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Chemistry

Catherine E. Housecroft, Edwin C. Constable

Chapter 11

Introduction to spectroscopy - all with Video Answers

Educators

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Chapter Questions

02:19

Problem 1

What are the relative energies of transitions observed in vibrational, rotational, electronic and nuclear magnetic resonance spectroscopies?

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Benjamin Smith
Numerade Educator
03:17

Problem 2

Convert the wavelengths (a) $500 \mathrm{nm}$ and
(b) $225 \mathrm{nm}$ to $\mathrm{cm}^{-1}$ (wavenumbers). (c) Do these wavelengths fall in the visible region?

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Benjamin Smith
Numerade Educator
03:07

Problem 3

(a) A solution of a compound X gives an absorbance reading of 0.446. What is the percentage transmittance (\% $T$ )? (b) The transmittance for another sample of $\mathbf{X}$ is $70.9 \% .$ To what absorbance reading does this correspond?

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Benjamin Smith
Numerade Educator
01:37

Problem 4

Aqueous solutions of $\mathrm{Ni}^{2+}$ ions appear green. What is the approximate wavelength of light absorbed by aqueous $\mathrm{Ni}^{2+}$ ions?

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Benjamin Smith
Numerade Educator
06:26

Problem 5

The absorption spectrum of benzene dissolved in cyclohexane contains bands at 183,204 and $256 \mathrm{nm} .$ (a) Which band corresponds to the lowest energy transition? (b) Which band corresponds to the lowest wavenumber? (c) For $\lambda=256 \mathrm{nm}$ $\log \varepsilon=2.30 .$ Determine the concentration of a solution (path length $=1.00 \mathrm{cm}$ ) which gives an absorbance of 0.25.

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Benjamin Smith
Numerade Educator
03:50

Problem 6

Refer to Figure $11.6 .$ (a) What does the gradient of the graph tell you? (b) Determine the concentration of $\mathrm{Fe}^{2+}$ ions in a solution that gives an absorbance of 0.20.

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Benjamin Smith
Numerade Educator
02:34

Problem 7

Solutions of azulene (11.5) in cyclohexane absorb at $357 \mathrm{nm}$ and the value of $\varepsilon$ for this absorption is $3980 \mathrm{dm}^{3} \mathrm{mol}^{-1} \mathrm{cm}^{-1} .$ Such a
solution contained in a cell of path length $1.0 \mathrm{cm}$ gives an absorbance of $0.58 .$ What is the concentration of the solution?
CAN'T COPY THE FIGURE

BS
Benjamin Smith
Numerade Educator
02:47

Problem 8

The absorption spectrum of a $5.00 \times 10^{-4} \mathrm{mol} \mathrm{dm}^{-3}$ solution of azulene in cyclohexane in a cell of path length $0.50 \mathrm{cm}$ shows an absorption with $A=0.995 .$ Calculate the corresponding extinction coefficient.

Tianyu Li
Tianyu Li
Numerade Educator
03:19

Problem 9

Solutions of naphthalene in ethanol absorb at $\lambda=312 \mathrm{nm} .$ A $2.50 \times 10^{-3} \mathrm{mol} \mathrm{dm}^{-3}$ solution gives an absorbance of 0.72. Determine the concentration of a solution for which the absorbance is $1.00 .$ The same solution cell was used for both readings.

Tianyu Li
Tianyu Li
Numerade Educator
03:56

Problem 10

Two solutions, I and II, of the same compound, in the same solvent and contained in identical solution cells are of concentrations $5.00 \times 10^{-3}$ and $1.75 \times 10^{-3} \mathrm{mol} \mathrm{dm}^{-3} .$ What is the ratio of their absorbances?

Tianyu Li
Tianyu Li
Numerade Educator
03:17

Problem 11

The compound $\mathrm{K}_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$ absorbs at $\lambda=418 \mathrm{nm}(\log \varepsilon=3.01) ;$ experiments are carried out in a cell of path length $1.00 \mathrm{cm}$. (a) Determine the absorbance of a solution of concentration $6.0 \times 10^{-4} \mathrm{mol} \mathrm{dm}^{-3} \cdot(\mathrm{b})$ What is the absorbance if the concentration is halved?

Tianyu Li
Tianyu Li
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04:17

Problem 12

Azobenzene has two geometrical isomers, 11.6 and 11.7, although 11.6 rapidly isomerizes to 11.7.

