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 P 0 Absorbing solution P

TERMS EMPLOYED IN ABSORPTION SPECTROSCOPY

Transmittance

- The fraction of incident radiation transmitted through the sample medium. P 0 Power of incident radiation b P Power of transmitted radiation

T = P P 0 A = -log T

Absorbing solution of concentration,

c

Commonly expressed as a percentage: %T = P x 100 P 0

Absorbance

- A measurement of the amount of radiant power absorbed by the sample defined as the negative log of transmittance. b P 0 Power of incident radiation Absorbing solution of concentration,

c

P Power of transmitted radiation

A = -log T A = log P 0 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

iii) 1.75

Answers: i) 0.474

ii) 0.0357

iii) 1.76

Answer:

i) %T = 33.6

T = 33.6 / 100 = 0.336

A = - log T = log 1/T = log 1/0.336

= 0.474

Questions:

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 -1 cm -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 = A / b c ε = 0.544

(1.00cm)(1.40x10

-3 mol/L) = 389 L/mol.cm

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 = abc log 1/T = 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

b • Width of cuvette 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.

A total = A 1 + A 2 + ………+ A n = ε 1 bc 1 + ε 2 bc 2 + ……… + ε n bc n

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 P 0 + P s P + P s Ps – power of nonabsorbed stray radiation % stray radiation = P s P 0 x 100

3. Chemical deviations - Occur when the analyte undergo dissociation, association or reaction with the solvent to give products that absorb differently than the analyte.