Questions 10-13 refer to the following information. Cu(s) + 4 HNO3(aq) → Cu(NO3)2(aq) + 2 NO2(g) + 2 — Solutions Chemistry Question

STEPS:

1. Understand the underlying chemistry principle (Beer's Law): Beer’s Law states that the absorbance ($A$) of a solution is directly proportional to its concentration ($C$) when the path length and wavelength are held constant:
$$A = \epsilon bC$$
Because of this direct, linear relationship, as the concentration of a chemical species increases, its measured absorbance must also increase in a highly predictable, linear fashion.
2. Examine the provided standard calibration data: Look closely at the recorded values in the student's table:
* At $0.025\text{ M}$: Absorbance is $0.059$
* At $0.050\text{ M}$: Absorbance is $0.235$
* At $0.100\text{ M}$: Absorbance is $0.117$
* At $0.200\text{ M}$: Absorbance is $0.468$
3. Identify the anomaly in the data:
* Comparing the $0.050\text{ M}$ and $0.100\text{ M}$ entries, the concentration doubles, but the recorded absorbance bizarrely drops by half (from $0.235$ down to $0.117$).
* This non-monotonic behavior directly violates Beer’s Law, indicating a major error in the preparation or recording of those specific standards.
4. Test the hypothesis of reversed cuvette labels:
Let's check what the data looks like if we assume the student accidentally swapped the labels on the $0.050\text{ M}$ and $0.100\text{ M}$ cuvettes:
* For $0.025\text{ M}$: $\frac{\text{Absorbance}}{\text{Concentration}} = \frac{0.059}{0.025} = \mathbf{2.36}$
* For $0.050\text{ M}$ (using swapped value $0.117$): $\frac{0.117}{0.050} = \mathbf{2.34}$
* For $0.100\text{ M}$ (using swapped value $0.235$): $\frac{0.235}{0.100} = \mathbf{2.35}$
* For $0.200\text{ M}$: $\frac{0.468}{0.200} = \mathbf{2.34}$
5. Conclude the correct option: Because the ratio of absorbance to concentration becomes beautifully constant ($\approx 2.35$) across all data points when we swap the $0.050\text{ M}$ and $0.100\text{ M}$ values, it is highly likely that the student accidentally swapped the labels on these two cuvettes. This matches Option C.

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WHY_OTHERS_WRONG:

• Option A is incorrect: If the copper solution from the original mixture was not diluted properly, it would only affect the measured absorbance of the "Unknown" sample (making the $0.330$ value inaccurate). It would have absolutely no impact on the four standard solutions, which are prepared separately to build the calibration curve.
• Option B is incorrect: Calibrating the spectrophotometer with tap water instead of distilled water would introduce impurities that absorb light. This would shift the baseline absorbance, causing a consistent systematic offset (either adding or subtracting a constant value) across all samples, but it would not cause the absorbance of a more concentrated solution to drop below that of a less concentrated one.
• Option D is incorrect: Setting the spectrophotometer to an inappropriate wavelength would reduce the overall sensitivity of the experiment (resulting in much lower absorbance readings for all trials because the light is not absorbed well). However, the relationship between concentration and absorbance would still remain strictly linear and increase monotonically, rather than dropping and rising erratically.