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Serial Dilution & Standard Curve Lab

Prepare a serial dilution from a stock solution and measure the absorbance of each tube. Plot the standard curve (absorbance vs. concentration), fit a regression line, and use Beer-Lambert Law to determine the concentration of an unknown sample.

Guided Experiment: Beer-Lambert Law Verification

If concentration of a colored solution doubles, what do you predict happens to the absorbance? How does this relate to Beer-Lambert Law?

Write your hypothesis in the Lab Report panel, then click Next.

Test Tube Rack — Color Gradient from Stock to Most Dilute

S1.000D10.500D20.250D30.125D40.063D50.031D60.016?Unknown0.0035S = StockD1...Dn = Dilutions? = UnknownA = 0.35

Controls

Stock Concentration1.00 mol/L
Dilution Factor2 x
Number of Dilutions6
Path Length1.0 cm
Molar Absorptivity (ε)100 L/(mol·cm)
Unknown Absorbance0.35 A

Results

A=εlc=100×1×cA = \varepsilon l c = 100 \times 1 \times c

Standard Curve (Regression)

Slope (εl)
100.00 L/mol
Intercept
0.0000
r²
1.0000

Unknown Sample

cunknown=Aεl=0.350100.0c_{unknown} = \frac{A}{\varepsilon l} = \frac{0.350}{100.0}
cunknown=3.5000e−3 mol/Lc_{unknown} = 3.5000e-3 \text{ mol/L}
Unknown %T
44.67 %

Standard Curve — Absorbance vs Concentration

Red points: dilution series. Amber point: unknown sample. Teal line: regression (Beer-Lambert).

Regression lineStandard data pointsUnknown concentration

Data Table

(0 rows)
#TubeConcentration(mol/L)Absorbance (A)%TDilution
0 / 500
0 / 500
0 / 500

Reference Guide

Beer-Lambert Law

When light passes through a colored solution, the absorbance is proportional to the concentration of the solute and the distance light travels through it.

A=εlcA = \varepsilon l c

A is absorbance (dimensionless), ε is the molar absorptivity in L/(mol·cm), l is the path length in cm, and c is the molar concentration in mol/L. Transmittance relates to absorbance as %T = 10-A × 100.

Serial Dilution

A serial dilution starts from a concentrated stock solution and dilutes it by a constant factor at each step. After n steps with dilution factor f:

Cn=C0fnC_n = \frac{C_0}{f^n}

A 1:2 dilution factor halves the concentration at each step. Six steps from 1.0 mol/L gives: 0.5, 0.25, 0.125, 0.0625, 0.0313, and 0.0156 mol/L. Each tube is darker or lighter depending on how many molecules absorb light.

Standard Curves

A standard curve is a graph of absorbance (y) vs. concentration (x) for a series of solutions with known concentrations. By Beer-Lambert Law, this should be linear through the origin.

A=(εl) c⇒y=mxA = (\varepsilon l)\,c \quad \Rightarrow \quad y = mx

Linear regression fits the best straight line. The slope m = εl. A high r² (close to 1) confirms the Beer-Lambert relationship holds across the concentration range.

Finding Unknown Concentration

Once a standard curve is established, measure the absorbance of the unknown sample and read its concentration off the line. Algebraically, rearrange Beer-Lambert Law:

cunknown=Aunknownεlc_{\text{unknown}} = \frac{A_{\text{unknown}}}{\varepsilon l}

For example, if ε = 100 L/(mol·cm), l = 1 cm, and the unknown absorbance is 0.35, then c = 0.35 / 100 = 0.0035 mol/L. The standard curve provides a visual check that the reading falls in the linear range.