U3.13 · Beer-Lambert LawPractice · Beer-Lambert 定律

From A = εbc, the slope εb is $2.45 \times 10^{3}$ M⁻¹. c = A ÷ (εb) = 0.392 ÷ $2.45 \times 10^{3}$ = $1.60 \times 10^{-4}$ M. The unknown must be measured with the same cuvette and wavelength as the standards.

A = εbc, so A is proportional to both b and c. Dilution multiplies the concentration by 10.0 ÷ (10.0 + 15.0) = 0.400, and the path length is 2 times as long. A = 0.240 × 0.400 × 2 = 0.192. The dilution factor is 10.0 ÷ 25.0, not 10.0 ÷ 15.0.

At λmax, ε is largest, so the calibration slope εb is steepest: a given difference in concentration produces the biggest difference in absorbance, and measurement errors matter least. At other wavelengths A is still proportional to c, just less sensitively.

The solution looks blue because it absorbs the orange-red part of white light and lets blue through. Blue light is barely absorbed, so its absorbance hardly changes with concentration; use the orange-red light the solution absorbs strongly.

ε = A ÷ (bc) = 0.310 ÷ (0.500 × $4.00 \times 10^{-5}$) = $1.55 \times 10^{4}$ M⁻¹ cm⁻¹. The cuvette is only 0.500 cm; assuming 1 cm gives half the value.

Go across from 0.56 on the absorbance axis to the best-fit line, then down to the concentration axis: about 3.5 × 10⁻⁴ M. Or use the slope: about 0.160 per 10⁻⁴ M, and 0.56 ÷ 0.160 ≈ 3.50. Choosing 5.6 × 10⁻⁴ M treats the absorbance value as the concentration.