Difficulty: Intermediate | Prerequisites: Solution concentration (molarity), dilution concepts, basic algebra
TL;DR
Beer's Law says the amount of light a solution absorbs is directly proportional to its concentration, provided the path length stays constant. In this lab you measure absorbance of KMnO₄ solutions at known concentrations, plot absorbance vs. concentration to get a straight line, then use that line to read off the concentration of an unknown. The whole method turns a colour measurement into a number you can do algebra with.
Absorbance (A)
A unitless measure of how much light a sample absorbs at a given wavelength. Calculated as A = −log₁₀(T) or A = 2 − log₁₀(%T). In simple terms, higher absorbance means a darker, more concentrated solution.
Transmittance (T)
The fraction of incident light that passes through a sample without being absorbed: T = I / I₀, where I is the transmitted intensity and I₀ is the incident intensity. Think of it as the percentage of light that makes it through.
Percent transmittance (%T)
Transmittance expressed as a percentage: %T = T × 100. A %T of 100 means all light passes through (no absorption); a %T near 0 means almost all light is absorbed.
Beer's Law (Beer-Lambert Law)
The linear relationship A = εbC, where absorbance is proportional to concentration. In simple terms, double the concentration and you double the absorbance, as long as the solution behaves ideally.
Molar absorptivity (ε)
Also called the molar extinction coefficient. A constant specific to a substance at a given wavelength, with units L mol⁻¹ cm⁻¹. It tells you how strongly that substance absorbs light per unit concentration and path length.
Path length (b)
The distance light travels through the sample, typically the internal width of the cuvette (usually 1.00 cm in standard lab equipment).
Spectrophotometer
An instrument that measures how much light a sample absorbs at a selected wavelength. It shines a beam through a cuvette, detects what comes out the other side, and reports absorbance or %T.
Cuvette (cuvet)
A small, transparent container (usually glass or quartz) that holds the liquid sample in the spectrophotometer's light path. Handle by the upper rim only; fingerprints on the optical faces scatter light and ruin your reading.
Analytical wavelength (λ_max)
The wavelength at which the substance absorbs the most light. You measure at λ_max because sensitivity is highest there, meaning small concentration differences produce the largest absorbance differences.
Blank (reference solution)
A solution containing everything except the analyte of interest (usually distilled water for a single-solute system). Calibrating with the blank sets the baseline so only the analyte's absorbance is measured.
Standard solution
A solution of precisely known concentration, used to build the calibration curve. In this lab, six standard KMnO₄ solutions are prepared by dilution.
Calibration curve (Beer's Law plot)
A graph of absorbance (y-axis) vs. concentration (x-axis) for the standard solutions. The best-fit line through these points lets you convert any measured absorbance into a concentration.
R-squared value (R²)
A measure of how well the data points fit the straight line. An R² of 1.00 is a perfect fit; this lab requires R² > 0.98 to confirm a good linear relationship.
A spectrophotometer isolates a narrow band of wavelengths from a white-light source and directs it through a sample in a cuvette.
A detector on the other side measures how much light arrives. The instrument compares this to the intensity that arrived when only the blank was in the light path.
The result is reported as either %T (how much light got through) or absorbance (a logarithmic scale where higher numbers mean more light was absorbed).
The instrument must warm up before use so the lamp output stabilises, giving consistent readings.
Every coloured substance absorbs certain wavelengths more strongly than others. The wavelength of maximum absorbance is called λ_max.
You always measure at λ_max because that is where a small change in concentration produces the largest change in absorbance, giving you the best sensitivity.
To find λ_max, you plot absorbance vs. wavelength across the visible spectrum and look for the peak. For KMnO₄, the analytical wavelength is around 525 to 545 nm (green light absorbed; the solution appears purple).
The law states A = εbC, where A is absorbance, ε is molar absorptivity, b is path length, and C is molar concentration.
With b fixed at 1.00 cm and ε constant for a given substance and wavelength, this simplifies to A = (constant) × C, a straight line through the origin.
