Final answer:
Using the Beer-Lambert law, the concentration of the substance in solution is calculated to be 2.5 x 10^-4 mol L^-1, based on the given absorbance of 1.0, molar absorptivity of 2 x 10^3 L mol^-1 cm^-1, and a path length of 2.0 cm.
Step-by-step explanation:
To calculate the concentration of the substance in solution using the spectrophotometric data provided, we will apply the Beer-Lambert law, which is given by the equation Absorbance (A) = ε * c * l, where A is the absorbance, ε is the molar absorptivity, c is the concentration of the solution in moles per liter (M), and l is the path length in centimeters.
In the given scenario, the absorbance (A) is 1.0, the molar absorptivity (ε) is 2 x 103 L mol-1 cm-1, and the path length (l) is 2.0 cm. Plugging these values into the Beer-Lambert law, we get:
1.0 = (2 x 103 L mol-1 cm-1) * c * (2.0 cm)
To isolate the concentration (c), we rearrange the equation to solve for c:
c = 1.0 / (2 x 103 L mol-1 cm-1 * 2.0 cm)
c = 1.0 / (4 x 103 L mol-1)
c = 2.5 x 10-4 mol L-1
Therefore, the concentration of the substance in the solution is 2.5 x 10-4 mol L-1.