Chapter 17, Problem 17.1QAP

Cyclohexnone exhibits its strongest IR absorption hand at 5.86 $\mu$ m, and at this wavelength there is a linear relationship between absorbance and concentration.
(a) Identify the part of the molecule responsible for the absorbance at this wavelength.
(b) Suggest a solvent that would be suitable for a quantitative analysis of cyclohexanone at this wavelength.
(c) A solution of cyclohexanone (4.0 mg/mL) in the solvent selected in part (b) exhibits a blank-corrected absorbance of 0.800 in a cell with a path length of 0.025 mm. What is the detection limit for this compound under these conditions if the noise associated with the spectrum of the solvent is 0.001 absorbance units?

Interpretation Introduction

(a)

Interpretation:

The part of the molecule that is responsible for absorbance at the given wavelength is to be stated.

Concept introduction:

The IR absorption spectroscopy makes use of a mid infrared light that detects the particular types of chemical bonds in a given sample for the purpose of the identification of organic and organomettalic compounds. In the IR absorption spectra, there are two regions: Functional group region and the fingerprint region.

Answer to Problem 17.1QAP

The part of the molecule that is responsible for absorbance at the given wavelength is Carbonyl ( $\text{C}=\text{O}$ ).

Explanation of Solution

Given information:

The IR absorption band is $5.86\text{μm}$.

The expression for the wave number is:

$\text{Wave}\text{Number}=\frac{1}{\lambda }$   ......(I)

Here, the wavelength is $\lambda$.

Substitute $5.86\text{μm}$ for $\lambda$ in Equation (I)

$\begin{array}{c}\text{Wave}\text{Number}=\frac{1}{5.86\times {10}^{-6}\text{m}}\\ =\left(0.1706\times {10}^6{\text{m}}^{-1}\right)\left(\frac{1\text{m}}{{10}^2\text{cm}}\right)\\ =1706{\text{cm}}^{-1}\end{array}$

$1706{\text{cm}}^{-1}$ is the value responsible for the absorption of the carbonyl group.

Interpretation Introduction

(b)

Interpretation:

A solvent that would be suitable for quantitative analysis of cyclohexanone at the given wavelength is to be stated.

Concept introduction:

Quantitative analysis refers to the determination of relative or absolute quantity of a substance in a given sample. There are several methods of carrying out the quantitative analysis of the samples. These methods include gravimetric and volumetric analysis.

Answer to Problem 17.1QAP

A solvent that would be suitable for quantitative analysis of cyclohexanone at the given wavelength is cyclohexane and any chlorinated solvent.

Explanation of Solution

The solvent that is suitable for quantitative analysis of cyclohexanone at the given wavelength should be cheap and less toxic in nature.

The solvents that can be used are cyclohexane and any chlorinated solvent.

Interpretation Introduction

(c)

Interpretation:

The detection limit for the compound is to be stated.

Concept introduction:

The detection limit refers to the smallest quantity of the substance that can be differentiated from the absence of that particular substance with a certain level of confidence.

Answer to Problem 17.1QAP

The detection limit for the compound is $0.005\text{mg}/\text{mL}$.

Explanation of Solution

Given information:

Noise associated with the spectrum of the solvent is 0.001 absorbance units.

The expression for the Beer’s Law,

$A=abc$   ......(I)

Here, the absorbance is $A$, the concentration is $c$ and the width of the sample cell is $b$.

Substitute $0.800$ for $A$ and $4.00\text{mg}/\text{mL}$ in Equation (I)

$0.800=ab\left(4.00\text{mg}/\text{mL}\right)$   ......(II)

Substitute $0.001$ for $A$ and $c_{\min }$ for $c$ in Equation (I)

$0.001=ab{c}_{\min }$   ......(III)

Divide Equation (III) by Equation (II)

$\begin{array}{l}\frac{0.001}{0.800}=\frac{c_{\min }}{4.00\text{mg}/\text{mL}}\\ c_{\min }=4.00\text{mg}/\text{mL}\left(\frac{0.001}{0.800}\right)\\ c_{\min }=0.005\text{mg}/\text{mL}\end{array}$