---
title: "A student uses a spectrophotometer set to a wavelength of \\(810\\text{ nm}\\) to determine the concentration of \\(\\text{Cu}^{2+}\\text{(aq)}\\) in aqueous \\(\\text{CuSO}_4\\) solutions. The student prepares a series of standard solutions and records their absorbances to construct the calibration plot shown. The solid curve represents the measured data points, and the dashed line represents the linear extrapolation of the data collected at concentrations \\(\\le 0.10\\text{ M}\\).  Which of the following best explains why the measured absorbance deviates from linearity at concentrations greater than \\(0.10\\text{ M}\\), and describes the effect on the calculated concentration if the linear equation from the dashed line is used for an unknown sample with a measured absorbance of \\(1.30\\)?"
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url: "https://nerd-notes.com/ubq/123731/"
date_modified: "2026-09-28T12:02:13+00:00"
---

# A student uses a spectrophotometer set to a wavelength of \(810\text{ nm}\) to determine the concentration of \(\text{Cu}^{2+}\text{(aq)}\) in aqueous \(\text{CuSO}_4\) solutions. The student prepares a series of standard solutions and records their absorbances to construct the calibration plot shown. The solid curve represents the measured data points, and the dashed line represents the linear extrapolation of the data collected at concentrations \(\le 0.10\text{ M}\).

Which of the following best explains why the measured absorbance deviates from linearity at concentrations greater than \(0.10\text{ M}\), and describes the effect on the calculated concentration if the linear equation from the dashed line is used for an unknown sample with a measured absorbance of \(1.30\)?

A student uses a spectrophotometer set to a wavelength of \(810\text{ nm}\) to determine the concentration of \(\text{Cu}^{2+}\text{(aq)}\) in aqueous \(\text{CuSO}_4\) solutions. The student prepares a series of standard solutions and records their absorbances to construct the calibration plot shown. The solid curve represents the measured data points, and the dashed line represents the linear extrapolation of the data collected at concentrations \(\le 0.10\text{ M}\).

Which of the following best explains why the measured absorbance deviates from linearity at concentrations greater than \(0.10\text{ M}\), and describes the effect on the calculated concentration if the linear equation from the dashed line is used for an unknown sample with a measured absorbance of \(1.30\)?

![A Cartesian coordinate graph titled 'Absorbance vs. Concentration at 810 nm'. The horizontal x-axis is labeled 'Concentration (mol/L)' and ranges from 0.00 to 0.25 with labeled tick marks at intervals of 0.05 (0.00, 0.05, 0.10, 0.15, 0.20, 0.25). The vertical y-axis is labeled 'Absorbance' and ranges from 0.00 to 1.60 with labeled tick marks at intervals of 0.20 (0.00, 0.20, 0.40, 0.60, 0.80, 1.00, 1.20, 1.40, 1.60). A solid curve passes through the origin (0.00, 0.00) and connects data points at (0.02, 0.20), (0.04, 0.40), (0.06, 0.60), (0.08, 0.80), (0.10, 1.00), (0.15, 1.25), (0.20, 1.38), and (0.25, 1.45). The solid curve is linear up to 0.10 mol/L, then curves downward with decreasing slope above 0.10 mol/L. A dashed straight line extends from (0.00, 0.00) through (0.10, 1.00) to (0.16, 1.60). A legend in the upper left indicates the solid curve with points as 'Measured Data' and the dashed line as 'Linear Extrapolation'. No other text, markers, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596932-m5eqHH.jpg)

- **A.** The deviation occurs because solute-solute collisions increase the effective optical path length through the solution; using the linear extrapolation will overestimate the true concentration.
- **B.** The deviation occurs because solute-solute collisions increase the effective optical path length through the solution; using the linear extrapolation will underestimate the true concentration.
- **C.** The deviation occurs because close interparticle interactions alter the electronic environment and reduce the effective molar absorptivity; using the linear extrapolation will overestimate the true concentration.
- **D.** The deviation occurs because close interparticle interactions alter the electronic environment and reduce the effective molar absorptivity; using the linear extrapolation will underestimate the true concentration.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123731/*