Physical Chemistry Third Edition

958 23 Optical Spectroscopy and Photochemistry

broadened by several effects, including the coupling of vibrational and electronic tran-

sitions, Doppler shifts from the translation of molecules and the uncertainty broadening

due to the finite life time of the states, introduced in Eq. (16.5-11).^4 If the absorption

spectrum of the same substance were taken in the gas phase instead of in a solvent,

the regions of absorption would be much narrower. However, every spectral line has

an inherent nonzero range of wavelengths that are absorbed (a nonzerolinewidth). In

addition, no spectrograph or spectrophotometer can disperse radiation so completely

that a single wavelength is separately detected. The difference in wavelength of the

most closely spaced narrow spectral lines that an instrument can distinguish is called

theresolutionof the instrument.

EXAMPLE23.2

A solution of a certain dye has a molar absorptivity of 1. 8 × 105 L mol−^1 cm−^1 at a wave-

length of 606 nm. Find the concentration of a solution of this dye that has an absorbance at

this wavelength equal to 1.65 in a cell 1.000 cm in length.

Solution

c

A

ab



1. 65

(1. 8 × 105 L mol−^1 cm−^1 )(1.000 cm)

 9. 2 × 10 −^6 mol L−^1

PROBLEMS

Section 23.1: Emission/Absorption Spectroscopy and
Energy Levels

23.1 A solution of phenylalanine in neutral water with
concentration equal to 0. 110 × 10 −^3 mol L−^1 has an
absorbance atλ 206 .0 nm of 1.027 in a 1.000-cm cell.
Find the molar absorptivity.

23.2 A cell of path length 1.50 cm is filled with gaseous
bromine at a pressure of 100.0 torr and a temperature of
298.15 K. It is found that 10.76% of light of wavelength
400 nm is transmitted through the cell. Find the molar
absorptivity of gaseous bromine at this wavelength.

23.3 The molar absorptivity ofpara-xylene at 212 nm is equal
to 6. 31 × 103 L mol−^1 cm−^1. What is the concentration of
para-xylene in a nonabsorbing solvent if the solution has a
percentage transmission of 11.35% at 212 nm in a cell of
length 1.000 cm?

23.4 Two solutions of the same dye in the same cell give
transmittances of 63.52% and 87.32%. Find the

concentration of the second solution if the concentration of

the first solution is 1.000 m mol L−^1.

23.5 If more than one absorbing substance is present, the

contributions to the absorbance are additive if the

Beer–Lambert law holds. A solution of azomethane in

ethanol with concentration of 1. 0 × 10 −^3 mol L−^1 has an

absorbance of 0.1285 at a wavelength of 357 nm in a cell

with path-length 2.00 cm. The absorbance of pure ethanol

in the same cell at the same wavelength is 0.0500. Find the

absorptivity of azomethane at this wavelength.

23.6 The absorptivity of hemoglobin at 430 nm is found to be

532 L mol−^1 cm−^1. The molar mass of hemoglobin is

68000 g mol−^1.

a.The concentration of hemoglobin inside red blood cells

is approximately 17% by mass. Estimate the absorbance

of such a solution in a cell of length 1.000 cm.

b. Find the concentration in mol L−^1 and in percent by

mass for a solution that would have an absorbance of

1.00 at 430 nm.

(^4) V. B. E. Thomsen,J. Chem. Educ., 72 , 616 (1995).