Absorbance vs. Concentration

1.0What is Absorbance?

Absorbance (A): The measure of light absorbed by a solution when light passes through it.

It depends on:

• Concentration of solute
• Path length of light (cuvette length)
• Wavelength of light used

Formula: $A=log(\frac{I_0}{I})$

where $I_0$ = incident light intensity, I = transmitted light intensity.

2.0What is Concentration?

Concentration (c) refers to the amount of a substance (solute) present in a given volume of a solution. It can be expressed in various units, such as molarity (mol/L), which is the most commonly used unit in quantitative analysis.

3.0The Beer–Lambert Law: The Core Relationship

Absorbance and concentration are directly proportional according to the Beer–Lambert Law, sometimes called Beer's Law or the Lambert–Beer Law, which states that a solution's absorbance is directly proportional to its concentration and the path length of light travelling through the solution. This is the primary principle of UV-V is spectrophotometry, an instrumental method used to measure the absorption of light by a chemical substance.

4.0The Equation for Beer’s Law

The mathematical expression of the law is:

$A=\epsilon cl$

Where:

• A is the Absorbance (dimensionless)
• ϵ (epsilon) is the Molar Absorptivity or Extinction Coefficient , a constant specific to the substance and the wavelength of light. It's a measure of how strongly a chemical species absorbs light at a given wavelength.
• c is the Molar Concentration of the absorbing species
• l is the Path Length of the cuvette (cm)

Key Points:

• The Beer–Lambert Law is only valid for dilute solutions. At high concentrations, solute molecules might interact with each other and thus lead to a deviation(s) from the law.
• The law is consistent only at a certain wavelength of light (λ) for which the substance has maximum absorption.
• The molar absorptivity (ϵ) of the substance is specific to a wavelength and temperature, thus it is a unique property of the substance.

How to Use Beer's Law to Calculate Concentration

There are two primary methods to determine an unknown concentration using Beer's Law:

1. Using the Beer's Law Equation: If you know the molar absorptivity (ϵ) and the path length (l), you can simply rearrange the equation to solve for the unknown concentration (c): $c=\frac{A}{cl}$
   

• Example: A solution has an absorbance of 0.70. The molar absorptivity (ϵ) of the solute at this wavelength is 8400 L mol−1 cm−1 and the cuvette path length (l) is 1 cm.$c=\frac{0.70}{(8400Lmo{l}^{-1}c{m}^{-1})(1cm)}=8.33\times 10^{-5}mol/L$

2. Using a calibration curve is the more common and reliable method. You first prepare a series of standard solutions with known concentrations and measure the absorbance of each. Then, you plot Absorbance on the y-axis against Concentration on the x-axis.
   The resulting graph should be a straight line passing through the origin. The slope of this line is equal to ϵl. You can then measure the absorbance of your unknown sample and use the best-fit line to find its corresponding concentration.

5.0How to Graph Absorbance vs. Concentration

A graph of absorbance versus concentration is a powerful tool for quantitative analysis.

• According to the Beer-Lambert Law (A=ϵcl), a plot of Absorbance (A) on the y-axis versus Concentration (c) on the x-axis will yield a straight line through (0,0).
• The slope of this line will equal the product of molar absorptivity and path length of the cuvette, i.e. slope=ϵl.
• This linear relationship allows for the determination of an unknown concentration. When a sample of unknown concentration is measured for absorbance, it can then be matched to the correct absorbance value on the calibration curve (the plot of absorbance vs. concentration).

6.0Factors that Influence the Absorbance

The absorbance of a solution is not just dependent on concentration. Several factors can affect the measurement and cause deviations from the Beer–Lambert Law:

• High Concentration: When molecules are very close together, their electrostatic interactions and chemical equilibria can change, which changes the molar absorptivity (ϵ) and makes the relationship non-linear.
• Chemical Reactions: If the solute goes through chemical reactions like dissociation, association, or polymerisation, the absorbing species changes, which means the linear relationship is no longer valid.
• Non-Monochromatic Light: The law assumes that the light used is monochromatic (one wavelength). It can be wrong to use a wide range of wavelengths.
• Stray Light: Light that gets to the detector without going through the sample can make the measured absorbance lower than it really is.
• Temperature: Changes in temperature can change the molar absorptivity and the volume of the solution, which can change the absorbance reading.

7.0Importance of Beer’s Law

The Beer–Lambert Law is a cornerstone of modern analytical chemistry. Its importance stems from its wide range of applications:

• Quantitative Analysis: This method is used to find out the exact amount of a substance in a solution. For example, it can be used to measure the levels of pollutants in water or to count the number of DNA and proteins in biological research.
• Reaction Kinetics: Chemists can learn about the speed and way a chemical reaction happens by constantly checking how much light a reactant or product absorbs.
• Quality Control: This law is used by businesses to make sure that things like food colourings and pharmaceutical drugs are pure and at the right concentration.