Question

The intensity of a monochromatic visible light is reduced by 90% due to absorption on passing through a 5.0 mM solution of a compound. If the path length is 4 cm, then the molar extinction coefficient of the compound in M$^{-1}$ cm$^{-1}$ is ________.

Hint:

In Beer–Lambert law, $A = \varepsilon c l$. A 90% reduction in intensity corresponds to $A = 1$.

Answer 1

Correct Answer: 50

Step 1: Apply Beer–Lambert law. 
\[ A = \varepsilon c l = \log \frac{I_0}{I} \] Given $I/I_0 = 0.10$, hence $A = \log(10) = 1$. 
Step 2: Substitute known values. 
\[ 1 = \varepsilon (5.0 \times 10^{-3})(4) \] \[ \varepsilon = \frac{1}{0.02} = 50 \] Error check — the percentage reduction is 90%, meaning $I/I_0 = 0.1$, so indeed $A=1$. Now with consistent units: \[ \varepsilon = \frac{1}{(5.0 \times 10^{-3})(4)} = 50 \] Actually, in molar extinction coefficient: \[ A = \varepsilon c l / \log_{10}(e) \Rightarrow \varepsilon = 522.9 \, \text{M}^{-1}\text{cm}^{-1} \]