To solve this problem, we will use Beer-Lambert's Law, which states that the absorbance (\(A\)) of a solution is related to its percent transmittance (%T) by the formula:
\(A = -\log_{10}(T)\)
where \(T\) is the transmittance in decimal form. Since percent transmittance is given, we first convert this to a decimal by dividing by 100:
\(T = \frac{39.8}{100} = 0.398\)
Now, we can calculate the absorbance:
\(A = -\log_{10}(0.398)\)
Calculating the above gives:
\(A \approx 0.4\)
Next, we need to find the molar extinction coefficient (\\(\epsilon\)), using the Beer-Lambert Law formula:
\(A = \epsilon \cdot c \cdot l\)
where \(c\) is the concentration (given as \(8 \times 10^{-5} \, \text{M}\)) and \(l\) is the path length (given as 1 cm). Substituting the known values:
\(0.4 = \epsilon \cdot (8 \times 10^{-5}) \cdot 1\)
Solving for \(\epsilon\) gives:
\(\epsilon = \frac{0.4}{8 \times 10^{-5}} = 5000 \, \text{M}^{-1} \, \text{cm}^{-1}\)
Thus, the absorbance is 0.4 and the molar extinction coefficient is 5000 \(\text{M}^{-1} \, \text{cm}^{-1}\).
The correct answer is therefore:
0.4 and 5000