Introduction to Spectroscopic Introduction to Spectroscopic Methods of AnalysisMethods of Analysis

(part 2)(part 2)

Lecture 2Lecture 2

This lecture will cover:

• Molecular absorption spectroscopy• Terms employed in absorption

spectroscopy: Absorbance & Transmittance

• Beer’s Law

- is based on measurement of the transmittance, T or the absorbance, A of solutions contained in transparent cells

Molecular Absorption Spectroscopy

Molecular absorption spectroscopy

Absorption

is a measure of the decrease in radiant power

P0 P

Absorbing solution

TERMS EMPLOYED IN ABSORPTION

SPECTROSCOPY

T = P P0

A = -log T

Transmittance - The fraction of incident radiation transmitted through the sample medium.

P0 P

Absorbing solution

of concentration, c

Power of transmitted radiation

Power of incident radiation

b

Commonly expressed as a percentage:

%T = P x 100P0

Absorbance - A measurement of the amount of radiant power absorbed by the sample defined as the negative log of transmittance.

P0 P

b

A = -log T

A = log P0

P

Power of incident radiation

Power of transmitted radiation

Absorbing solution

of concentration, c

• 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) 0.474ii) 0.0357iii) 1.76

i) %T = 33.6

T = 33.6 / 100

= 0.336

A = - log T

= log 1/T

= log 1/0.336

= 0.474

Answer:

Questions:

2. Convert the following absorbance data into percent transmittance:

i) 0.375 ii) 1.325 iii) 0.012

Answers: i) 42.2% ii) 4.73%

iii) 97.3%

Beer’s Law

A = bc

ε = molar absorptivity, liter mol-1 cm-

1

b = sample path length, cm

c = concentration, mol per liter

- shows linear relationship between absorbance, concentration of the species measured, sample path length and the absorptivity of the species.

A = abc

The term “a” is a proportionality constant called absorptivity.

Absorptivity is a constant for a given chemical species at a specific wavelength.

absorbance

Pathlength (cm)

Absorptivity (Lg-1cm-1)

Concentration (g/liter)

Beer’s Law

Examples: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 = A / εb

c = 0.742

(1.00cm) (1500L/mol.cm)

= 4.95 x 10-4 M

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

A = abc

• Concentration• Width of cuvette• Inherent ability for the absorbing species to

absorb light

PARAMETERS THAT AFFECT ABSORBANCE

• Width of cuvette

b

b

Wider cuvette more absorbing species present in the path of the light, hence absorbance is greater.

• 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

• 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.

APPLICATION OF BEER’S LAW

Atotal = A1 + A2 + ………+ An

= ε1bc1 + ε2bc2 + ……… + εnbcn

- Deviations are frequently observed from the direct proportionality btw absorbance, A and concentration, c when pathlength, b is constant.

LIMITATIONS TO THE APPLICABILITY OF BEER’S LAW

Deviations may be due to:

1. Fundamental2. Instrumental3. 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.