Question

The molar absorption coefficient of a substance dissolved in cyclohexane is 1710 L mol\(^{-1}\) cm\(^{-1}\) at 500 nm. The reduction in intensity of light of the same wavelength that passes through a cell of 1 mm path length containing a 2 mmol L\(^{-1}\) solution (rounded off to one decimal place) is \(\underline{\hspace{2cm}}\) %.

Hint:

The reduction in intensity can be found using the Beer-Lambert Law, where absorbance is proportional to concentration and path length.

Answer 1

Correct Answer: 54

The reduction in intensity \( % \) can be calculated using the Beer-Lambert Law:
\[ A = \epsilon c l \] where \( A \) is the absorbance, \( \epsilon \) is the molar absorption coefficient, \( c \) is the concentration, and \( l \) is the path length in cm.
For this case, \( \epsilon = 1710 \, \text{L mol}^{-1} \text{cm}^{-1} \), \( c = 2 \times 10^{-3} \, \text{mol L}^{-1} \), and \( l = 0.1 \, \text{cm} \). Substituting the values:
\[ A = 1710 \times (2 \times 10^{-3}) \times 0.1 = 0.342. \] The reduction in intensity is related to absorbance by:
\[ \text{Reduction in intensity} = 10^{-A} \times 100 = 10^{-0.342} \times 100 \approx 55%. \] Thus, the reduction in intensity is \( 55% \).