The slope of the Beer's Law plot equals εb. A steeper slope means the substance absorbs more strongly at that wavelength.
The law holds for dilute solutions. At very high concentrations, molecular interactions and instrumental limitations cause deviations from linearity.
The relationship is A = 2 − log₁₀(%T), or equivalently A = −log₁₀(T) where T = %T / 100.
When %T = 100, A = 0 (no absorption). When %T = 10, A = 1. When %T = 1, A = 2.
The conversion is logarithmic, so equal steps in absorbance do not correspond to equal steps in %T.
You start with a concentrated stock solution of known molarity.
Using a volumetric pipette, you transfer a precise volume (1.00, 2.00, 3.00, 4.00, 5.00 or 6.00 mL) into a 100 mL volumetric flask and fill to the mark with deionised water.
The dilution equation M₁V₁ = M₂V₂ gives the final concentration: M₂ = M₁ × (V_pipetted / 100.0 mL).
Six solutions at increasing concentrations provide the data points for the calibration curve.
Measure absorbance of each standard at the analytical wavelength, always starting from the least concentrated solution and working up.
Plot A (y-axis) vs. C (x-axis). Fit a linear trendline and display the equation (y = mx + b) and R² value.
R² must exceed 0.98. If it does not, check for an outlier, re-make that solution, and re-measure.
To find an unknown concentration, measure its absorbance and read across to the line, then down to the x-axis. Algebraically: C_unknown = (A_unknown − b) / m, using the trendline equation.
If the unknown's absorbance is higher than your most concentrated standard, the concentration is too high to read from the plot.
Dilute the unknown by a known factor, re-measure, then multiply the result by the dilution factor to recover the original concentration.
Compare the colour intensity of the unknown to your standards as a rough guide for choosing how much to dilute.
The blank zeroes the instrument so that absorbance readings reflect only the analyte. For a single-solute-in-water system, distilled water is the blank. For a multi-component system, the blank contains everything except the analyte.
Always rinse the cuvette three times with the solution you are about to measure, to avoid dilution from residual liquid.
Handle cuvettes by the upper rim. Fingerprints, scratches or lint on the optical faces scatter light and introduce error.
Wipe the outside with lint-free tissue before every reading.
Measure all standards on the same spectrophotometer in the same session, because individual instruments can differ slightly.
A = \varepsilon b CBeer-Lambert Law. A = absorbance (unitless), ε = molar absorptivity (L mol⁻¹ cm⁻¹), b = path length (cm), C = concentration (mol L⁻¹).
A = -\log_{10}(T) = 2 - \log_{10}(\%T)Converting transmittance to absorbance. T is the decimal fraction (0 to 1); %T is the percentage (0 to 100).
M_1 V_1 = M_2 V_2Dilution equation. Use this to calculate the concentration of each standard solution after diluting the stock into a 100 mL volumetric flask.
C_{\text{unknown}} = \frac{A_{\text{unknown}} - b_{\text{intercept}}}{m}Using the best-fit line (y = mx + b) from the Beer's Law plot to solve for an unknown concentration from its measured absorbance.
Spectrophotometry is the workhorse technique for measuring concentrations in clinical labs (blood glucose, haemoglobin), environmental monitoring (pollutant levels in water), food and beverage quality control, and forensic chemistry. Any time you need to know "how much of substance X is in this liquid," a Beer's Law calibration is often the first method reached for.
Students often assume absorbance and %T are linearly related. They are not. The relationship is logarithmic: A = 2 − log₁₀(%T). A drop from 50%T to 25%T is not the same change in absorbance as a drop from 25%T to 0%T.
Students sometimes think a higher %T means a more concentrated solution. The opposite is true. Higher concentration means more light absorbed, so less light transmitted, so lower %T.
Forgetting to calibrate with the blank before measuring standards is a common error. Without zeroing the instrument, every reading includes absorbance contributions from the solvent and cuvette.
Students often force the best-fit line through the origin. While Beer's Law predicts y-intercept = 0, real data may have a small nonzero intercept due to instrumental offset. Use the equation the software gives you, intercept and all.
