11 Instrumental Analysis Tutorial 1

22 By the end of this session the student should be able to: 1.Use mathematical formulae to calculate absorbance, transmittance of a sample and wave parameters. 2.Determine factors affecting absorption of radiation. 3.Identify exceptions to Beer’s law. 4.Apply Beer’s law in chemical analysis 5.Define complementary colors. Objectives

33 Energy of a photon in joule Beer’s Law A= ε b c Absorbance A = – log P/P o = – log T Transmittance% Transmittance E = h = hc/λ =hc 10 6 photons 500 nm 0.7x10 6 photons Remember that

44 For the UV radiation, the increase in energy is: ΔE = h = h c/ λ = (6.626 x J.s) (2.998 x 10 8 m/s) / (147 nm)(10 -9 m/nm) = 1.35 x J / molecule. (1.35 x J/molecule) (6.022 x molecules/mol) = 814 kJ/mol This is enough energy to break the O=O bond in oxygen. For CO 2, the increase in energy is: ΔE = h = hc/ λ =hc (Recall that =1 / λ ) = (6.626 x J.s) (2.998 x 10 8 m/s)(2300 cm -1 )(100 cm/m) = 4.6 x J/molecule = 28 KJ/mol. Infrared absorption increases the amplitude of the vibration of the CO 2 bond. Photon energies By how many kilojoules per mole is the energy of O 2 increased when it absorbs ultraviolet radiation with a wavelength of 147 nm? How much is the energy of CO 2 increased when it absorbs infrared radiation with a wavenumber of 2300 cm -1 ?

55 1- Fill in the blanks a- If you double the frequency of electromagnetic radiation, you __________ the energy. b- If you double the wavelength, you __________ the energy. c- If you double the wavenumber, you __________ the energy 2- How many kilojoules are carried by one mole of photon of violet light with = 400 nm? 3- Calculate the frequency (in hertz), wavenumber (in cm -1 ), and energy (in joules per photon and joules per mole of photons) of visible light with wavelength of 562 nm. 4- Which molecular process correspond to the energies of microwave, infrared, visible and ultraviolet photons? Exercise 1:

66 It is clear that absorbance of a sample depends on: 1.Type and nature of sample. 2.Concentration of the absorbing species. 3.Path length of light through the absorbing medium. 4.Wavelength of radiation (the energy used for stimulation) If the effect of any of these factors is to be studied, the other factors should be kept constant. In order to study the effect of changing the concentration of the absorbing species on absorbance, wavelength of radiation as well as the path length of the light through the same absorbing medium should be constant. Thus Beer’s Law is obeyed only when monochromatic radiation is used (fixed ).     

77 When Beer’s law fails? Beer’s law: Absorbance α concentration It applies to monochromatic radiation and works very well for dilute solutions (<0.01 M). Deviation from Beer’s law: 1- At high concentrations: the proximity of molecules to each others alters their absorptivity. 2- If the absorbing molecule participates in a concentration-dependent chemical equilibrium: HA A - + H + 3- The monochromator generally fails to choose only one λ, instead it projects a very narrow band on the sample (recall that Beer’s law is applied at one certain λ).

88 (a)Find the molar absorptivity of benzene at this wavelength Solution: The concentration of benzene is: [ C 6 H 6 ]= {( g) / (78.11 g/mol)} / L = 1.32 x M We find the molar absorptivity form Beer’s law: Molar absorptivity = ε = A / b c = (0.266) / (1 cm)(1.32 x M) = 201 M -1 cm -1. (b) A sample of hexane contaminated with benzene had an absorbance of at 256 nm in a cuvet with a 5 cm path length. Find the concentration of benzene in mg/L. Solution: Using Beer’s law with the molar absorptivity form part (a), we find [ C 6 H 6 ] = A / ε b = 0.07/ (201 M -1 cm -1 )(5 cm) = 6.9 x M. [ C 6 H 6 ] = (6.9 x mol/L)(78.11 x 10 3 mg/mol) = 5.4 mg/L Pure hexane has negligible UV absorbance above a λ of 200 nm. A solution, prepared by dissolving 25.8 mg of benzene in hexane and diluting to 250 mL, had an absorption peak at 256 nm and an absorbance of in a 1 cm cell. Beer’s law in chemical analysis

9 Solution: (a)A = – log P/P o = – log T = – log (0.45) = (b)Absorbance is proportional to concentration, so the absorbance will double to T = 10 -A = = %T = 20.2% Example 1 a)What value of absorbance corresponds to 45% T? b) If a 0.01 M solution exhibits 45% T at a certain wavelength, what will be the percent transmittance for a 0.02 M solution of the same substance?

10 Solution: ε = A/c b = (0.624 – 0.029) / (3.96 x M)(1 cm) = 1.5 x 10 3 M -1 cm -1. Example 2 A 3.96 x M solution of compound A exhibited an absorbance of at 238 nm in a 1 cm cuvet; a blank solution containing only solvent had an absorbance of at the same wavelength. Find the molar absorptivity of compound A. Value of absorbance corrected for blank

11 Example 3 At 480 nm, a 4.0x10 -5 M solution of [FeSCN] 2+ has a transmittance of 50% when measured in 1.0 cm cell. What is the transmittance when measured in 4.0 cm cell? Solution: At first you have to convert Transmittance to absorbance A 1 = – log P/P o = – log T 1 = – log (0.5) = 0.30 Second, relate absorbance to pathlength T 2 = 10 –A 2 = 10 –1.2 = = 6.3% Absorbance is the parameter that is linearly related to concentration, as well as pathlength, but not transmittance. Thus, it is not correct to assume that: Finally convert back from absorbance to the required transmittance

12 Molecule absorbs a certain range of  of visible light  we see non-absorbed colors. The absorbed  are the  complementary wavelengths (complementary colors) of Max. Absorption Color Absorbed violet violet-blue blue blue-green green yellow-green yellow orange red purple Color Observed green-yellow yellow orange red purple violet violet-blue blue blue-green green Complementary Colors

13 Absorbance by Molecules: Carotene Carotene is the molecule responsible for the colour orange in carrots. It absorbs light in the blue ( nm) and green ( nm) ranges. Carotene transmits or reflects longer wavelengths, and appears orange Absorbance

14 Assignment: 1- Explain the difference between transmittance, absorbance, and molar absorptivity. Which is proportional to concentration? 2- Describe, using diagram, what happens when a molecule absorbs UV-Vis radiation. 2- What is absorption spectrum? 3- Why does a compound whose visible absorption maximum is at 480 nm (blue-green) appear to be red? 4- why is it most accurate to measure the absorbance in the range of A = 0.2–1.5? 5- A compound (M. Wt = 180) absorbs 65% of the radiation at certain wavelength in a 1.0 cm cell at a concentration of 15  g/mL. Calculate its molar absorptivity.