, it is electronic energy levels of molecules that absorb the energy of the photons. When a photon is absorbed by a molecule, one of its electrons moves to a higher energy orbital.

Usually the electron drops back down to its HOMO by way processes that internally convert the absorbed energy of the photon to heat - energy of molecular motion.

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For nitrate, the energy gap between its HOMO and its LUMO is relatively large and it requires a fairly energetic photon to excite the electron. Nitrate absorbs photons with a wavelength of 214 nm.

E = hc/ = 6.62 x 10-34 J*s x 3.00 x 108 m/s x 109 nm/m x 6.02 x 1023 photons/mol

214 nm

= 558 kJ/mol

Let’s compare this value to that of phenolphthalein which had an absorption max at 555 nm.

= 215 kJ/mol

We see there is lots more energy in uv photons than visible photons. What is the energy of a typical C-C bond? ~90 kcal/mol or 360 kJ/mol. From the energy of the uv photon you can see why uv light causes skin damage.

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Advantages of Absorption Spectroscopy

Absorption spectroscopy based upon ultraviolet and visible radiation is one of the most used tools for quantitative analysis. The important characteristics of spectrophotometric and photometric methods are

1.Wide applicability. Enormous numbers of inorganic, organic, and biochemical species absorb ultraviolet or visible radiation and are thus amenable to direct quantitative determination.

Many nonabsorbing species can also be determined after chemical conversion to absorbing derivatives. It is estimated that over 90% of the analyses performed in medical laboratories are based upon ultraviolet and visible absorption spectroscopy.

High sensitivity. Typical detection limits for absorption spectroscopy range from 104 to 10-5 M. This range can often be extended to 10-6 or even 10-7 M with certain procedural modifications.

Moderate to high selectivity. If a wavelength can be found at which the analyte alone absorbs, preliminary separations become unnecessary. Furthermore, where overlapping absorption bands do occur, corrections based upon additional measurements at other wavelengths sometimes eliminate the need for a separation step.

Procedures for dealing with overlapping bands are part of this week’s chapter – talk about next week.

Good accuracy. The relative errors in concentration encountered with a typical ultraviolet /visible spectrophotometric or photometric procedure lie in the range from 1% to 5 %. Such errors can often be decreased to a few tenths of a percent with special precautions.

Ease and convenience. Spectrophotometric and photometric measurements are easily and rapidly performed with modern instruments. In addition, the methods readily lend themselves to automation.

The applications of absorption analysis are not only numerous but also touch upon every area in which quantitative information is sought. You can get a sense of the scope of spectrophotometry by looking at a copy of the Journal Analytical Chemistry in the library or down in our lab.

A substance that absorbs uv and/or visible light is said to have a chromophoric group. This is the region of the molecule or ion that undergoes the electronic transition.

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For example, the hemoglobin molecule has a heme group that absorbs light. The huge protein portion of molecule does not absorb visible light. The heme group contains a conjugated ring.

What does conjugated mean? -- alternating carbon single-double bonds. The double bonds contain pi electrons so the conjugates system becomes an extented pi electron region. Thus the electronic transitions are usually π  π*.

The more double bonds that are conjugated the lower the energy difference between the HOMO and the LUMO. The lower the energy the longer the wavelength of light that is absorbed.

Note also that we can analyze many nonabsorbing species by spectrophotometry. Many organic molecules can reacted with other organic molecules to make colored species called derivatives.

The successful application of these color-forming reagents usually requires that their reaction with the analyte be forced to near completion.

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Many colorless inorganic substances are detected by the addition of a substance that either complexes with the ion or forms a chelate that is colored. As an example iron forms a red complex with thiocyanate.

Fe3+ + SCN- < == > Fe(SCN)2+ (red)

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For analysis of iron in natural water samples, the chelate 1,10-phenanthroline is used.

The reagent is a weak base that reacts to form a cation in acid solution. The complex formation with iron is best described by the equation

Fe2+ + 3 phenH+ < == > Fe(phen)32+ + 3 H+

The formation constant for this equilibrium is 2.5 x 106 at 25C. Iron(II) is quantitatively complexed in the pH range between 3 and 9.

An excess of a reducing agent is added to maintain iron in the +2 state. The complex, once formed, is very stable. The complex has a very large molar absorbtivity (ε), another way to say intensely colored.

