Lab, Quantitative Spectroscopy (Beer's Law) · AP Chemistry

Why is a copper(II) solution blue, and what exactly does a spectrometer measure? In this lab you point white light through copper(II) nitrate, Cu(NO₃)₂, and watch how the reading changes as you vary three things, wavelength, concentration, and path length. From those patterns you will discover the Beer–Lambert Law for yourself, A = εbc, instead of being handed it.

CED 3.12–3.13 (Spectroscopy & Beer–Lambert) · Unit 3. ~1 block · FORMATIVE-category activity: concept-building, not the graded write-up. This is the partner to the Percent Copper in Brass lab: here you DISCOVER the law; there you APPLY it to a real unknown.

Background CED 3.12–3.13

A coloured solution looks coloured because it absorbs some wavelengths of visible light and lets the rest through. Copper(II) nitrate absorbs orange/red light most strongly, so the light that survives to your eye is the leftover blue, that is why it looks blue. The wavelength it absorbs most strongly is called λmax.

Percent transmittance vs. absorbance. The spectrometer measures %T: the percent of light that makes it through the sample (100% = nothing absorbed, 0% = all absorbed). That is convenient to read but it is not proportional to how much stuff is in the way. The quantity that is proportional is absorbance:

A = −log(T) = −log(%T ⁄ 100) = 2 − log(%T)

Worked example: a reading of %T = 40% gives A = 2 − log(40) = 2 − 1.602 = 0.398. Notice high %T → low A, and low %T → high A.

The Beer–Lambert Law. A = εbc. Absorbance climbs in a straight line with three things: c, the concentration; b, the path length the light travels through the solution (a standard cuvette = 1.00 cm); and ε, the molar absorptivitya constant that belongs to a particular substance at a particular wavelength. Hold two of the three fixed and A is directly proportional to the third, through the origin (A = 0 when c = 0 or b = 0). You will test the c-leg in Part B and the b-leg in Part C.

Why colours and λmax differ. An ion absorbs light when a photon's energy exactly matches a gap between its electron energy levels. Different ions (Cu²⁺ vs. Ni²⁺ vs. Fe²⁺) have different gaps, so they absorb different wavelengths, different λmax, different ε, different colour. The colour you see is the complement of the colour absorbed: absorb orange/red → look blue (Cu²⁺); absorb violet + red → look green (Ni²⁺).

Why measure at λmax? Absorbance is largest (and changes fastest with concentration) at λmax, so a reading there is the most sensitive to how much Cu²⁺ is present. That is exactly the wavelength the brass lab uses (650 nm).

Safety read before you start

Copper, nickel & iron nitrate solutions, irritants and toxic if swallowed. Nickel(II) is also a skin sensitizer. None of these go anywhere near your mouth or hands. Wash any splash off skin immediately with water.

PPE, every student, the whole period: splash goggles on, sleeves/long hair back, no food or drink at the bench. Gloves when handling the metal-ion solutions.

Disposal: all blue (Cu²⁺) and green (Ni²⁺) solution goes in the labelled metal-ion waste container, never down the sink. Iron solution to the same container. Empty cuvettes get rinsed into the waste container, not the drain.

Glass & instrument: cuvettes and volumetric flasks are glass, report breakage to Dr. Mulinta. Do not force a cuvette into the spectrometer; it seats gently.

Materials & Equipment pre-set for you

The one specialized instrument is the Spectronic 200 spectrometer, shared at a station. Everything else is standard glassware.

Per group: Spectronic 200 spectrometer (shared) · cuvettes · 18 × 150 mm test tubes (5) + rack · 50 mL beakers (3) · 100 mL beaker (1) · 25 mL volumetric flasks · buret (to dispense stock) · plastic pipets · wash bottle of distilled water · 4 Plexiglas sheets/spacers (for path length) · waste container.

Solutions at the station: 0.500 M Cu(NO₃)₂ · 0.100 M Cu(NO₃)₂ · 0.100 M Ni(NO₃)₂ (green) · 0.100 M Fe(NO₃)₂ (pale).

Mrs. Kathy (lab tech) pre-sets everything: the Spectronic 200 is powered on, warmed up, and blanked with distilled water; the four nitrate solutions are bottled and labelled at each station; the test tubes, buret, cuvettes, Plexiglas spacers, and metal-ion waste container are laid out. You walk in to a ready bench, your job is the measuring and the thinking.

Procedure read %T, then convert to A

For every reading: fill a clean cuvette ¾ full, wipe the clear faces, seat it in the Spectronic 200, and record the %T at the wavelength named. You will convert each %T to absorbance afterward with A = 2 − log(%T).

Part A: Find the spectrum & λmax (0.100 M Cu²⁺)

Fill a cuvette with 0.100 M Cu(NO₃)₂. Beginning at 400 nm, read and record %T at each wavelength in the Part A table (every 50 nm to 750 nm).
The wavelength where %T is lowest (absorbance highest) is your λmax. Confirm it lands near 650 nm: you will use this wavelength for Parts B, C, and D.

Part B: How absorbance depends on concentration (at λmax)

Set the spectrometer to 650 nm. Using the buret, dispense the volume of 0.100 M Cu(NO₃)₂ below into a clean test tube, then add distilled water to a total of 10.0 mL. Mix. This is a serial set from 0.0200 M up to the undiluted 0.100 M.

