Worked example 1
A calibration plot of FeSCN₂⁺ gives a slope of 4.5 × 10³ L/mol. An equilibrium mixture has A = 0.360. Find [FeSCN₂⁺].
Try it first: Rearrange Beer''s law for concentration before substituting.
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Chemical Equilibrium & SolubilityLaboratoryContent level: Core 24 min
Lab: Determining an Equilibrium Constant by Spectrophotometry
What you'll be able to do: Use absorbance data and a Beer's law calibration to find equilibrium concentrations and calculate K.
Introduction
Measuring an equilibrium constant means measuring concentrations without disturbing the equilibrium. Light does exactly that: a colored species absorbs in proportion to how much of it is there.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Construct and use a Beer's law calibration curve
- Convert absorbance to concentration using the slope
- Use one measured concentration to complete an ICE table
- Identify the main sources of error in the determination
Lesson
Why light works
A spectrophotometer measures how much light a solution absorbs at a chosen wavelength. Because the measurement takes no material out of the flask, the equilibrium is left completely undisturbed, which is exactly what a titration or an extraction would fail to do.
Beer''s law
Absorbance is the product of the molar absorptivity, the path length and the concentration. With a fixed 1 cm cuvette and a fixed wavelength, absorbance is directly proportional to concentration.
A = e b c
Choose the wavelength of maximum absorbance so that small concentration changes give the largest signal.
The calibration curve
Prepare standards of known concentration, measure each absorbance, and plot A against c. The line should pass through the origin and its slope equals e b. Any unknown is then c = A / slope.
c = A / slope
The FeSCN₂⁺ system
Fe³⁺(aq) + SCN⁻(aq) ⇌ FeSCN₂⁺(aq) produces an intensely red complex, while both reactants are effectively colorless at 447 nm. That selectivity is what makes the absorbance a direct measure of [FeSCN₂⁺].
K = [FeSCN₂⁺] / ([Fe³⁺][SCN⁻])
From one concentration to K
The measured [FeSCN₂⁺] is the x of the ICE table. Subtract it from the initial concentrations of Fe³⁺ and SCN⁻ to get their equilibrium values, then substitute all three into the K expression. Remember that mixing the two stock solutions dilutes both, so the initial concentrations must be corrected with M₁V₁ = M₂V₂ before the table is written.
Correct for dilution on mixing before filling in the initial row.
Sources of error
Failing to blank the instrument with the solvent adds a constant offset to every reading. Absorbances above about 1.0 fall off the linear range and give concentrations that are too low. Fingerprints and bubbles on the cuvette scatter light. Because K depends on temperature, standards and samples must be measured at the same temperature.
Account for dilution before the ICE table
Concentrations in stock bottles are not the initial concentrations in a reaction mixture. Convert moles added to the total mixed volume before using absorbance to infer the colored equilibrium species. Then subtract the measured complex concentration from each reactant's initial concentration according to reaction stoichiometry.
Initial after mixing comes before equilibrium change.
Key ideas
Definition
Absorbance A
A unitless log measure of how much light a sample absorbs at a given wavelength.
Definition
Molar absorptivity e
A constant for a given species and wavelength, in L/mol cm.
Rule
Calibration slope
The slope of A against c equals e b, and dividing an absorbance by it gives a concentration.
Rule
Linear range
Keep absorbance between about 0.1 and 1.0 for reliable results.
Key concept
Non-invasive measurement
Light-based measurement does not disturb the equilibrium being measured.
Equation
Beer's law
A = e b c
- A = absorbance, unitless
- e = molar absorptivity in L/mol cm
- b = path length in cm
- c = concentration in mol/L
Equation
Dilution on mixing
M₁V₁ = M₂V₂
- V₂ = total volume after mixing
Equation
Formation constant
K = [FeSCN₂⁺] / ([Fe³⁺][SCN⁻])
- [FeSCN₂⁺] = found from absorbance
Worked examples
Worked example 2
Mixing gives initial concentrations [Fe³⁺] = 1.00 × 10⁻³ M and [SCN⁻] = 2.00 × 10⁻⁴ M. At equilibrium [FeSCN₂⁺] = 8.0 × 10⁻⁵ M. Calculate K.
Try it first: Treat the measured complex concentration as x in an ICE table.
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Worked example 3
A student forgets to blank the spectrophotometer with the solvent. How does this affect the calculated K?
Try it first: Decide whether the error raises or lowers every absorbance reading.
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Worked example 4
Mix 2.00 mL of 0.00200 M Fe³⁺ stock with enough SCN⁻ solution to total 10.00 mL. If [FeSCN₂⁺]eq=1.00×10⁻⁴ M, find [Fe³⁺]eq.
Try it first: First calculate the diluted initial iron concentration.
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Common mistakes
Using initial concentrations of Fe³⁺ and SCN⁻ directly in the K expression.
Why it's wrong: K requires equilibrium values, which are the initial values minus the complex formed.
Check instead: Complete the ICE table first.
Skipping the dilution correction when the stock solutions are mixed.
Why it's wrong: Both concentrations drop when the volumes combine.
Check instead: Apply M₁V₁ = M₂V₂ with the total volume.
Using an absorbance well above 1.0 without dilution.
Why it's wrong: Beer''s law becomes non-linear there, so the concentration is underestimated.
Check instead: Dilute the sample back into the 0.1 to 1.0 range.
Assuming the molar absorptivity is a universal constant.
Why it's wrong: It depends on the species and the wavelength.
Check instead: Use the slope from your own calibration at your own wavelength.
Comparing measurements taken at different temperatures.
Why it's wrong: K itself changes with temperature.
Check instead: Keep standards and samples thermostatted.
After the lesson · Question bank
Independent practice
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What you should now know
Beer's law states that absorbance is proportional to concentration, A = e b c, so a calibration line of absorbance against known concentration gives a slope of e b. Measuring the absorbance of an equilibrium mixture and dividing by that slope returns the concentration of the colored species without removing any sample. That single measured concentration feeds the change row of an ICE table, from which every other equilibrium concentration follows, and then K. The classic system is Fe³⁺ + SCN⁻ ⇌ FeSCN₂⁺, where only the deep red thiocyanatoiron complex absorbs strongly at about 447 nm. Good practice means blanking with the solvent, staying in the linear absorbance range of roughly 0.1 to 1.0, and holding the temperature constant because K depends on it.
- Absorbance is proportional to concentration through Beer''s law
- A calibration line gives the slope needed to convert A to concentration
- One measured concentration completes the whole ICE table
- Correct for dilution on mixing before writing the initial row
- Blank the instrument, stay in the linear range, and control temperature
Sources and further reading
This lesson is original Chem Help content. No external sources were adapted.