Final answer:
The molarity (M) of the unknown solution is found by applying Beer's law and using the ratio of the absorbances and the concentration of the known solution. In this case, the molarity of the unknown solution is 0.0288 M.
Step-by-step explanation:
To determine the molarity (M) of the unknown based on its absorbance, we can apply Beer's law, which states that the absorbance (A) of a solution is directly proportional to the concentration (c) and the path length (l), and is also dependent on the molar absorptivity (ε). The formula is A = εcl. Assuming the path length (l) is the standard 1 cm and that ε is constant for both the known and unknown solutions, we can set up a proportion to find the unknown concentration using the data from the known solution.
Using the provided information:
- Known solution concentration: 0.05 M
- Known solution absorbance: 0.399
- Unknown solution absorbance: 0.231
By dividing the absorbances, we get the ratio of the concentrations:
0.231 / 0.399 = c_unknown / 0.05 M
Solving for c_unknown:
c_unknown = (0.231 / 0.399) * 0.05 M
Therefore, the molarity of the unknown is calculated as follows:
c_unknown = 0.0288 M