Exploring Chemical Analysis
Exploring Chemical Analysis
5th Edition
ISBN: 9781429275033
Author: Daniel C. Harris
Publisher: Macmillan Higher Education
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Chapter 19, Problem 19.11P
Interpretation Introduction

Interpretation:

Values of [MnO4] and [Cr2O72] have to be calculated.

Concept Introduction:

Molar absorptivity is a coefficient that appears in Beers’ law. It measures the extent of light absorbed at a certain wavelength. Molar absorptivity is denoted by the symbol ε. SI unit for Molar absorptivity is M1cm1.

Relation between path length and dimension is as follows:

  D=b(ε'Xε"Yε'Yε"X)

Here,

ε denotes molar absorptivity in M1cm1.

b denotes path length in centimeters.

D denotes dimension.

Expression to compute absorbance from transmittance is as follows:

  A=logT

Formula to calculate molar absorptivity from absorbance is as follows:

  ε=Abcl

Here,

ε denotes molar absorptivity of species capable to absorb.

b denotes path length in centimeters.

c denotes concentration of species capable to absorb.

A denotes absorbance.

T denotes transmittance.

Expert Solution & Answer
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Explanation of Solution

Relation between path length and dimension is as follows:

  D=b(ε'Xε"Yε'Yε"X)        (1)

Substitute 420 M1cm1 for ε'X, 1580 M1cm1 for ε"Y, 1680 M1cm1 for ε'Y, 4010 M1cm1 for ε"X, and 1.00 cm for b in equation (1).

  D=(1 cm)[(420)(1580)(1680)(4100)] M1cm1=6224400 M1

Expression to compute [MnO4] is as follows:

  [MnO4]=A'ε"MnO4A"ε'MnO4D        (2)

Substitute 0.766 for A', 0.422 for A", 1580 M1cm1 for ε"MnO4, 4100 M1cm1 for ε'MnO4, and 6224400 M1 for D in equation (2).

  [MnO4]=(0.766)(1580 M1cm1)(0.422)(4100 M1cm1)(6224400 M1)=8.352×105 M

Expression to compute [Cr2O72] is as follows:

  [Cr2O72]=A"ε'Cr2O72A'ε"Cr2O72D        (3)

Substitute 0.422 for A', 0.766 for A", 420 M1cm1 for ε'X, 1680 M1cm1 for ε"X,and 6224400 M1 for D in equation (3).

  [Cr2O72]=(0.442)(420 M1cm1)(0.766)(1680 M1cm1)6224400 M1=1.78×104 M

Thus, value of [MnO4] and [Cr2O72] are 8.352×105 M and 1.78×104 M respectively.

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