Final answer:
To find the molar absorptivity of KMnO4 at 520 nm, calculate the absorbance from the transmittance, determine the molarity by converting ppm to mol/L, and apply Beer's law. However, the calculated molar absorptivity does not match the options given, suggesting there may be an error in the provided data.
Step-by-step explanation:
To calculate the molar absorptivity of KMnO₄ at 520 nm, we need to use Beer's law, which states that absorbance (A) is equal to the molar absorptivity (ε) multiplied by the concentration (C) and the path length (l), where A = εCl. Here, the transmittance (T) of 0.145 corresponds to an absorbance (A), since A = -log(T). First, calculate the absorbance from the transmittance:
A = -log(0.145) = 0.839
Next, we need to find the concentration in mol/L (molarity) of the KMnO₄ solution. Since 1 ppm is equivalent to 1 mg/L, a solution containing 7.35 ppm KMnO₄ is 7.35 mg/L. Now determine the molar mass of KMnO₄ (which is approximately 158.04 g/mol) and convert mg to g to mol.
Molar mass of KMnO₄ = 158.04 g/mol
Concentration (C) in g/L = 7.35 mg/L = 0.00735 g/L
Number of moles = 0.00735 g / 158.04 g/mol = 4.65 x 10^-5 mol/L
Finally, apply Beer's law to find the molar absorptivity by rearranging the equation to solve for ε:
ε = A / (Cl) = 0.839 / (4.65 x 10^-5 mol/L * 1.00 cm) = 18029 L/(mol·cm)
However, none of the options provided in the question match this calculated value. Please check the starting data for transmittance, path length, or the ppm value as any inconsistencies could affect the result.