Measuring how much light a solution absorbs is a fundamental technique in analytical chemistry used to determine the amount of a substance present. The two defining concepts in this process are absorbance and concentration, which are inextricably linked.
Absorbance is a quantitative measure of how much light is blocked by a sample at a specific wavelength. Concentration refers to the amount of a substance (solute) dissolved in a given volume of liquid (solvent). The direct link between these factors means that as the amount of solute increases, the solution absorbs more light. Therefore, accurately measuring the absorbance makes it possible to calculate the unknown concentration.
Understanding the Proportional Relationship
The core principle linking light absorption to concentration is the Beer-Lambert Law. This law states that the absorbance of a solution is directly proportional to the concentration of the absorbing substance and the distance the light travels through the solution.
The relationship is mathematically expressed as \(A = epsilon bc\). Here, ‘A’ is the measured absorbance, and ‘c’ is the molar concentration of the substance. The term ‘b’ represents the path length, which is the distance the light travels through the sample, typically the width of the cuvette (often \(1\) centimeter). The final term, \(epsilon\), is the molar absorptivity, a unique constant for each substance at a given wavelength that quantifies how strongly it absorbs light.
This proportional relationship exists because a more concentrated solution contains a higher density of light-absorbing molecules. This increases the probability of a photon interacting with a molecule as the light beam passes through the sample. When a photon is absorbed, less light reaches the detector, allowing the Beer-Lambert Law to convert this light loss into a precise concentration value.
Measuring Absorbance with a Spectrophotometer
Light absorption is measured using a spectrophotometer. This device shines a beam of light at a specific, selected wavelength through the sample and measures the amount of light that passes through to the detector. The most effective wavelength is typically chosen because the substance absorbs most strongly at that point, ensuring maximum measurement sensitivity.
To isolate the absorption caused only by the substance of interest, the instrument must first be calibrated using a reference solution called a blank. The blank contains the solvent and any reagents, but not the compound being measured. Running the blank allows the spectrophotometer to subtract background light loss caused by the container or solvent, effectively setting the absorbance to zero.
After calibration, the sample solution is placed into the light path. The spectrophotometer compares the intensity of the light entering and exiting the sample, calculating the numerical absorbance value. This dimensionless reading becomes the input data for subsequent concentration calculations.
Creating a Standard Curve
While the Beer-Lambert Law provides the theoretical basis, the most reliable method for finding an unknown concentration involves creating a standard curve. This procedure is necessary because the molar absorptivity constant (\(epsilon\)) may vary slightly based on the specific instrument, temperature, or solvent. A standard curve empirically determines the precise proportional relationship for the experiment.
The process begins by preparing a series of standard solutions containing known, precisely measured concentrations of the substance. These concentrations are chosen to span the expected range of the unknown samples. The absorbance for each standard solution is then measured using the spectrophotometer.
The collected data is plotted on a graph, with absorbance values on the y-axis and known concentrations on the x-axis. A line of best fit is drawn through these data points, creating the standard curve. This resulting straight line serves as a mathematical representation of the linear relationship between absorbance and concentration, providing a reliable constant for calculating the concentration of any unknown sample measured under the same conditions.
Determining the Final Concentration and Method Limitations
Once the standard curve is established, the final step is measuring the absorbance of the unknown sample. This value is then applied to the standard curve to determine the corresponding concentration.
This determination can be done graphically by finding the unknown’s absorbance value on the y-axis, tracing across to the line, and then down to the x-axis to read the concentration.
Alternatively, the linear equation for the line of best fit (\(y = mx + b\)) is used mathematically. The measured absorbance is substituted for ‘y,’ the slope ‘m’ is the proportional constant derived from the standards, and the x-value (the unknown concentration) is solved for. This converts the raw light absorption data into a final, precise concentration value.
Method Limitations
This analytical method has limitations that can cause the proportional relationship to break down. Deviations from the straight-line relationship often occur at very high concentrations (typically above \(0.01\) M). At these levels, molecules are packed too closely, causing intermolecular interactions that change the substance’s light-absorbing properties.
Chemical reactions, such as the substance associating or dissociating in the solvent, can also alter the absorbing species, invalidating the initial constant. Therefore, the unknown sample’s absorbance must fall within the linear range established by the standard curve to maintain accuracy.