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The analysis is performed at 508 nm. A very common undergraduate lab using this method to determine the iron content of vitamin tablets.

The following topics about instrument design are common to most form of optical instrumentation.

Now I want to talk about Spectral Purity and Spectral Resolution.

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Up to this point we have talked about the interaction of a single wavelength of light with a sample. In reality, no matter what method is used to produce any specific wavelength of light or to select a "single" wavelength from a broad range of wavelengths, the best that can be done is to isolate a range of wavelengths.

A quantitative measure of the range of wavelengths of light (the spectral purity) is a number called the spectral bandwidth, spectral linewidth, or, simply, bandwidth or linewidth.

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For all of these cases a plot of the power vs. the wavelength of the light looks something like that this figure.

As shown in the figure, the quantitative measurement used is the width of the band at a point halfway between the baseline and the peak. This is called the full width at half height(fwhh) or the full width at half maximum(fwhm).

Incidentally, the band envelope is not in the shape of a Gaussian peak. The lineshape is closer to a shape called lorentzian. Compared with a Gaussian, it is narrower in the middle and spreads over a wider range at lower power regions at the edges.

In summary, you should understand that while we might say there is a single wavelength –or more correctly, that the light is monochromatic (from the Greek one color)the truth is that all monochromatic light has a finite spectral bandwidth.

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Spectrophotometers are designed around these principles:

1.Narrowbandwidth light can be produced at a fixed wavelength.

2.Light intensity can be measured over a narrow bandwidth.

Furthermore,

3.Wavelengths can be changed continuously and smoothly over some wavelength range. This last method is called, simply, scanning the wavelength. This allows for automation.

Let’s look at how spectrophotometers take advantage of these principles.

Spectrometers can be separated into two general groups: dispersive and nondispersive.r

Dispersivespectrometers depend on the separation of the colors of light over a range of angles.

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A large number of different designs exist, and this transparency merely indicates their basic parts. Of critical importance is to have a slitor some construction that has the same purposeto select a narrow angle of the dispersed colors, that is, to pick a narrow range of wavelengths.

The section of a dispersive scanning instrument that selects a single wavelength at a time is the monochromator. (Notice that the name is monochromator not –meter).

Itpasses a single wavelength of light but does not measure it. One benefit of a dispersive optical element is that a number of detectors can be distributed across the spread of dispersed light.

A dispersive polychromator can be fabricated. The light at a number of wavelengths is detected simultaneously, and subsequently these intensities can be read out into a computer and the spectrum constructed. This is the design of the HP diode array that you use in the lab.

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Nondispersivespectrometers separate light by allowing a specific color to propagate while the other colors are suppressed along the same direction. A simple colored filter can be used, which depends on chemical dyes to block the unwanted wavelengths.

A second type of filter, an interference filter or interferometer, does not absorb the unwanted light but instead limits the color by the destructive interference of the unwanted colors and the constructive interference of the desired wavelength.

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Both monochromators and interferometers function because of the constructive and destructive interference of light waves. Interference filters can be constructed with very narrow bandpass. Only filters based on absorption of light by dyes do not function this way.

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Let us consider the operation of a monochromator. Minimally, the monochromator requires a dispersing element (can be a prism or grating) and two slits. Slits of a monochromator are exactly that, slits cut out of metal.

The slit widths are usually in the range of ten to a few hundred micrometers. As pictured in the transparency, light enters through the entrance slit, and is dispersed.

The different colors of the light propagate at different angles, and only over a narrow range of these angles can the light pass through a second, exit slit. It should be clear from the figure that the resulting spectral bandwidth depends on the width of the exit slit.

But the bandwidth also depends on how broadly the colors are spread out and on the distance from the dispersing element to the exit slit. For a fixed slit width, the bandwidth that passes through depends on the wavelength of the light.

Thus a statement of the spectral bandpass will be similar to "0.5 nm at 350 nm." This means that for light of 350 nm wavelength the width at half height is 0.5 nm.

The wider the slit, the greater the spectral power that passes through it. However, the spectral bandwidth is larger then as well. This tradeoff always exists. When the spectral power is raised by using a wider slit, spectral purity is reduced.

For polychromators with multichannel detectors, the width of the elements of the detectors (the fraction of the total spread) also becomes a factor in the spectral purity. On the other hand, the spectral purity of an interference filter does not depend on a slit but on the number of times the light is reflected before passing through.