Tianyu Li
Tianyu Li
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06:09

Problem 13

Solutions of phenanthrene (11.8) in cyclohexane absorb at $357 \mathrm{nm} ;$ this is one of four absorptions. The absorbance is measured as a function of solution concentration (path length $=1.00 \mathrm{cm}$ ):
$$\begin{aligned}
&\begin{array}{ll}
\text { Concentration/moldm }^{-3} & \text {Absorbance } \\
0.0012 & 0.220 \\
0.0017 & 0.355 \\
0.0030 & 0.627 \\
0.0035 & 0.720 \\
0.0050 & 1.045 \\
\hline
\end{array}\\
&.
\end{aligned}$$
(a) Use the data to determine the molar extinction coefficient for the absorption band at $357 \mathrm{nm}$
(b) Why is it more accurate to measure $\varepsilon$ from a series of readings rather than a single reading?
CAN'T COPY THE FIGURE

Tianyu Li
Tianyu Li
Numerade Educator
06:09

Problem 14

Solutions of acridine ( $11.9)$ in ethanol absorb at $\lambda=250 \mathrm{nm}(\log \varepsilon=5.3) .$ (a) What is the
concentration of acridine in a solution within a cell of path length $0.50 \mathrm{cm}$ for which the absorbance is $0.96 ?$ (b) What mass of acridine is required to prepare $250 \mathrm{cm}^{3}$ of this solution?
CAN'T COPY THE FIGURE
CAN'T COPY THE GRAPH

Tianyu Li
Tianyu Li
Numerade Educator
05:39

Problem 15

The conversion of compound 11.10 to its
(Z)-isomer (see Section 6.11) is induced by a flash of light (flash photolysis). Isomer 11.10 absorbs light at $435 \mathrm{nm},$ and the $(Z)$ -isomer absorbs at $316 \mathrm{nm} .$ Figure 11.11 shows the change in absorbance at $\lambda=435 \mathrm{nm}$ for a solution of 11.9 in cyclohexane over a period of 1200 s during which time the solution is subjected to a flash of light. (a) Rationalize the shape of the curve in Figure $11.11 .$ (b) If the path length of the solution cell is $1 \mathrm{cm},$ and the solution concentration is $9.00 \times 10^{-6} \mathrm{mol} \mathrm{dm}^{-3},$ determine a value for $\log \varepsilon$ corresponding to the absorption at $435 \mathrm{nm}$ [Data from: S. R. Hair et al. (1990) J. Chem. Ed., vol. $67, p .709 .]$
CAN'T COPY THE FIGURE

Tianyu Li
Tianyu Li
Numerade Educator
02:41

Problem 16

The reaction between $\mathrm{I}^{-}$ and $\left[\mathrm{S}_{2} \mathrm{O}_{8}\right]^{2-}$ occurs as follows:
$$
\left[\mathrm{S}_{2} \mathrm{O}_{8}\right]^{2-}+2 \mathrm{I}^{-}--2\left[\mathrm{SO}_{4}\right]^{2-}+\mathrm{I}_{2}
$$
$\mathrm{I}_{2}+\mathrm{I}^{-} \longrightarrow=\left[\mathrm{I}_{3}\right]^{-}$
The second step occurs so long as there is an excess of $\mathrm{I}^{-}$ present in solution; $\left[\mathrm{I}_{3}\right]^{-}$ absorbs at $353 \mathrm{nm}$ $(\log \varepsilon=4.41) .$ Explain how measurements of the absorbance at $\lambda=353 \mathrm{nm}$ would enable you to measure the change in concentration of $\mathrm{I}_{2}$ during the reaction.

Tianyu Li
Tianyu Li
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11:13

Problem 17

An anion $L^{4-}$ reacts with aqueous $C r^{3+}$ ions to give a coloured complex $\left[\mathrm{CrL}_{x}\right]^{n-} .$ To find the stoichiometry of this species, $10 \mathrm{cm}^{3}$ solutions composed of $V \mathrm{cm}^{3}$ of a $0.002 \mathrm{mol} \mathrm{dm}^{-3}$ aqueous solution of $\operatorname{Cr}\left(\mathrm{NO}_{3}\right)_{3}$ and $(10-V) \mathrm{cm}^{3}$ $0.002 \mathrm{mol} \mathrm{dm}^{-3}$ aqueous $\mathrm{H}_{4} \mathrm{L}$ were prepared. With a colorimeter tuned to absorb light corresponding to that absorbed by $\left[\mathrm{CrL}_{x}\right]^{n-},$ a Job's plot was recorded. Use the following results to determine $x$ and $n$ in $\left[\mathrm{CrL}_{x}\right]^{n-}$.
$$\begin{array}{cc}
V / \mathrm{cm}^{3} & \text { Absorbance } \\
0 & 0 \\
1.0 & 0.21 \\
2.0 & 0.40 \\
3.0 & 0.59 \\
4.0 & 0.81 \\
6.0 & 0.80 \\
7.0 & 0.60 \\
8.0 & 0.38 \\
9.0 & 0.20 \\
10.0 & 0
\end{array}$$

