Chemistry

Problem

A student prepares five aqueous cobalt(II) nitrate standards of known concentration and measures their absorbance at 510 nm using a 1.00 cm quartz cuvette. The data are recorded in the table below.

Concentration (mol L⁻¹)	Absorbance
0.0200	0.286
0.0400	0.570
0.0600	0.854
0.0800	1.140
0.100	1.422

Answer the following questions about the relationship between the two variables. (a) Describe the mathematical relationship you would expect between absorbance and concentration for this experiment, citing evidence from the data above. (b) Explain why keeping both the optical path length and the wavelength of the incident light constant is critical for the validity of the relationship you identified in part (a). (c) The slope of the best-fit line through the data is

14.2\;\text{L mol}^{-1}

. State the physical quantity represented by this slope and interpret its meaning in the context of this experiment.

Intuitive explanation

This problem tests Beer's Law, which relates absorbance to concentration through a linear relationship: $A = \varepsilon bc$ , where $\varepsilon$ is the molar absorptivity, $b$ is the path length, and $c$ is concentration. Your job is to verify that the data follows this law by checking if absorbance and concentration are proportional—meaning a plot should be linear and pass through the origin. The slope of that line tells you the product $\varepsilon b$ , which characterizes how strongly the cobalt(II) ions absorb light at this wavelength.

Intuitive explanation

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