⚠️ You must be able to convert between %T and absorbance using A = 2 − log₁₀(%T). This conversion appears in the worksheet problems and is a common exam calculation.
⚠️ Know what R² means in context: it measures how well absorbance and concentration follow a linear pattern. An R² of 0.98 or higher confirms Beer's Law holds for your data.
⚠️ Expect a problem where you are given a Beer's Law plot equation (y = mx + b) and an unknown absorbance, and must solve for concentration. This is the payoff calculation of the entire lab.
⚠️ Understand why you measure at λ_max and not some arbitrary wavelength: maximum sensitivity means the smallest detectable concentration difference.
⚠️ Be ready to explain the purpose of the blank. A blank is not "no sample"; it is a sample containing everything except the analyte.
True or false: If a solution has a %T of 50, its absorbance is 0.50. (False. A = 2 − log₁₀(50) = 2 − 1.699 = 0.301.)
Fill in the blank: The wavelength at which a substance absorbs the most light is called the ____. (analytical wavelength, or λ_max)
True or false: Doubling the concentration of a solution should roughly double its absorbance, assuming Beer's Law holds. (True.)
Fill in the blank: The purpose of the blank is to set the instrument so that only the ____ contributes to the absorbance reading. (analyte)
True or false: An R² value of 0.85 on a Beer's Law plot means the data show a good linear fit. (False. The lab requires R² > 0.98.)
Q: A standard KMnO₄ solution has a concentration of 2.40 × 10⁻⁴ mol/L and an absorbance of 0.482 at 525 nm in a 1.00 cm cuvette. What is the molar absorptivity (ε) of KMnO₄ at this wavelength?
A: From A = εbC, rearrange to ε = A / (bC) = 0.482 / (1.00 × 2.40 × 10⁻⁴) = 2008 L mol⁻¹ cm⁻¹.
Q: A solution of Cu⁺-cuproine complex has a %T of 14.1. What is its absorbance?
A: A = 2 − log₁₀(14.1) = 2 − 1.149 = 0.851.
Q: Your Beer's Law plot gives the equation y = 2450x + 0.005. An unknown solution has an absorbance of 0.738. What is its concentration?
A: C = (A − b) / m = (0.738 − 0.005) / 2450 = 2.99 × 10⁻⁴ mol/L.
Q: An unknown KMnO₄ solution has an absorbance higher than your most concentrated standard. What should you do?
A: Dilute the unknown by a known factor (e.g. take 10.0 mL and dilute to 100.0 mL for a 10× dilution), re-measure the absorbance of the diluted solution, read the concentration from the plot, then multiply by the dilution factor to get the original concentration.
Q: Why is distilled water used as the blank when measuring KMnO₄ solutions, but 3-methyl-1-butanol is used as the blank for the Cu⁺-cuproine complex?
A: The blank must match the solvent and all other components of the solution except the analyte. KMnO₄ is dissolved in water, so water is the blank. The Cu⁺-cuproine complex is dissolved in 3-methyl-1-butanol, so that solvent is the blank.
This lab connects directly to solution stoichiometry and molarity calculations from earlier in the course: every standard concentration comes from the dilution equation M₁V₁ = M₂V₂. The concept of electromagnetic radiation and the visible spectrum ties back to atomic structure and electron transitions. Quantitative analysis using calibration curves is also foundational for later analytical chemistry courses and any lab work involving instrumental methods.
Beer-Lambert Law, Beer's Law plot, spectrophotometry, absorbance, transmittance, percent transmittance, molar absorptivity, extinction coefficient, cuvette, cuvet, spectrophotometer, calibration curve, standard solution, analytical wavelength, lambda max, λ_max, blank solution, reference solution, KMnO₄, potassium permanganate, dilution, M₁V₁ = M₂V₂, R-squared, linear regression, concentration determination, molecular spectroscopy, visible spectrum, colorimetry, Cu-cuproine complex, 3-methyl-1-butanol