Question

question 4 12.5 pts after the calibration curve is created, the cuvette is misplaced. it is replaced for the drink samples measurements with a new cuvette that absorbs more light than the original cuvette. what can be said about the value of the dye concentration in the drink samples that is calculated? transmittance $(t)=\frac{i_{t}}{i_{o}}$ absorbance $(a)=-\log (t)=-\log \left(\frac{i_{t}}{i_{o}}\
ight)$ figure 3: diagram of incident light $i_{0}$ passing through a sample of concentration $c$ in a cuvette with path length $b$, and the resulting intensity of the transmitted light $i$. $i_{0}=$ intensity of incident light $i=$ intensity of light transmitted through the sample $c=$ concentration of the species in solution $b=$ path length of the cell the concentration will be higher because the absorbance measured for the unknown will be smaller. the concentration will be higher because the absorbance measured for the unknown will be larger. the concentration will be lower because the absorbance measured for the unknown will be larger. the concentration will be lower because the absorbance measured for the unknown will be smaller.

Explanation:

Step1: Understand Beer - Lambert Law

Beer - Lambert Law is \(A=\epsilon bc\), where \(A\) is absorbance, \(\epsilon\) is molar absorptivity (constant for a given species and wavelength), \(b\) is path length (constant here as it's the same cuvette for measurements), and \(c\) is concentration. Calibration curve is \(A = kc\) ( \(k=\epsilon b\), constant for calibration setup).

Step2: Analyze effect of cuvette change on absorbance

Original cuvette: Calibration curve \(A_{cal}=k c\). New cuvette absorbs more light. For the same sample (same dye concentration \(c\) in reality), \(I = I_0 - I_{absorbed}\). Since new cuvette absorbs more light (\(I_{absorbed}\) is larger for the cuvette itself), the \(I\) (transmitted light through the sample - cuvette system) is smaller. Using \(A=-\log(\frac{I}{I_0})\), a smaller \(I\) (for the same \(I_0\)) gives a larger \(A\) reading for the sample (but this is due to cuvette, not dye).

Step3: Relate absorbance to concentration calculation

From calibration curve \(c=\frac{A}{k}\). If \(A\) (measured) is larger (due to cuvette, not actual dye concentration increase), then \(c\) (calculated) will be larger. But in reality, the dye concentration is the same. So the calculated concentration will be higher because the measured absorbance (due to cuvette - sample system, with cuvette contributing more absorbance) is larger.

Answer:

The concentration will be higher because the absorbance measured for the unknown will be larger.