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The bandwidth does not tell us when two different colors are "different." Two terms are used to define this difference. One is the resolving power of the instrument and the other is the resolution of the spectrum.

These are defined on this transparency. The resolution is measured in terms of Δλ.

The dip between the two peaks can be any value, so the idea that two wavelengths are "resolved" can have many meanings depending on the depth of the valley. That information must be included.

For instance, the resolution of a spectrum can be reported as “2 nm resolution with 90% valley”. This means that the peaks are considered resolved when the valley depth is 90% of the height of equal peaks.

In spectrometry, the measurement of spectra depends intimately on both the spectral properties of the sample and the instrument used to make the measurement. With respect to the instrument, as much light as possible from a stable source is directed into a scanning monochromator.

As light of continuously varying wavelengths passes through the sample and through the exit slit onto a transducer, a graph of power detected vs time results in a spectrum. By calibrating the instrument we can relate time to wavelength to get a more familiar spectrum.

Lets look briefly at errors in this form of spectroscopy.

The random error associated with measurements of light is called the photometric error, and the precision of a measurement depends this error.

However, because of the logarithmic relationship between T and A, the precision of the measurement of concentration differs over the range of measurable absorbance. Recall that the transmittance P/Po is the directly measured quantity.

But normally, absorbance is used in analyses because its value is directly proportional to the concentration of the lightabsorbing species. To see how the precision changes, let us assume that the relative error in measuring T is ±0.5% for all values of T from 0 to 1.

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This is a relative error of 0.005 for T. As shown in this transparency, the absolute error in A decreases continuously from high to low values of A.

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Next, let us look at the relative error in absorbance; it is the measure of our analytical precision. In the next transparency, notice that at the low concentrations, 90% T (A = 0.045), and at relatively high concentrations, < 2% T (A > 1.70), the relative error is greater than 5%.

Clearly, under these conditions the measurement is less precise than in other ranges. The range in which the results produce the smallest relative error occurs between absorbance values 0.40.7 or 2060% T and is ~1.5%, while in the absorbance range 0.2 to 1.0 the relative error is <2%.

In other words, to achieve the best precision in an absorption experiment, the concentration of the sample or the pathlength through the sample should be adjusted so that the output of the instrument is in absorbance range 0.40.7 if possible.

This conclusion is reached by considering only the relationship between the absorbance and transmittance with a fixed, random error in transmittance. In fact, the error in T is not constant over its entire range, and each instrumental design has its own characteristics.

However, the general trend described here still is applicable and should be considered when developing an assay.

One other often ignored but significantcontribution to photometric error in all spectrometries is the lack of reproducibility of the condition and position of samples in the instrument.

For instance, for numerous analytical methods the sample is put in a cuvette or other sample cell that is placed in the instrument. If its placement is not reproducible, then some error will be introduced due to simply the slightly different geometry in each measurement. Tilting, twisting, or rotating the sample cell by 90o all cause errors.

You might try in the lab to see how reproducible you can be using a cuvette and what kind of errors are introduced with slight changes in cuvette position.

A major source of student error results from not filling the cuvette properly.

Rince several times with new solution before taking a reading.

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Here is a diagram of a Spectronic 20, a relatively low-cost single-beam instrument. This means there is a single light beam that passes through a sample compartment with one cuvette holder. [describe features]

Here is the light path of a high-quality Cary 118 double-beam instrument. [describe features]

One way to get a sense of the magnitude of the error inherent in an instrument is by making repeated independent measurements of the same standard solution and determining the standard deviation of the measurements.

You do this 20 or 30 times with each time putting a new sample in the cuvette and placing it in the machine. This should be done at a number of different absorbances and different wavelengths.

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Here are the results from the two different instruments we have examined. The curve of the Spec 20 looks like the error curve we saw earlier. The error is pretty much independent of transmittance. It is probable that the major source of uncertainty lies in the limited resolution of the transmittance scale that is read by eye.

Errors that are independent of T include readout resolution, thermal detector noise – i.e. the noise in the detector when no light falls on it, and amplifier and other electronic noise.

Some sources of error are proportional to T. These include cell positioning uncertainty and fluctuations in source intensity. One of the methods used to reduce cell positioning errors is to insert and remove samples by syringe. Unfortunately this means you must wash the cell in place as well. Some instruments have a flow-through cell so that the sample flow into and out of the cell compartment without the cell being moved.