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

Since path length and wavelength stay the same for both solutions, the Beer-Lambert law $A=\varepsilon c l$ says absorbance is directly proportional to concentration. That means we do not even need to solve for $\varepsilon$ separately, doubling the concentration simply doubles the absorbance.

1. Get the absorbance at 0.005 M from the given transmittance: 80% transmittance means $T=0.80$, and $A=-\log_{10}T$, so $$A_1 = -\log_{10}(0.80) = -\log_{10}(4/5) = \log_{10}(5/4) = \log_{10}(1.25)$$ Working this out, $\log_{10}(1.25) \approx 0.09691$, so $A_1 \approx 0.0969$.
2. Scale by the concentration ratio: The second solution is $0.01$ M, exactly twice $0.005$ M, and path length and compound (hence $\varepsilon$) are unchanged. So $$A_2 = A_1 \times \frac{c_2}{c_1} = 0.09691 \times \frac{0.01}{0.005} = 0.09691 \times 2 = 0.19382$$

Rounding $0.19382$ to three decimal places gives $0.194$.

Let's summarize:

• Transmittance and absorbance are linked by $A = -\log_{10}T$.
• At fixed path length, absorbance scales linearly with concentration, so doubling concentration doubles absorbance directly, without needing $\varepsilon$ as an intermediate number.

The absorbance of the 0.01 M solution is 0.194.