Week 4: The Spectra of Conjugated Dyes and Investigation of Beer's Law Overview Getting Started Techniques Procedure FAQ Full Lab Manual Introduction & Goals Chemistry & Background Key Questions Prelab Problems Safety Procedure In Your Write-up Experiments Index ChemLab Home		Before Lab Before coming to lab, complete the four prelab problems. Write the procedure and sample calculations in your notebook. In Lab While in the lab, record your observations and data in your notebook. Plot the spectrum of Dye A or B and your Beer's Law plot(s) using graph paper available in the lab. Attach scanned spectra with tape or staples to the pages of your notebook. Your complete data and results should consist of the following: • Scanned spectrum of Dye B and Dye A • Scanned spectrum of drink solution • Paper chromatogram of drink mix • Concentration vs. absorbance data at max for each food dye, including Beer's Law plot. • Absorbance of drink solution at all relevant wavelengths After Lab You are required to do a formal laboratory report for this experiment, as described in the introduction of this manual. Please prepare a word-processed lab report which includes a(n) title page, abstract, theory section, procedure section, your data, results, calculations, uncertainty analsis, discussion and references. You should address the following in the write up of your formal report: Spectra of Conjugated Dyes Summarize your results and relate them to the appropriate theory. This means that you should • Discuss the colors of the dyes and the relation between absorbance and transmittance spectra and perceived color. Compare the wavelength of maximum absorbance to your predictions, based on the observed color of each solution. Plot the absorbance and transmittance spectra and relate your results to the color wheel. • Summarize the experimental results and theoretical results using the free electron model. Count the number of "free" electrons and calculate an estimated box length using the assumptions given in the introduction. Use Equation (7) or the Electrons in a box applet to calculate a theoretically predicted wavelength and compare to the maximum absorbance wavelength from the experiment. These theoretical calculations are part of the prelab problems and need not be repeated, but should be discussed, briefly. • Discuss the agreement between experiment and theory, including possible reasons why the two results may not agree. Determination of Food Dye Concentration in Drink Mix Your analysis should include a least squares fit to the Beer's Law equation for each individual dye present in your drink mix. Remember that you measured the absorbance of the blank solution, so you should include a point at the origin in your least squares fit. The concentrations of your solutions should be calculated and plotted in units of molarity. From the slope of each plot, calculate the extinction coefficient, , at the wavelength of maximum absorption. Report the uncertainty in the slope as a 95% confidence interval. If more than one plot is required, a least squares analysis should be done on each one. The concentration of all identified food dyes in the drink solution should be determined from the standard Beer's Law plot(s) for the pure dye(s) and reported in units of molarity, moles dye per gram drink mix, and percent dye by mass in the powdered drink mix. Your concentrations should be reported with an uncertainty value, calculated from the 95% confidence interval given by the Least Squares program. More details about the uncertainty analysis are given below. For this experiment, your discussion should include: • Identification of the dyes present in your drink solution from the absorption spectrum and the chromatogram, and a discussion of the relationship between the two results. • Summary of results for the concentration of dye(s) present in the drink mix • Discussion of contributions to the uncertainty of your results. Uncertainty Analysis Since the final results of the Koolaid experiment consist of the concentration(s) of dye(s) in the drink solution, it is appropriate to estimate the accuracy with which this concentration has been determined. A significant figures analysis will give an estimate of the uncertainty. A more thorough analysis would use the error propagation results described in the beginning of this manual. The following paragraph describes the error propagation for this experiment. The concentration of dye in the Koolaid is calculated from the slope of your Beer's Law plot and the absorbance reading of your Koolaid solution, using the Beer's Law equation: c = A / L = A / slope Since the concentration is calculated by dividing the absorbance by the slope, we will use the error propagation results multiplication and division. The relative uncertainty in the concentration of the unknown dye solution is related to the relative uncertainty in the slope and the absorbance reading of your Koolaid solution: (10) The relative uncertainty in the absorbance measurement can be calculated by dividing the uncertainty with which you measured the absorbance, estimated in the lab, by the absorbance value. To determine the relative uncertainty in the slope you will make use of the statistical uncertainty determined by the Least Squares program for your Beer's Law plot. The program will report an uncertainty in the slope as a 95% confidence interval. This means that there is a 95% probability that the actual value of the slope lies within the range given by the slope plus or minus the interval. To determine the relative uncertainty in the slope, divide this 95% confidence interval by the value of the slope. Then use the two relative uncertainties to calculate the relative uncertainty in the concentration of the dye in the drink mix using Equation (10). The magnitude of the two relative uncertainties in Equation (10) will show you which factor contributes the most to the uncertainty in your final result. Finally, you can use the relative uncertainty and the value of the concentration to calculate the absolute uncertainty in the concentration, concentration. Your final result should be reported as the concentration ± concentration. Note that the relative uncertainty of concentration will be the same for different concentration units, but the absolute uncertainty will be different.
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