Beer’s Law describes how a colored solution absorbs light as the light passes through it. It matters because chemists can use light measurements to determine the concentration of a substance without destroying the sample. A spectrophotometer shines a selected wavelength of light through a cuvette and compares the incoming and outgoing light intensities.
The darker or more concentrated the solution is, the more light it absorbs.
The law is written as A = εlc, where absorbance depends on molar absorptivity, path length, and concentration. Molar absorptivity describes how strongly a substance absorbs a specific wavelength of light, while path length is usually the width of the cuvette. In the useful linear range, a graph of absorbance versus concentration is a straight calibration curve.
The concentration of an unknown solution can be found by measuring its absorbance and comparing it to the calibration curve.
Understanding Chemistry: Beer's Law
Light is absorbed when its energy matches an allowed change in a molecule or ion. In many colored substances, electrons can move between energy levels after taking in light. Each substance absorbs some wavelengths more strongly than others.
A blue solution, for example, often transmits blue light while absorbing more of its complementary orange or red light. The best measurement wavelength is usually near the absorption peak.
At that peak, a small concentration change produces a clearer change in the reading. Using the wrong wavelength gives weak results because too little light is being absorbed.
A reliable measurement begins with a blank. The blank contains the solvent and any reagents except the substance being measured. It accounts for light lost through the cuvette, solvent, and other materials in the sample.
The instrument uses the blank as its zero reference before standards are measured. Standards are solutions with accurately known concentrations.
Students prepare several standards, measure each one, and plot the results. The line from these data is more useful than a single reading because it shows whether the method behaves consistently over the chosen range.
The straight line does not continue forever. Very concentrated solutions can give unreliable readings because little light reaches the detector. Molecules may interact with one another at high concentration, changing how they absorb.
Cloudy samples create another problem. Suspended particles scatter light rather than truly absorbing it, yet the detector still receives less light. This can make the calculated concentration seem too high.
Chemical changes matter too. A sample may have a different color if its temperature, acidity, or reaction state changes. Standards and unknowns need the same conditions for a fair comparison.
Careful handling of cuvettes makes a large difference. Fingerprints, scratches, droplets, and bubbles can block or scatter light. The clear faces must point along the light path every time.
A student should wipe those faces with lint free tissue and hold the cuvette near its top. Filling it to a similar level for each trial helps keep the light path consistent.
Repeating measurements reveals random variation. If one result is far from the others, the cause may be a bubble, poor mixing, or an error during dilution.
This method appears in water testing, medical laboratories, food analysis, and reaction studies. A water sample can be tested for a colored pollutant after a reagent forms a colored compound with it. In biology, absorbance can track the amount of a protein or DNA related product.
During a reaction, readings taken over time can show whether a reactant is being used up. The main learning goal is not memorizing a formula. It is connecting a light reading to a graph, then judging whether the graph and the sample conditions make the reported concentration believable.
Key Facts
- Beer’s Law: A = εlc.
- Absorbance is defined by A = log10(I0 / I), where I0 is incident light intensity and I is transmitted light intensity.
- Transmittance is T = I / I0, and percent transmittance is %T = 100T.
- For a fixed substance and wavelength, absorbance is directly proportional to concentration: A ∝ c.
- For a fixed substance and concentration, absorbance is directly proportional to path length: A ∝ l.
- A calibration curve often has the form A = mc + b, where c is concentration and m is the slope.
Vocabulary
- Absorbance
- Absorbance is a measure of how much light a sample removes from a beam passing through it.
- Molar absorptivity
- Molar absorptivity is the constant ε that describes how strongly a chemical species absorbs light at a particular wavelength.
- Path length
- Path length is the distance light travels through the sample, often 1.00 cm in a standard cuvette.
- Calibration curve
- A calibration curve is a graph made from standards of known concentration that is used to find the concentration of an unknown.
- Spectrophotometer
- A spectrophotometer is an instrument that measures how much light a sample transmits or absorbs at selected wavelengths.
Common Mistakes to Avoid
- Using percent transmittance as if it were absorbance is wrong because absorbance is logarithmic, not linear with transmitted light.
- Forgetting to blank the spectrophotometer is wrong because the solvent, cuvette, and instrument background can add absorbance that should not be counted for the analyte.
- Using the wrong wavelength is wrong because ε depends on wavelength, and measurements are usually most sensitive near the wavelength of maximum absorbance.
- Assuming Beer’s Law is always linear is wrong because very concentrated solutions, chemical changes, stray light, or instrument limits can cause deviations.
Practice Questions
- 1 A solution has ε = 5200 L mol^-1 cm^-1, l = 1.00 cm, and c = 2.50 x 10^-5 mol/L. Calculate its absorbance.
- 2 A calibration curve is A = 14800c + 0.015, where c is in mol/L. An unknown solution has A = 0.459. Find the concentration of the unknown.
- 3 Two solutions of the same dye are measured at the same wavelength in identical cuvettes. One has twice the concentration of the other, but its absorbance is not twice as large. Give two possible reasons for this observation.