# Measuring the concentration

Jan Hein HooijschuurLevelBasic

The relation of absorbance to concentration is given by Lambert-Beer's law (Beer's law): A = ɛlc

(where A is absorbance (unitless), ɛ (epsilon) is molar absorption coefficient (or molar absorption constant) of the analyte for a certain wavelength (l⋅mol^{-1}⋅cm^{-1}), l is path length (cm) through your cuvette and c is the concentration of the analyte (mol⋅l^{-1}).)

Demo of how to calculate a concentration from a series of measuments(4:58 mins):

How to generate a standard curve, and use that standard curve to determine the concentration of an unknown solution, titled "Determining the Concentration of an Unknown Sample Using the Standard Curve Excel 2010" (10:58 mins):

**Examples of a calculation with Beer's law:**

1. A solution of 1 mg paracetamol in 100 ml methanol (MeOH) is measured with UV-Vis.

The intensity of the light through a blank solution of MeOH (I_{0}) is 100% by definition.

The measured intensity of sample solution (I) is 13.18%

Formula: A = - log_{10}T = -log_{10} (I/I_{0}).

Known values: I_{0} = 100%

I = 13.18 %

A = -log_{10} (13.18/100)

A = -log_{10} (0.1318)

A = -(-0.880)

A = 0.880

2. A solution of 1 mg paracetamol (MW=151.17 g/mol) in 100 ml MeOH (c) is measured in a 10 mm cuvet (l) with UV-Vis.

The absorption maximum of paracetamol in MeOH is at 247nm with a molar absorption coefficient of 12850 l⋅mol^{-1}⋅cm^{-1} (ɛ).

Formula: A = ɛlc

Known values: ɛ = 12850

l = 10 mm = 1 cm

c = 1 mg/100ml = 10mg/l = 0.01g/l

c = 0.01 × 1/151.17 = 6.61⋅10-5 mol/l

A = 12850 × 1 × 6.61⋅10-5

A = 0.849

**Advanced understanding of Beer's law:**

For a theoretical explanation on the derivation of the Beer’s law, click this link.

*An example of the linear correlation – a straight line - between the concentration of the analyte and the absorbance.*

A whiteboard presentation on the calibration curve and how to find an unknown concentration (13:35 mins):

**Summary of tips and tricks from the experts** We suggest that at this stage you do a virtual UV-Vis measurement. Try this nice java-applet from the website of the chemistry department of the Davidson College in North Carolina, click here[VirtMeas].