A solution was prepared using 0.0010 g of an unknown steroid (of molecular weight around 255) in 100 mL of ethanol. Some of this solution was placed in a 1-cm cell, and the UV spectrum was measured. This solution was found to have λ_max = 235 nm, with A = 0.74.


(a) Compute the value of the molar absorptivity at 235 nm.
(b) Which of the following compounds might give this spectrum?


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Verified step by step guidance

1. Step 1: To calculate the molar absorptivity, we first need to calculate the molarity of the solution. The molarity (M) is calculated by dividing the number of moles of solute by the volume of the solution in liters. The number of moles of solute is calculated by dividing the mass of the solute by its molecular weight. In this case, the mass of the solute is 0.0010 g and the molecular weight is approximately 255 g/mol. The volume of the solution is 100 mL or 0.1 L.
2. Step 2: After calculating the molarity, we can use the Beer-Lambert law to calculate the molar absorptivity. The Beer-Lambert law is A = εlc, where A is the absorbance, ε is the molar absorptivity, l is the path length of the light through the solution (in cm), and c is the concentration of the solution (in M). In this case, A = 0.74, l = 1 cm, and c is the molarity we calculated in step 1.
3. Step 3: To identify which of the given compounds might give this spectrum, we need to consider the λ_max value. The λ_max value is the wavelength at which the compound absorbs the most light. In this case, the λ_max value is 235 nm. Compounds that absorb light at this wavelength typically contain conjugated double bonds or aromatic rings.
4. Step 4: Look at the structures of the given compounds and identify any that contain conjugated double bonds or aromatic rings. These are the compounds that are most likely to give a spectrum with a λ_max of 235 nm.
5. Step 5: Keep in mind that other factors can also influence the UV spectrum of a compound, such as the presence of functional groups and the overall shape of the molecule. Therefore, the identification of the compound based on the UV spectrum should be considered as a hypothesis that needs to be confirmed with additional data or experiments.

Key Concepts

Molar Absorptivity (ε)

Molar absorptivity, also known as molar extinction coefficient, is a measure of how strongly a chemical species absorbs light at a given wavelength. It is defined as the absorbance (A) of a solution divided by the product of the concentration (c) in moles per liter and the path length (l) in centimeters. The formula ε = A / (c * l) allows for the calculation of ε, which is crucial for understanding the light-absorbing properties of compounds in UV-Vis spectroscopy.

UV-Vis Spectroscopy

UV-Vis spectroscopy is an analytical technique used to measure the absorbance of ultraviolet or visible light by a substance. The technique relies on the electronic transitions of molecules, where specific wavelengths of light are absorbed, leading to quantifiable data. The resulting spectrum provides information about the electronic structure of the compound, allowing for the identification of functional groups and the determination of concentration based on Beer-Lambert Law.

Beer-Lambert Law

The Beer-Lambert Law describes the relationship between absorbance and concentration of a solution. It states that absorbance (A) is directly proportional to the concentration (c) of the absorbing species and the path length (l) of the light through the solution, expressed as A = ε * c * l. This law is fundamental in quantitative analysis, enabling the calculation of unknown concentrations from measured absorbance values, which is essential for interpreting UV-Vis spectra.