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Chapter 19: QC E (page 483)

19-C. The protein bovine serum albumin can bind several molecules of the dye methyl orange. To measure the binding constant K for one dye molecule, solutions were prepared with a fixed concentration \(\left( {{X_0}} \right)\) of dye and a larger, variable concentration of protein (P). The equilibrium is Reaction 19-18, with X 5 methyl

orange.

Experimental data are shown in cells A16-D20 in the spreadsheet on the next page. The authors report the increase in absorbance \((\Delta A)\) at 490 nm as P is added to X. X and PX absorb visible light, but P does not. Equilibrium expression 19-20 applies and (PX) is given by Equation 19-21. Before P is added, the absorbance is \({\varepsilon _X}{X_{0 - }}\). The increase in absorbance when P is added is

The spreadsheet uses Solver to vary K and \(\Delta E\) in cells B10:B11 to minimize the sum of squares of differences between observed and calculated \(\Delta A\) in solutions with different amounts of P. Cell E16 computes (PX) from Equation 19-21, which is Equation A on line 6 of the spreadsheet. Cells F16 and G16 find (X) and (P) from mass balances. Cell H16 computes \(\Delta {A_{calc}} = \Delta E(PX)\)which is Equation B on line 7.

To estimate a value of K in cell B10, suppose that 50% of X has reacted in row 20 of the spreadsheet. The total concentration of X is\({X_0} = 5.7\mu M\). If half is reacted, then \((X) = (PX) = 2.85\mu M\) and\((P) = {P_0} - (PX) = 40.4 - 2.85 = 37.55\mu M\). The binding

constant is \(K = (PX)/(P)(X)) = (2.85\mu M)/(37.55\mu M)(2.85\mu M)) = \)\(2.7 \times 1{0^4}\) which we enter as our guess for K in cell B10. We estimate \(\Delta \varepsilon \)in cell B11 by supposing that 50% of X has reacted in row 20. In Equation B on line 7, \(\Delta A = \Delta \varepsilon (PX)\).The measured

value of \((\Delta A)\)in row 20 is 0.0291 and we just estimated that \((PX) = \)\(2.85\mu M\). Therefore, our guess for \(\Delta \varepsilon \)in cell B11 is \(\Delta \varepsilon = \Delta A/\)\((PX) = (0.0291)/(2.85\mu M) = 1.0 \times 1{0^4}\)

Your assignment is to write formulas in columns E through J of the spreadsheet to reproduce what is shown and to find values in cells E17:J20. Then use Solver to find K and \(\Delta \varepsilon \)in cells B10:B11 to minimize \(\Sigma {\left( {{A_{oths\;}} - {A_{calc\;}}} \right)^2}\)in cell I21.

Short Answer

Expert verified

The value of\({\rm{\Delta }}\varepsilon \)and K which is in cell B10:B11 will minimize \({\rm{\Sigma }}{\left( {{A_{{\rm{oths\;}}}} - {A_{{\rm{calc\;}}}}} \right)^2}\)in cell I21. We get the spreadsheet as,

Step by step solution

01

Find K:

The value of\({\rm{\Delta }}\varepsilon \)and K which is in cell B10:B11 will minimize \({\rm{\Sigma }}{\left( {{A_{{\rm{oths\;}}}} - {A_{{\rm{calc\;}}}}} \right)^2}\)in cell I21. We get the spreadsheet as,

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Most popular questions from this chapter

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.

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

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.

Iodine reacts with mesitylene to form a complex with an absorption maximum at 332 nm in CCl4 solution:

(b)Spectrophotometric data for this reaction are shown in the table.Because[mesitylene]tot>>[I2],we can say that [mesitylene]≈[mesitylene]tot. Prepare a graph ofA/([mesitylene][I2]tot)versusA/[I2]totand find the equilibrium constant and molar absorptivity of the complex.

Method of continuous variation. Make a graph of absorbance versus mole fraction of thiocyanate from the data in the table.

(c)Why does one solution containacid and the otheracid?
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