Tube	0.100 M stock (mL)	dH₂O (mL)	Total (mL)	[Cu²⁺] (M)
1	2.00	8.00	10.00	0.0200
2	4.00	6.00	10.00	0.0400
3	6.00	4.00	10.00	0.0600
4	8.00	2.00	10.00	0.0800
5	10.00	0.00	10.00	0.100

Read and record %T at 650 nm for each of the five tubes. Keep the 0.0200 M tube, you reuse it in Part C.

Part C: How absorbance depends on path length (at λmax)

Keep concentration fixed at 0.0200 M Cu²⁺ and stay at 650 nm. Now change how far the light travels through the solution. Stack the Plexiglas spacers/cells to build path lengths of 1.00, 2.00, 3.00, and 4.00 cm (one cell = 1.00 cm; two stacked in series = 2.00 cm; and so on).
For each path length, read and record %T at 650 nm. Concentration never changes, only the distance the light travels.

Part D: A concentrated solution (compare to Part A)

Fill a cuvette with the 0.500 M Cu(NO₃)₂. Stay at 650 nm. Record %T and note the colour depth versus the 0.100 M tube.
Try to read it, you will find %T is very low (absorbance very high). Note whether the instrument still reads cleanly or pegs near zero %T.

Part E: Other compounds, other colours

For 0.100 M Ni(NO₃)₂ (green) and 0.100 M Fe(NO₃)₂ (pale): scan each across 400–750 nm and find its λmax (lowest %T). Record λmax and the %T there in the Part E table.
Compare: does each compound have the same λmax as copper, or its own? Tie the λmax you find to the colour you see.

Data Tables fill in lab

Part A, wavelength scan, 0.100 M Cu(NO₃)₂ (convert each %T to A = 2 − log(%T))

λ (nm)	400	450	500	550	600	650	700	750
%T	___	___	___	___	___	___	___	___
A	___	___	___	___	___	___	___	___

λmax (lowest %T) = __________ nm

Part B, absorbance vs. concentration (650 nm)

Tube	[Cu²⁺] (M)	%T	A = 2 − log(%T)
1	0.0200	__________	__________
2	0.0400	__________	__________
3	0.0600	__________	__________
4	0.0800	__________	__________
5	0.100	__________	__________

Part C, absorbance vs. path length (0.0200 M Cu²⁺, 650 nm)

Path length b (cm)	%T	A = 2 − log(%T)
1.00	__________	__________
2.00	__________	__________
3.00	__________	__________
4.00	__________	__________

Part D, concentrated solution (0.500 M Cu²⁺, 650 nm): %T = __________ A = __________

Part E, three compounds compared (0.100 M each)

Compound	Colour seen	λmax (nm)	%T at λmax	A at λmax
Cu(NO₃)₂	__________	__________	__________	__________
Ni(NO₃)₂	__________	__________	__________	__________
Fe(NO₃)₂	__________	__________	__________	__________

Analysis Questions show all work · units · sig figs

Answer on your own paper. Show every formula and substitution, the point of this lab is the reasoning that builds Beer's Law, not just the final number.

%T → A. Show your conversion for one Part A reading using A = 2 − log(%T). Then state which wavelength is λmax and why it is the lowest %T but the highest A.
The spectrum & the colour. Sketch A (y) vs. wavelength (x) for Part A. Using which wavelengths Cu²⁺ absorbs most, explain in one or two sentences why the solution looks blue.
Absorbance vs. concentration. Plot A (y) vs. [Cu²⁺] (x) for the five Part B tubes. Is it a straight line? Does it pass through the origin? Find the slope (with units).
Slope = εb. In Part B the path length was fixed at b = 1.00 cm, so the slope of A vs. c equals εb. Use it to find the molar absorptivity ε of Cu²⁺ at 650 nm (units M⁻¹cm⁻¹).
Absorbance vs. path length. Plot A (y) vs. path length b (x) for Part C. Straight line? Through the origin? Here concentration was fixed, so the slope = εc. Solve for ε again. Does it match your Part B value?
Build the law. You have now shown A ∝ c (Part B) and A ∝ b (Part C). Combine them into a single equation and identify each symbol. You have just derived the Beer–Lambert Law.
The concentrated solution (Part D). Compare the 0.500 M %T/A to the 0.100 M values. Predict the A you'd expect from A = εbc at 0.500 M, then explain why such a reading is unreliable, what goes wrong at very high absorbance, and why do we keep standards dilute?
Different compounds (Part E). Compare the λmax of Cu²⁺, Ni²⁺, and Fe²⁺. Why does each ion have its own λmax and colour? Why is iron(II) so pale, what does that say about its ε in the visible range?
Predict. Using A = εbc, predict the absorbance if you doubled both the concentration and the path length of a 0.0200 M, 1.00 cm sample. By what factor does A change? Predict the new %T.
Bridge to the brass lab. In one or two sentences, explain how today's findings set up the Percent Copper in Brass lab: why 650 nm is the wavelength to use, and how a line of slope εb lets you read an unknown [Cu²⁺] straight off a graph.
Error analysis, the cuvette & blank. Identify one optical error that would make a measured absorbance (and the c or ε you compute from it) read too high and one that would make it read too low. Explain each through A = 2 − log(%T) and A = εbc.
Error analysis, the standard's concentration. Identify one preparation error that would make your molar absorptivity ε read too high and one that would make it read too low. Reason through A = εbc, with absorbance plotted against the labelled concentration.

Lab · Quantitative Spectroscopy