Allura Red (FD&C; Red 40, molar mass = 496.42 g/mol) is a common red dye that is

Question

Allura Red (FD&C; Red 40, molar mass = 496.42 g/mol) is a common red dye that is used in cosmetics, medicine, and food. A student made three different solutions of red dye and used them to construct a Beer's law calibration curve using the wavelength of maximum absorption. The path length of the cuvette used was 1.20 cm. The equation for the line of best fit is given on the graph. A student wanted to determine the concentration of Allura red dye in a 1.00 L bottle off red Mountain Dew The student used a 10-mL volumetric pipet to transfer 20 mL of the Mountain Dew to a 100-mL volumetric flask and then added distilled water to the mark on the flask. The absorbance of this diluted solution at 504 nm was 0.480. Using the line of best fit given above, determine the concentration (in ppm) of Allura red dye in a 1.00 L bottle of red Mountain Dew. You can assume the density of Mountain Dew is 1.00 g/mL. Was it necessary for the student to dilute the red Mountain Dew before taking the absorbance? Briefly explain your reasoning. How do you expect the slope of the line-of-best fit for a Beer's law calibration graph of blue Mountain Dew at 504 nm to compare to the slope of the line-of-best fit for a Beer's law calibration graph of blue Mountain Dew at 620 nm? Briefly explain your answer.

Explanation / Answer

(1)

Using the calibration plot equation:

y = 30451x + 0.0132

Putting y = 0.48, we get:

x = 1.53*10-5 M

This is the conc when the original solution was diluted 5 times in the 100 mL flask

So conc in the original 1 L solution is:

5*1.53*10-5 = 7.65*10-5 M

Moles of dye in 1 L solution = 7.65*10-5

MW of allura red dye is 496.4 g

So, mass of dye in 1 L solution = 7.65*10-5*496.4 = 0.038 g = 38 mg

So, conc of dye = 38 mg/mL

Since 1 mg/mL = 1 ppm

So, conc of dye = 38 ppm

(2)

It was necessary to dilute the solution before taking absorbance readings because Beer's law is valid only for dilute solutions. The absorbance reading values greater than 1 are considered absurd.

So it is necessary to bring the solution to such a conc such that its absorbance reading is recorded below 1

(3)

The slope will be the same, because the slope just tells the rate of change for absrorbance readings with change in conc values. Since we don't change the solution, and only the absorption wavelength is changed, the slope remains the same for both cases.

It's possible to have different intercept readings in these cases though.

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