Calculate percent recovery for each dye extract using the grape Kool-Aid spectrum as the starting value. Generically, percent recovery is calculated using this formula: \% recovered = \frac{recovered \, amount}{starting \, amount} \times 100\% Since absorbance is directly related to concentration, the ratio of absorbances will be the same as the ratio of concentrations. Hint: use values corresponding to
. Show calculations. red dye 0.8Calculate percent recovery for each dye extract using the grape Kool-Aid spectrum as the starting value. Generically, percent recovery is calculated using this formula: \% recovered = \frac{recovered \, amount}{starting \, amount} \times 100\% Since absorbance is directly related to concentration, the ratio of absorbances will be the same as the ratio of concentrations. Hint: use values corresponding to
. Show calculations. red dye 0.8
The Correct Answer and Explanation is:
To calculate the percent recovery of the red dye from grape Kool-Aid, we use the fact that absorbance is directly proportional to concentration, according to Beer-Lambert Law. Therefore, we can substitute absorbance values in place of concentration in the percent recovery formula: %Recovered=(Recovered absorbanceStarting absorbance)×100%\% \text{Recovered} = \left( \frac{\text{Recovered absorbance}}{\text{Starting absorbance}} \right) \times 100\%
Given:
- Starting absorbance (grape Kool-Aid spectrum) for red dye: 0.800
- Let’s say after extraction, the absorbance of the recovered red dye is measured as: 0.600
Calculation:
%Recovered=(0.6000.800)×100%=0.75×100%=75%\% \text{Recovered} = \left( \frac{0.600}{0.800} \right) \times 100\% = 0.75 \times 100\% = \boxed{75\%}
Explanation
In this experiment, the goal is to quantify how much of the red dye was successfully extracted from the grape Kool-Aid solution. The method relies on UV-Vis spectroscopy, which measures how much light is absorbed by a sample at a particular wavelength. The more dye present in a solution, the higher the absorbance will be at its characteristic wavelength.
According to the Beer-Lambert Law, absorbance (A) is directly proportional to the concentration (C) of the absorbing species: A=ε⋅b⋅CA = \varepsilon \cdot b \cdot C
where:
- ε\varepsilon is the molar absorptivity (a constant),
- bb is the path length of the cuvette (usually 1 cm),
- CC is the concentration of the dye.
Since ε\varepsilon and bb remain constant during measurements, any change in absorbance directly reflects a change in concentration. Therefore, we can use the absorbance ratio to represent the concentration ratio.
If the starting red dye absorbance in the Kool-Aid solution was 0.800, and the absorbance of the recovered extract is 0.600, it indicates that 75% of the red dye was successfully recovered. This means the extraction process was fairly efficient but not perfect.
Such calculations are vital in analytical chemistry and quality control. They help assess the efficiency of purification, extraction, or recovery methods. A lower percent recovery may suggest incomplete extraction, degradation of the dye, or loss during handling. Conversely, values close to 100% suggest a highly efficient process.
In real lab scenarios, you would measure the recovered dye’s absorbance at the red dye’s maximum absorbance wavelength (λmax), ensuring accuracy.
