Two different benchtop spectrophotometers are available in a teaching laboratory
CHEMISTRY · Multi-part · AP · Chemistry · Properties of Substances and Mixtures · Properties of Substances and Mixtures
Problem
Two different benchtop spectrophotometers are available in a teaching laboratory. Instrument A employs a fixed rectangular cell with an optical path length of 0.800 cm, whereas Instrument B uses a cylindrical flow cell with an effective path length of 2.00 cm. A student prepares a series of standard solutions of an organic pigment, each having the same concentration.
Answer the following questions about the effect of path length on signal strength and sensitivity.
(a) For a given standard solution, derive an expression for the ratio absorbanceAabsorbanceB in terms of the two path lengths.
(b) Using your expression from part (a), calculate the numerical value of the ratio for the path lengths provided.
(c) Explain how the difference in path length influences the sensitivity of each instrument when constructing a calibration curve for the pigment. Your discussion should address both the slope of the curve and the practical detection limit for low-concentration samples.