Answer Happy

in the results sheet how do i find the Aln- and the AHIn?
Figure 1 . Molecular strictiares of acid and base forms of bromophenot Mier Equation 2 shows the equilibrium constant expression for a typical acid-base indicator, in which Ka ​ represents the equilibrium constant. KΔ​=[HIn]H+∣In​−1​ If we take the logarithm of both sides of Equation 2, multiply both sides by −1, and rearrange the terms, we can obtain Equation 3, in which pKa ​ equals −logKar ​ and pH equals log[H+]. (Eq. 3) In this experiment, we will determine the pKa​ of the acid-base indicator, bromophenol blue. This indicator's acid form predominates below pH3.0, resulting in a yellow solution. Its base form predominates above pH 4.6, producing a violet solution. The molecular structures of the acid and base forms of bromophenol blue are shown in Figure 1 . Bromophenol blue is a useful indicator for an acid-base titration in which the equivalence point occurs at about pH 3.8. For example, we could use bromophenol blue as the indicator when titrating a weak base, such as hydrogen carbonate ion (HCO3​7, with a strong acid, such as hydrochloric acid (HCl). Determining the pKn​ of Because the acid and base forms of bromophenol blue are both colored, we Bromophenol Blue Using can use spectrophotometry to monitor the concentrations of the two forms Spectroscopy in solution. We do so by measuring the intensity of light transmitted by the solution at a maximum absorbance wavelength, λmax ​ unique to each color. We then relate the percent transmittance (\%T) at each λmax​ to the absorbance (A) of the solution, using Equation 4 . A=−log(%T/100) Beer's law states that the absorbance of a species in solution is directly proportional to the concentration of that species. Thus, for bromophenol blue, we can relate A at the λmax​ for the yellow Hin to the concentration of the acid form. Similarly, we can relate A at the λmax​ for the violet ln−to the concentration of the base form.
Problem 1 What is the absorbance of a solution with a 7T of 23.95 ? Solufion: We use Equation 4, A​=−log(%T/100)=−log(23.9/100)=−log0.239=0.622​ However, to best determine the |f finl/in 1 concentration ratio in Equation 3 for bromophenol blue, we use orly the λ mas for the base form. This is because the absorbance at the λmax ​ for the base form is much greater than the absorbance at the D mas for the acid form. In addition, the scid form absorbs almost no light at the 7 mes for the base form, resulting in little interference. The λmax​ for the base form of bromophenol blue is around 590 nm, as shown in Figure 2 in this experiment, we will first determine the exact value of λmix​ for the base form, using a spectrophototneter. After determining the exact value of 7 mar for the base form of bromophenol bluc, we can modify Equation 3 by replacing the concentrations of Hin and In −with the following bromophenol blue absortances, measured at the λmax​ for the base form. These substitutions result in Equation 5 . pK4​=pH+log[(AHL−A)(A−A/−)​] In Equation 5, A is the absorbance of a mixture of the acid and base forms at a known total indicator concentration. Ath - ​ is the absorbance of the pure base form at the same concentration. A1​ in is the absorbance of the pure acid form at the same concentration. To determine the pK, of bromophenol blue using Equation 5 , we must prepare a bromophenol blue solution with a precisely known pH value that is between 3.0 and 4.6. This pH range is crucial because the ratio has a measurable value only for solutions within this pH range. (AHln​−A)(A−Aln​−)​ Figure 2 Absorption spectra for the acid and kase forms of bromophenio blue
We can determine the pK, for an acid-base indicator either algebraically or graphically. In the algebrale method, we use Equation 5 to calculate the pKes for several different indicator solutions. We then use these values to determine the average pKw​ from which we can derive the average Ka​ as well. To determine the pKe ​ for an acid-base indicator uaing the graphical method, we rearrange Equation 5 to yleld Equation 6. pH=−log[((A+​Hm​−A)A−Am−)​)+pK4​ This equation is in the form of a straight-line equation, y=max+b, in which pH corresponds to y, log[(A+lin​−A)(A−Aln−2​)​] corresponds to x, the slope m is −1, and pKd​ corresponds to b, the y. intercept. Our graph of pl versus. log[(A+ln−A4)(A−A An −)​] data will have a y-intercept equal to the pKo- The following data were obtained for solutions of the acid-base indicator. bromocresol green. The absorbance readings were taken at the λ mas for the base form of this indicator. The total indicator concentration was the same in all five solutions. absorbunce readings for bromocresol green solutions with different pH bulues In addition, the absorbance was 0.953 for the pure base form of the indicator, In −, at the same total indicator concentration. The absorbance was 0.016 for the pure acid form of the indicator, HIn, at the same total indicator concentration. Problem 2 Algebraically determine pK, for each bromocresol green solution. Determine the average pK. Using the average pK. calculate K0​ for bromocresol green. Solution We use Equation 5 for each solution. The calculations for the data for the pH4.20 solution are shown below: (AHln ​−A)(A−Aln−)​)​=(0.016−0.281)(0.281−0.983)​=(−0.265)(−0.702)​=2.65log2.65=0.423pKKd​=pH+log[(AHlln ​−A)(A−Aln−−​)​]=4.20+0.423=4.62​
The following table compiles the results for all five solutions. The average pK, is ​ 5(4.62+4.62+4.61+4.61+4.62)​=4.62 Using the definition of PK∞​ we can calculate K, as follows: Ks​=10−pK4​=10−6e2=2.4×10−5 Problem 3 Graphically determine the average pK, for bromocresol green. Solution To determine the average pKa ​ graphically, we plot pH versus log[(Athls ​−A)(A−Abn ​)​] as shown in Figure 3 . The y-intercept for the straight line drawn through the data points is 4.62; thus, the average pKa​ is 4.62. The slope of this line is −0.99, well within experimental-error range of the −1 predicted by Equation 6 . We note that the average pKdetermined ​ using the graphical method and the average pK, determined using the algebraic method are identical. demonstrating that the two methods are equally accurate. Figure 3 Plot of μH tersus log[A+−A)(A−As−)​] for bromocresol grect solvtions
I. Determining the λmax​ of the Base Form of Bromophenol Blue λmax​=100 nm II. Preparing Bromophenol Blue Solutions with Different pH Values
III. Measuring Percent Transmittance Values of the Bromophenol Blue Solutions
Results Sheet