How do you determine the concentration of an unknown solution using spectroscopy?

To determine the concentration of an unknown solution using spectroscopy, it's essential to measure the absorbance of the solution and apply the Beer-Lambert Law. This law establishes a direct relationship between the absorbance of light by a solution and its concentration, along with the path length of the light through the solution and the molar absorptivity, which is a characteristic of the compound being measured.

When light passes through a solution, some of the light is absorbed by the solute, and the amount of light absorbed (which is measured as absorbance) can be quantitatively related to the concentration using the equation:

[ A = \epsilon c l ]

In this equation:

• ( A ) is the absorbance (a unitless measure),

• ( \epsilon ) is the molar absorptivity (in L/(mol·cm)),

• ( c ) is the concentration of the solution (in mol/L), and

• ( l ) is the path length of the light through the solution (in cm).

By measuring the absorbance at a specific wavelength where the solute absorbs light and knowing the molar absorptivity and the path length, one can rearrange the equation to solve for the concentration of the unknown