An Introduction to Ultraviolet-Visible Molecular Spectrometry (Chapter 13)

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1 An Introduction to Ultraviolet-Visible Molecular Spectrometry (Chapter 13) Beer s Law: A = -log T = -logp 0 / P = e x b x C See Table 13-1 for terms. In measuring absorbance or transmittance, one should compensate for reflections and scatter occurring at the interface of the cuvette. Compensation is always done by running the blank. 128

2 Absorbance Application of Beer s Law to Mixtures Before applying these equations, you need to know the following: For compound 1: e 1 at l 1 and l 2 For compound 2: e 2 at l 1 and l 2 If their values are not know, you should obtain them via calibration curves. It is also common to obtain e values from single standard solutions. You should always remember: e is a constant that depends on: Wavelength Temperature Solvent e 1 e 2 l l 2 Concentration, M

3 Absorbance Limitations of Beer s Law Three types of limitations cause deviations from linearity: a) Real Limitations b) Instrumental Limitations c) Chemical Limitations Real Limitations: Result from analyte-analyte interactions at high analyte concentrations (usually C > 0.01M). The upper limit of the LDR depends on the compound. For the same compound, it also depends on the solvent and the temperature. You should always determine experimentally the upper limit of the LDR. LDR Concentration High analyte concentration causes average distances among analyte molecules to decrease Solute-solute interactions are mainly dipole-dipole interactions Electrostatic interactions can also occur among strong electrolytes 130

4 Chemical deviations: Arise when an analyte dissociates, associates, or reacts with a concomitant (including solvent) to produce a product with different absorption spectrum than the analyte. Typical example: Acid-Base Indicators (HIn). HIn <=> H + + In - (Color 1, l 1 ) (Color 2, l 2 ) Spectrum looks like: => There is a dissociation constant associated to the equilibrium above: Ka = [H + ][In - ] / [HIn] HIn and In - concentrations depend on the ph of solution: [H + ] = Ka x [HIn] / [In - ] => log [H + ] = logka + log [HIn] / [In - ] => - log [H + ] = - logka - log [HIn] / [In - ] => ph = pka + log [In - ] / [HIn] Assuming an indicator with pka = 5 (Ka = 10-5 ): ph log[in - ] / [HIn] [In - ] / [HIn] [In - ] =? X [HIn] At any given wavelength, the total absorbance intensity of the solution is the sum of the individual intensities of HIn and In - : A Total, l = A HIn, l + A In-, l 131

5 According to Beer s law, the absorbance intensities of HIn and In - are the following: A HIn, l = e HIn, l. b. [HIn] A In-, l = e In-, l. b. [In - ] Substituting in the total absorbance equation: A Total, l = e HIn, l. b. [HIn] + e In-, l. b. [In - ] => At any given wavelength, the total absorbance intensity of the solution (A Total ) depends on the concentrations of HIn and In -. => Because [HIn] and [In - ] depend on ph, A Total depends on ph. You should also remember that the indicator concentration is given by: C Indicator = C = [HIn] + [In - ] HIn <=> H + + In - C x x x where x = [In - ] = [H + ]. From Ka: Ka = x 2 / C x => x 2 = Ka (C x) => x 2 + Ka.x Ka.C = 0 => x = -Ka ± {Ka 2 + 4KaC} 1/2 / 2 This equation demonstrates that the concentration of indicator varies non-linearly with the ionized fraction of the acid. The same is true for [HIn] ( = C x). A graph of intensity of absorption as a function of concentration of indicator of an un-buffered solution provides a non-linear plot. At 430nm: the absorbance is primarily due to the ionized In - form of the indicator and is proportional to the ionized fraction, which varies non-linearly with the total indicator concentration. At 530nm: the absorbance is due principally to the un-dissociated acid HIn, which increases nonlinearly with the total concentration. 132

6 Instrumental deviations due to polychromatic light Beer s law is only followed when measurements are made with mocnochromatic radiation. Wavelength selection of continuous sources radiation made with filters or monochromators provides a Gaussian wavelength profile with a central wavelength of maximum intensity. Consider a beam of radiation consisting of two wavelengths: Only when the two molar absorptivities are the same, this equation simplifies to A = e.b.c and Beer s law is followed. This condition is best met at the maximum absorption wavelength of the absorber. 133

7 Instrumental deviations in the presence of stray radiation Similar considerations are true for stray radiation. In the presence of stray light radiation (P s ), absorption is given by: A = log [P 0 + P s ] / [P + P s ] Depending on its relative magnitude, stray light radiation can cause significant deviations from linearity. At high stray levels and high concentrations, i.e. strong absorbance and low transmittance, the radiant power transmitted through the sample can become comparable to or lower than stray-light level. Mismatched Cells If the analyte and blank cells are optically different and/or have different path-lengths, deviations from Beer s law can occur. You should always use optically equivalent cells! 134

8 Effects of instrumental noise on spectrophotometric analyses The relative standard deviation (s c /c) of a concentration (c) obtained via a transmittance measurement (T) is given by the equation: s c /c = 0.434s T / T. logt where s T is the absolute standard deviation of the transmittance measurement. This equation shows that the uncertainty in a measurement varies non-linearly with the magnitude of the transmittance. Non-linearity as a function of relative standard deviation is also true for absorbance measurements. The sources of noise (uncertainties) in transmittance (absorbance) measurements can be divided in three cases. K 1, k 2 and k 3 are proportionality constants. Only for Case I s T is independent of T. If the limiting source for uncertainty in a measurement is instrumental noise, the best standard deviation within the calibration curve will then be obtained at the absorbance value where s c /c is minimum. 135

9 Types of Instruments Single channel systems Multi-channel systems Multi-channel systems present the advantage of real-time spectra but the upper concentration limit of their LDR is usually lower than single-beam systems. 136

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