Interpreting a Graph of Absorbance vs. Concentration
A student prepares a series of standard solutions of a colored compound and measures their absorbance using a spectrophotometer. The data are plotted with concentration (M) on the x-axis and absorbance on the y-axis. The line of best fit passes through the points (0.00, 0.00) and (0.0200, 0.450). The student then measures the absorbance of an unknown solution and obtains a value of 0.675. The student uses the graph to find the concentration of the unknown. However, the student notices that the point for the highest standard (0.0300 M, absorbance 0.720) deviates from the line. The student wonders if the unknown concentration is reliable and how to handle the deviation.
1. Determine the slope of the line of best fit and use it to calculate the concentration of the unknown solution.
Read the worked answer
Slope = (0.450 - 0.00) / (0.0200 - 0.00) = 0.450 / 0.0200 = 22.5 M^-1. Using Beer's law: A = slope × c. So c = A / slope = 0.675 / 22.5 = 0.0300 M. The unknown concentration is 0.0300 M.
2. The student notices that the standard at 0.0300 M has an absorbance of 0.720, which is lower than the value predicted by the line (0.675? Wait, predicted would be 22.5*0.0300=0.675). Actually, the predicted absorbance for 0.0300 M is 0.675, but the measured is 0.720, which is higher. Re-read: The point is (0.0300, 0.720). The line predicts 0.675. So the measured absorbance is higher than expected. Does this affect the reliability of the unknown concentration? What should the student do?
Read the worked answer
The point at 0.0300 M deviates from linearity (measured 0.720 vs predicted 0.675). This suggests that at higher concentrations, the relationship may no longer be linear (due to instrumental deviations or chemical interactions). Since the unknown's absorbance (0.675) falls within the linear range (up to 0.0200 M), the concentration calculated from the line (0.0300 M) is actually outside the linear range. The student should either dilute the unknown to bring its absorbance into the linear range or prepare a new calibration curve that includes higher concentrations if linearity holds. Using the current line to determine a concentration outside the calibrated range is unreliable.