Question

A 0.005 M solution of compound X transmits 80% of the incident light of wavelength (\(\lambda\)) 500 nm. The absorbance of 0.01 M solution of X is (rounded off to three decimal places).
(Given: path length = 1.0 cm)

Hint:

Find \(A_1=-\log_{10}(0.80)\) for the 0.005 M solution, then use that absorbance is directly proportional to concentration at fixed path length to scale up to 0.01 M.

Answer 1

Correct Answer: 0.194

Step 1: Find the absorbance of the 0.005 M solution.
Transmittance \(T\) is the fraction of light that passes through, so 80% transmission means \(T = 0.80\). Absorbance is related to transmittance by
\[ A = -\log_{10}(T) \]
\[ A_1 = -\log_{10}(0.80) = \log_{10}(1.25) = 0.09691 \]

Step 2: Find the molar absorptivity \(\varepsilon\).
By the Beer-Lambert law, \(A = \varepsilon c l\), with path length \(l = 1.0\) cm and concentration \(c_1 = 0.005\) M:
\[ \varepsilon = \frac{A_1}{c_1 l} = \frac{0.09691}{0.005 \times 1.0} = 19.382\ \mathrm{M^{-1}cm^{-1}} \]

Step 3: Find the absorbance of the 0.01 M solution.
The same compound at the same wavelength and path length has the same \(\varepsilon\), so for \(c_2 = 0.01\) M:
\[ A_2 = \varepsilon c_2 l = 19.382 \times 0.01 \times 1.0 = 0.19382 \]

Step 4: Round to three decimal places.
\[ A_2 \approx 0.194 \]

Final Answer:
\[ \boxed{A_2 = 0.194} \]