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Introduction to Spectroscopic Methods of Analysis (part 2) Lecture 2 This lecture will cover: • Molecular absorption spectroscopy • Terms employed in absorption spectroscopy: Absorbance & Transmittance • Beer’s Law Molecular Absorption Spectroscopy - is based on measurement of the transmittance, T or the absorbance, A of solutions contained in transparent cells Molecular absorption spectroscopy Absorption is a measure of the decrease in radiant power P0 P Absorbing solution TERMS EMPLOYED IN ABSORPTION SPECTROSCOPY Transmittance - The fraction of incident radiation transmitted through the sample medium. b T = P P0 P0 P Power of incident radiation Absorbing solution of concentration, c Power of transmitted radiation A = -log T Commonly expressed as a percentage: %T = P x 100 P0 Absorbance - A measurement of the amount of radiant power absorbed by the sample defined as the negative log of transmittance. b A = -log T P0 P Power of incident radiation Absorbing solution of concentration, c Power of transmitted radiation A = log P0 P • Absorbance has a linear relationship with sample concentration defined by Beer’s Law. Questions: 1. Convert the following percent transmittance data into absorbance: i) 33.6 ii) 92.1 Answers: i) 0.474 ii) 0.0357 iii) 1.76 iii) 1.75 Answer: i) %T T = 33.6 = 33.6 / 100 = 0.336 A = - log T = log 1/T = log 1/0.336 = 0.474 Questions: 2. Convert the following absorbance data into percent transmittance: i) 0.375 ii) 1.325 Answers: i) 42.2% ii) 4.73% iii) 97.3% iii) 0.012 Beer’s Law - shows linear relationship between absorbance, concentration of the species measured, sample path length and the absorptivity of the species. A = bc ε = molar absorptivity, liter mol-1 cm-1 b = sample path length, cm c = concentration, mol per liter Beer’s Law A = abc absorbance Absorptivity (Lg-1cm-1) Pathlength (cm) Concentration (g/liter) The term “a” is a proportionality constant called absorptivity. Absorptivity is a constant for a given chemical species at a specific wavelength. Examples: E.g. 1 What is the concentration of an absorbing species if its molar absorptivity is 1500 L/mol cm and the measured absorbance in a 1.00 cm cuvette is 0.742? Answer: A = εbc c = 0.742 (1.00cm) (1500L/mol.cm) = 4.95 x 10-4 M c = A / εb E.g. 2 The measured absorbance of a sample in a 1.00cm cuvette is 0.544. If the concentration is 1.40 x 10-3 M, what is the molar absorptivity for the species? Answer: A = εbc ε = 0.544 (1.00cm)(1.40x10-3 mol/L) = 389 L/mol.cm ε=A/bc E.g. 3 A sample in a 1.0cm cell is determined with a spectrometer to transmit 80% light at a certain wavelength. If the absorptivity of this substance at this wavelength is 2.0, what is the concentration of the substance? Answer: The percent transmittance is 80%. So, T = 0.80 A log 1/T = abc = 2.0 L/g.cm x 1 cm x c log 1/0.80 = 2.0 L/g x c c = 0.10 2.0 L/g = 0.050 g/L PARAMETERS THAT AFFECT ABSORBANCE A = abc • Concentration • Width of cuvette • Inherent ability for the absorbing species to absorb light • Width of cuvette b Wider cuvette more absorbing species present in the path of the light, hence absorbance is greater. b • Inherent ability for the absorbing species to absorb light - Chemical species vary with respect to this inherent ability since absorption depends on individual electronic and vibrational transitions available in a given species APPLICATION OF BEER’S LAW • Applying Beer’s Law to Mixtures - Beer’s law also applies to solutions containing more than one kind of absorbing substance, provided there is no interaction among the various species - Total absorbance for a multicomponent system at a single wavelength is the sum of the individual absorbances. Atotal = A1 + A2 + ………+ An = ε1bc1 + ε2bc2 + ……… + εnbcn LIMITATIONS TO THE APPLICABILITY OF BEER’S LAW - Deviations are frequently observed from the direct proportionality btw absorbance, A and concentration, c when pathlength, b is constant. Deviations may be due to: 1. Fundamental 2. Instrumental 3. Chemical deviations 1. Fundamental deviations - Real limitation to the law - At high concentration (0.01M) each particle affects the charge distribution of its neighbours. - Therefore, this interaction alter the ability of analyte species to absorb a given wavelength of radiation. Causing deviation from the linear relationship between absorbance and concentration. 2. Instrumental deviations - due to polychromatic radiation - Beer’s Law strictly applies when measurements are made with monochromatic source radiation. - In practice, polychromatic sources that have a continuous distribution of wavelengths are being used. - Deviations occur if the radiation is polychromatic since the relationship btwn A and c is no longer linear when is differ. 2. Instrumental deviations - due to presence of stray radiation - Due to instrument imperfections. - This stray radiation is the result of scattering and reflection off the surfaces of gratings, lenses or mirrors, filters and windows. - The wavelength of stray radiation differs greatly from the principal radiation & may not have passed thru’ the sample. - When measurements are made in the presence of stray radiation, A’ = log P0 + Ps P + Ps Ps – power of nonabsorbed stray radiation % stray radiation = Ps x 100 P0 3. Chemical deviations - Occur when the analyte undergo dissociation, association or reaction with the solvent to give products that absorb differently than the analyte.