To calculate the molar absorptivity (ε) of a solution using the Beer-Lambert Law, we can follow these steps:
1. Understand the Beer-Lambert Law:
The Beer-Lambert Law is given by the equation:
[tex]\[
A = \varepsilon \cdot c \cdot l
\][/tex]
where:
- [tex]\( A \)[/tex] is the absorbance,
- [tex]\( \varepsilon \)[/tex] is the molar absorptivity (in units of M[tex]\(^{-1}\)[/tex] cm[tex]\(^{-1}\)[/tex]),
- [tex]\( c \)[/tex] is the concentration of the solution (in moles per liter, M),
- [tex]\( l \)[/tex] is the path length of the cell (in cm).
2. Identify the given values:
- Concentration ([tex]\( c \)[/tex]) = [tex]\( 0.5 \times 10^{-3} \)[/tex] M
- Absorbance ([tex]\( A \)[/tex]) = 0.17
- Path length ([tex]\( l \)[/tex]) = 1.3 cm
3. Rearrange the Beer-Lambert equation to solve for molar absorptivity [tex]\( \varepsilon \)[/tex]:
[tex]\[
\varepsilon = \frac{A}{c \cdot l}
\][/tex]
4. Substitute the given values into the rearranged equation:
[tex]\[
\varepsilon = \frac{0.17}{(0.5 \times 10^{-3}) \cdot 1.3}
\][/tex]
5. Perform the calculation:
[tex]\[
\varepsilon = \frac{0.17}{0.0005 \cdot 1.3}
\][/tex]
[tex]\[
\varepsilon = \frac{0.17}{0.00065}
\][/tex]
[tex]\[
\varepsilon \approx 261.538
\][/tex]
6. Result:
The molar absorptivity [tex]\( \varepsilon \)[/tex] of the solution is approximately [tex]\( 261.54 \)[/tex] M[tex]\(^{-1}\)[/tex] cm[tex]\(^{-1}\)[/tex].
Therefore, the molar absorptivity of a [tex]\( 0.5 \times 10^{-3} \)[/tex] M solution with an absorbance of 0.17 and a path length of 1.3 cm is [tex]\( 261.54 \)[/tex] M[tex]\(^{-1}\)[/tex] cm[tex]\(^{-1}\)[/tex].
