10.8 Spectroscopic Methods (Exercises)

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10.E: Spectroscopic Methods (Exercises) - Chemistry LibreTexts

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Practice Exercise 10.2 The photon’s energy is


Practice Exercise 10.3 To find the transmittance, T , we begin by noting that

Solving for T

gives a transmittance of 0.054, or a %T of 5.4%. Click here to return to the chapter.

Practice Exercise 10.4 Making appropriate substitutions into Beer’s law

and solving for C gives a concentration of 3.37×10 -4 M. Click here to return to the chapter.

Practice Exercise 10.5 For this standard addition we can write the following equations relating absorbance to the concentration of Cu 2+ in the sample. First, for the sample, we have

and for the standard addition we have

The value of εb is the same in both equation. Solving each equation for ε b and equating

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leaves us with an equation in which C Cu is the only variable. Solving for C Cu gives its value as


Practice Exercise 10.6 Substituting into equation 10.11 and equation 10.12 gives

To determine C Cr and C Co we solve the first equation for C Co

and substitute the result into the second equation.

Solving for C Cr gives the concentration of Cr3+ as 8.86 × 10 –3 M. Substituting this concentration back into the equation for the mixture’s absorbance at 400 nm gives the concentration of Co 2+ as 3.60 × 10 –2 M. Click here to return to the chapter.

Practice Exercise 10.7 Letting X represent MnO 4 – and Y represent Cr 2O 72–, we plot the equation

placing Amix/ ASX on the y -axis and ASY/ ASX on the x -axis. For example, at a wavelength of 266 nm the value of Amix /ASX is 0.766/0.042, or 18.2, and the value of ASY/ ASX is 0.410/0.042, or 9.76. Completing the calculations for all wavelengths and plotting the data gives the result shown in Figure 10.67. Fitting a straight-line to the data gives a regression model of

Using the y -intercept, the concentration of MnO4 –is

or 8.15 × 10 –5 M MnO4 –, and using the slope, the concentration of Cr 2O 72– is

or 1.78×10 –4 M Cr 2O 72–.


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Figure 10.67 Multiwavelength linear regression analysis for the data in Practice Exercise 10.7.


Practice Exercise 10.8 Figure 10.68 shows a continuous variations plot for the data in this exercise. Although the individual data points show substantial curvature—enough curvature that there is little point in trying to draw linear branches for excess metal and excess ligand—the maximum absorbance clearly occurs at an X L of approximately 0.5. The complex’s stoichiometry, therefore, is Fe(SCN)2+.

Figure 10.68 Continuous variations plot for the data in Practice Exercise 10.8.


Practice Exercise 10.9 The value of K a is


Practice Exercise 10.10 To determineK a we use equation 10.21, plotting log[( A – AHIn) / ( AIn – A)] versus pH, as shown in Figure 10.69. Fitting a straight-line to the data gives a regression model of

The y -intercept is –pK a; thus, the pK a is 3.80 and the K a is 1.58×10 –4.


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Figure 10.69 Determining the pKa of bromothymol blue using the data in Practice Exercise 10.10.


Contributors David Harvey (DePauw University)


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Figure 10.69 Determining the pKa of bromothymol blue using the data in Practice Exercise 10.10.


Contributors David Harvey (DePauw University)


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10.8 Spectroscopic Methods (Exercises)

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