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Chapter 19: QBE (page 483)

The spreadsheet lists molar absorptivities of three dyes and the absorbance of a mixture of the dyes in a 1.000-cm cell. Use the least-squares procedure in Figure 19-3 to find the concentration of each dye in the mixture.

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The solution for the concentration of mixture is estimated using least square method.

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01

Find the concentration of each dye in the mixture:

The concentration of mixture is estimated using least square method.

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Most popular questions from this chapter

This problem can be worked by calculator or with the spreadsheet in Figure 19-4. Consider compounds X and Y in the example labeled “Analysis of a Mixture, Using Equations 19-6” on page 464. Find [X] and [Y] in a solution whose absorbance is 0.233 at 272 nm and 0.200 at 327 nm in a 0.100-cm cell.

What is the advantage of a time-resolved emission measurement with Eu3+versus measurement of fluorescence from organic chromophores?

Now we use Solver to find Kfor the previous problem. The only absorbing species at 332 nmis the complex, so, from Beer’s law [complex]=A/ε(becausepathlength=1.000cm).I2is either free or bound in the complex,so [I2]=[I2]tot-[complex].There is a huge excess of mesitylene, so[mesitylene]≈[mesitylene]tot

K=[complex][l2][mesitylene]=A/ε(l2tot-A/ε)[mestitylene]tot

The spreadsheet shows some of the data. You will need to use all the data. Column A contains [mesitylene] and column B contains [l2]tot. Column C lists the measured absorbance. Guessa value of the molar absorptivity of the complex,ε,incellA7.Then compute the concentration of the complex (=A/ε)in column D. The equilibrium constant in column EisgivenbyE2=[complex]/([I2][mesitylene])=(D2)/((B2-D2)*A2).

should we minimize with Solver? We want to varyεin cell A7 until the values of Kin column E are as constant as possible. We would like to minimize a function like ∑(Ki-Kaverage)2, where Kiis the value in each line of the table and Kaverage is the average of all computed values. The problem with ∑(Ki-Kaverage)2is that we can minimize this function simply by making Kivery small, but not necessarily constant. What we really want is for all the Kito be clustered around the mean value. A good way to do this is to minimize the relative standard deviationof the K, which is (standard deviation)/average. In cell E5we compute the average value of Kand in cell E6the standard deviation. Cell E7contains the relative standard deviation. Use Solver to minimize cell E7by varying cell A7. Compare your answer with that of Problem 19-13.

Here is an immunoassay to measure explosives such as trinitrotoluene (TNT) in organic solvent extracts of soil. The assay employs a flow cytometer, which counts small particles (such as living cells) flowing through a narrow tube past a detector. The cytometer in this experiment irradiates the particles with a green

laser and measures fluorescence from each particle as it flows past the detector.

1. Antibodies that bind TNT are chemically attached to 5mmdiameter latex beads.

2. The beads are incubated with a fluorescent derivative of TNT to saturate the antibodies, and excess TNT derivative is removed. The beads are resuspended in aqueous detergent.

3. 5mlof the suspension are added to 100mlof sample or standard. TNT in the sample or standard displaces some derivatized TNT from bound antibodies. The higher the concentration of TNT, the more derivatized TNT is displaced.

4. An aliquot is injected into the flow cytometer, which measures fluorescence of individual beads as they pass the detector. The figure shows median fluorescence intensity 6 standard deviation. TNT can be quantified in the ppb to ppm range.

Draw pictures showing the state of the beads in steps 1, 2, and 3and explain how this method works.

Simulating a Job’s plot. Consider the reaction A+2B⇌AB2,forwhichK=[AB2]/[A][B]2. Suppose that the following mixtures of A and B at a fixed total concentration of

10-4 M are prepared:

(b)Prepare a graph by the method of continuous variation in which you plot[AB2]versus mole fraction offor each equilibrium constant. Explain the shapes of the curves.
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