Tianyu Li
Tianyu Li
Numerade Educator
13:37

Problem 18

In case study $3,$ we showed how colorimetry can be used to follow the oxidation of $\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-} \mathrm{by}$ $\left[\mathrm{MnO}_{4}\right]^{-}$ ions in acidic aqueous solution. The data shown in Figure 11.8 refer to an experiment in which $2.0 \mathrm{cm}^{3}$ of aqueous $\mathrm{KMnO}_{4}\left(4.0 \times 10^{-4} \mathrm{moldm}^{-3}\right)$
are mixed with $1.0 \mathrm{cm}^{3}$ aqueous sulfuric acid solution that contains $\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-}$ ions $\left(x \mathrm{moldm}^{-3}\right)$ in a cuvette of path length $1.0 \mathrm{cm}$. (a) Rationalize the shape of the curve shown in Figure $11.8 .$
(b) The initial absorbance (time $=0 \mathrm{s}$ ) is 0.65 Determine the molar extinction coefficient of $\mathrm{KMnO}_{4} \cdot(\mathrm{c})$ If the final absorbance is 0.14, calculate the concentration of $\left[\mathrm{MnO}_{4}\right]^{-}$ ions remaining in solution at the end of the reaction. (d) How many moles of $\left[\mathrm{MnO}_{4}\right]^{-}$ are used during the reaction? How many moles of $\left[\mathrm{C}_{2} \mathrm{O}_{4}\right]^{2-}$ were present initially (see equation 11.6 )? Hence determine the concentration of $\left[\mathbf{C}_{2} \mathbf{O}_{4}\right]^{2-}$ present in the original $1.0 \mathrm{cm}^{3}$ sample of oxalate ions.

Tianyu Li
Tianyu Li
Numerade Educator
04:00

Problem 19

Colour vision in humans relies on three types of cones in the retina of the eye, and these absorb light at wavelengths of about 445,530 and $565 \mathrm{nm} .$ (a) To what colours do these wavelengths correspond? (b) Do you expect plots of absorbance against wavelength for each absorption to be sharp or broad? Give reasons for your answer. (c) The colour vision of the honeybee (Apis mellifera) depends on three visual pigments which absorb at 344,436 and $556 \mathrm{nm} .$ To which regions of the spectrum do these wavelengths correspond?

Tianyu Li
Tianyu Li
Numerade Educator
04:29

Problem 20

Phosphates are applied as fertilizers, but high concentrations of phosphates are associated with the eutrophication of lakes (see Box 22.8 ). Some commercial kits sold to determine the
concentration of phosphates in water sources rely upon the reaction of $\left[\mathrm{PO}_{4}\right]^{3-}$ ions with ammonium molybdate, $\left[\mathrm{NH}_{4}\right]_{2}\left[\mathrm{MoO}_{4}\right],$ followed by reduction to give a blue complex. The intensity of the blue colour allows you to determine the concentration of phosphate ions in solution. A rough determination can be carried out by comparing the depth of blue observed with a colour chart provided with the text kit. Explain the scientific basis of the test.

Tianyu Li
Tianyu Li
Numerade Educator
07:54

Problem 21

Chlorine is used as a disinfectant in swimming pools, and a 5 ppm level of chlorination is typically maintained (ppm = parts per million). One method of testing the chlorine concentration is to use the compound shown below (commonly called DPD) which gives a red-purple coloured radical cation when oxidized:
CAN'T COPY THE FIGURE
Kits containing DPD are available commercially. Accurate concentrations of $\mathrm{Cl}_{2}$ can be obtained spectrophotometrically; the radical absorbs at $515 \mathrm{nm} .$ A calibration curve can be constructed by using standardized chlorine solutions (by titration against $\mathrm{Fe}^{2+}$ ions). (a) What mass of $\mathrm{Cl}_{2}$ must be dissolved in $1.0 \mathrm{dm}^{3}$ of water to give a standard solution containing 5 ppm by weight? (Density of water $=1.0 \mathrm{g} \mathrm{cm}^{-3} .$ ) To what concentration (in mol $\mathrm{dm}^{-3}$ ) does 5 ppm of $\mathrm{Cl}_{2}$ correspond?
(b) Write a balanced equation for the redox reaction between $\mathrm{Fe}^{2+}$ and $\mathrm{Cl}_{2}$. (c) Explain how you would set up the calibration curve described above, and suggest a suitable range of $\mathrm{Cl}_{2}$ concentrations.

Tianyu Li
Tianyu Li
Numerade Educator