---
title: "A student uses a spectrophotometer to construct a standard calibration curve of absorbance versus concentration for \\(\\text{Co(NO}_3\\text{)}_2\\text{(aq)}\\) at \\(\\lambda = 510\\text{ nm}\\). All standard solutions are measured using a rectangular cuvette in the standard orientation shown, where the path length is \\(1.00\\text{ cm}\\).  When measuring the absorbance of a \\(\\text{Co(NO}_3\\text{)}_2\\text{(aq)}\\) solution of unknown concentration, the student accidentally places the cuvette in the rotated orientation, so the path length of the light beam is \\(0.50\\text{ cm}\\). The student then uses the calibration curve to determine the concentration of the unknown solution without correcting for the change in orientation.  Which of the following correctly predicts the effect of this error on the calculated concentration of the unknown solution, and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/119585/"
date_modified: "2026-08-21T06:54:04+00:00"
---

# A student uses a spectrophotometer to construct a standard calibration curve of absorbance versus concentration for \(\text{Co(NO}_3\text{)}_2\text{(aq)}\) at \(\lambda = 510\text{ nm}\). All standard solutions are measured using a rectangular cuvette in the standard orientation shown, where the path length is \(1.00\text{ cm}\).

When measuring the absorbance of a \(\text{Co(NO}_3\text{)}_2\text{(aq)}\) solution of unknown concentration, the student accidentally places the cuvette in the rotated orientation, so the path length of the light beam is \(0.50\text{ cm}\). The student then uses the calibration curve to determine the concentration of the unknown solution without correcting for the change in orientation.

Which of the following correctly predicts the effect of this error on the calculated concentration of the unknown solution, and provides the correct justification?

A student uses a spectrophotometer to construct a standard calibration curve of absorbance versus concentration for \(\text{Co(NO}_3\text{)}_2\text{(aq)}\) at \(\lambda = 510\text{ nm}\). All standard solutions are measured using a rectangular cuvette in the standard orientation shown, where the path length is \(1.00\text{ cm}\).

When measuring the absorbance of a \(\text{Co(NO}_3\text{)}_2\text{(aq)}\) solution of unknown concentration, the student accidentally places the cuvette in the rotated orientation, so the path length of the light beam is \(0.50\text{ cm}\). The student then uses the calibration curve to determine the concentration of the unknown solution without correcting for the change in orientation.

Which of the following correctly predicts the effect of this error on the calculated concentration of the unknown solution, and provides the correct justification?

![A top-down schematic diagram showing two cuvette orientations relative to a horizontal incident light beam represented by a horizontal black arrow pointing from left to right. On the left, labeled 'Standard Orientation', a rectangular cuvette is oriented with its longer internal dimension of \(1.00\text{ cm}\) parallel to the light beam and its shorter internal dimension of \(0.50\text{ cm}\) perpendicular to the light beam; the arrow passes straight through the \(1.00\text{ cm}\) path length. On the right, labeled 'Rotated Orientation', the same rectangular cuvette is oriented with its shorter internal dimension of \(0.50\text{ cm}\) parallel to the light beam and its longer internal dimension of \(1.00\text{ cm}\) perpendicular to the light beam; the arrow passes straight through the \(0.50\text{ cm}\) path length. Inside both cuvettes, uniform light gray shading represents the solution. No other text, labels, rays, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787295244-mzg4iG.jpg)

- **A.** The calculated concentration will be higher than the actual concentration because the shorter path length allows less light to be transmitted, resulting in a higher measured absorbance.
- **B.** The calculated concentration will be higher than the actual concentration because a smaller path length mathematically requires a higher concentration to produce the observed absorbance.
- **C.** The calculated concentration will be lower than the actual concentration because the molar absorptivity (\(\epsilon\)) of \(\text{Co}^{2+}\text{(aq)}\) decreases when the light beam traverses a shorter distance.
- **D.** The calculated concentration will be lower than the actual concentration because the light beam encounters fewer absorbing particles over the shorter distance, resulting in a lower measured absorbance.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119585/*