Spectrometry of absorption

The spectrometry of absorption is a physical method of chemical analysis. It is used mainly on the liquids.

The Couleur of a body in transmission (transparency) represents its capacity to absorb some wavelengths. The absorption a wavelength λ by a product is modelled by the Loi of Beer-Lambert:

$I\; =\; I\_0\; \backslash \; cdot\; e^\; \{-\; \backslash \; driven\; \backslash \; cdot\; \backslash \; rho\; \backslash \; cdot\; X\}$

where

• I ₀ is the incidental intensity of radiation λ, and I is the outgoing intensity;
• µ is the absorption coefficient, which depends on the product and λ;
• ρ is the Density product;
• X is the way traversed in the product.

Qualitative analysis

Knowing the density D of a product and the way X traversed by the light, if one measures the intensity leaving the product, one can determine the absorption coefficient for the wavelength considered.

The peaks of absorption ( maximum of µ) correspond to transition electronic (quantified), and are thus characteristic of the nature of the Atome S and their chemical bonds.

This makes it possible to recognize the chemical nature of certain products. It is in particular the absorption wavelengths given of the solar light which made it possible to discover that the Sun was surrounded by gas, which brought to discovered Hélium.

Quantitative analysis

Let us suppose that one has

• a product 1 having a very important absorption coefficient µ₁ for a wavelength λ₁ and negligible for λ₂;
• a product 2 having contrary a coefficient µ₂ to negligible for λ₁ but very important absorption for λ₂;

then, for a mixture of products 1 and 2, with a respective density ρ₁ and ρ₂, one will have:

$I\; (\backslash \; lambda\_1)\; =\; I\_0\; (\backslash \; lambda\_1)\; \backslash \; cdot\; e^\; \{-\; (\backslash \; mu\_1\; (\backslash \; lambda\_1)\; \backslash \; cdot\; \backslash \; rho\_1\; +\; \backslash \; mu\_2\; (\backslash \; lambda\_1)\; \backslash \; cdot\; \backslash \; rho\_2)\; \backslash \; cdot\; X\}\; \backslash \; simeq\; I\_0\; (\backslash \; lambda\_1)\; \backslash \; cdot\; e^\; \{-\; \backslash \; mu\_1\; (\backslash \; lambda\_1)\; \backslash \; cdot\; \backslash \; rho\_1\; \backslash \; cdot\; X\}$

$I\; (\backslash \; lambda\_2)\; =\; I\_0\; (\backslash \; lambda\_2)\; \backslash \; cdot\; e^\; \{-\; (\backslash \; mu\_1\; (\backslash \; lambda\_2)\; \backslash \; cdot\; \backslash \; rho\_1\; +\; \backslash \; mu\_2\; (\backslash \; lambda\_2)\; \backslash \; cdot\; \backslash \; rho\_2)\; \backslash \; cdot\; X\}\; \backslash \; simeq\; I\_0\; (\backslash \; lambda\_2)\; \backslash \; cdot\; e^\; \{-\; \backslash \; mu\_2\; (\backslash \; lambda\_2)\; \backslash \; cdot\; \backslash \; rho\_2\; \backslash \; cdot\; X\}$

The measurement of the intensity respective of λ₁ and λ₂ thus makes it possible to determine ρ₁ and ρ₂, and thus to determine the proportions of the mixture. That requires a calibration in order to be abstracted from the intensity I ₀ (λ) and clean absorption of the apparatus. One works in general in report/ratio of intensity:

$\backslash \; frac\; \{I\; (\backslash \; lambda\_1)\}\{I\; (\backslash \; lambda\_2)\}\; \backslash \; simeq\; \backslash \; frac\; \{I\_0\; (\backslash \; lambda\_1)\}\{I\_0\; (\backslash \; lambda\_2)\}\; \backslash \; cdot\; e^\; \{(\backslash \; mu\_2\; (\backslash \; lambda\_2)\; \backslash \; cdot\; \backslash \; rho\_2\; -\; \backslash \; mu\_1\; (\backslash \; lambda\_1)\; \backslash \; cdot\; \backslash \; rho\_1)\; \backslash \; cdot\; X\}$

that is to say

$\backslash \; mu\_2\; (\backslash \; lambda\_2)\; \backslash \; cdot\; \backslash \; rho\_2\; -\; \backslash \; mu\_1\; (\backslash \; lambda\_1)\; \backslash \; cdot\; \backslash \; rho\_1\; \backslash \; simeq\; \backslash \; frac\; \{1\}\; \{X\}\; \backslash \; cdot\; \backslash \; ln\; \backslash \; left\; (\backslash \; frac\; \{I\; (\backslash \; lambda\_1)\}\{I\; (\backslash \; lambda\_2)\}\; \backslash \; cdot\; \backslash \; frac\; \{I\_0\; (\backslash \; lambda\_2)\}\{I\_0\; (\backslash \; lambda\_1)\}\; \backslash \; right)$

The second equation is that giving the total density ρ:

ρ = ρ₁ + ρ₂

Generally, if there is a mixture of produced N having each one a characteristic peak of absorption for a given wavelength λ _I , there is then a system of N equations to solve:

$I\; (\backslash \; lambda\_i)\; =\; I\_0\; (\backslash \; lambda\_i)\; \backslash \; cdot\; \backslash \; exp\; \backslash \; left\; (-\; X\; \backslash \; cdot\; \backslash \; sum\_\; \{J\; =\; 1\}\; ^n\; \backslash \; mu\_j\; (\backslash \; lambda\_i)\; \backslash \; cdot\; \backslash \; rho\_j\; \backslash \; right)$

and

$\backslash \; sum\_\; \{J\; =\; 1\}\; ^n\; \backslash \; rho\_j\; =\; \backslash \; rho$

Application

In addition to the chemical analysis, one uses this method to determine the percentage of oxygenation of the Sang (Oxymétrie) as well as the pulse.

See too

Internal bonds

• Atomic absorption spectrometry

• Spectrometry of absorption of x-rays (XANES)
• EXAFS (Extended X-ray absorption fine structure)

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