Question

Explain how the absorbance of mixtures is additive. Describe the “two unknowns, two equations” system used to find the concentrations of two absorbing species in mixtures.

Answer 1

The absorbance of a solution is derived from its transmittance of light.

i.e. T = e^-cl, where = molar absorption coefficient of the solution, c = concentration of the solution and l = length of sample

Apply 'ln' on both sides, then we will get

lnT = -cl

i.e. - 2.303 LogT = cl

i.e. -LogT = (/2.303)cl

i.e. A = 'cl, where ' = molar extinction coefficient of the solution

If the sample has two different absorbing species having the absorbances A₁ and A₂, then

T₁*T₂ = e^-₁c₁l₁*e^-₂c₂l₂

i.e. T₁*T₂ = e^{-₁c₁l₁-₂c₂l₂}

Apply 'ln' on both sides, then we will get

ln(T₁*T₂) = -₁c₁l₁-₂c₂l₂

i.e. -lnT1 - lnT2 = ₁c₁l₁+₂c₂l₂

i.e. 2.303(-LogT₁ - LogT₂) = ₁c₁l₁+₂c₂l₂

i.e. -LogT₁ - LogT₂ = (₁c₁l₁+₂c₂l₂)/2.303

i.e. A₁ + A₂ = ₁^'c₁l₁+₂^'c₂l₂, where ₁^', ₂^' are the molar extinction coefficients of two absorbing solutions