Measurement and Data Processing — IB Chemistry SL Study Guide

For: IB Chemistry SL candidates sitting IB Chemistry SL.

Covers: IB Topic 11 — uncertainties in measurement, propagation through calculations, graphical techniques, mass spectrometry interpretation, IR / NMR / UV-Vis spectroscopy basics. Critical for the IA report.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the IB Chemistry SL style for educational use. They are not reproductions of past IBO papers.

1. Why Measurement & Data Processing Matters

Topic 11 is central to the Internal Assessment (IA) — every IA report demands proper uncertainty analysis and one of these spectroscopic techniques. About 5-7% of Paper 1+2, but the IA accounts for 20% of your overall grade and depends entirely on Topic 11 skills.

2. Uncertainties

Random errors (precision): vary unpredictably. Reduce by repeated trials and averaging.

Systematic errors (accuracy): same magnitude and direction every time (calibration error, parallax error). Repeating doesn't help.

Absolute uncertainty $\Delta x$: same units as $x$.

Percentage uncertainty: $\Delta x/x\times 100\%$.

For analogue scales: $\Delta x=$ half the smallest division (e.g. 50 mL graduated cylinder has 1 mL marks → $\Delta x=0.5$ mL).

For digital instruments: $\Delta x=$ smallest displayed unit (e.g. 0.1 g balance → $\Delta x=0.05$ g, or whatever the manufacturer states).

3. Propagation rules

Example: titration of base with acid.

• Volume of acid $V_a=25.00\pm 0.05$ cm³ (burette: 0.05 cm³ × 2 readings).
• Concentration of acid $c_a=0.100\pm 0.005$ mol·dm⁻³.
• Moles of acid $n=c_a{V}_a=0.100\cdot 0.025=0.00250$ mol.
• $\Delta n/n=5\%+0.2\%=5.2\%$, so $\Delta n=0.00013$ mol.

4. Graphical techniques

When suspecting $y=mx+c$, plot $y$ vs $x$ with error bars. Find:

• Slope from two distant points: $m=(y_2-y_1)/(x_2-x_1)$.
• Intercept from where line crosses y-axis.
• Slope uncertainty: (m_\max - m_\min)/2 from extreme lines through error bars.

Non-linear relations need linearization: e.g. $y=a{x}^n$ → $\log y=\log a+n\log x$, linear when plotting $\log y$ vs $\log x$.

5. Mass spectrometry

A sample is ionised, accelerated, and deflected in a magnetic field. The mass-to-charge ratio ($m/z$) determines the deflection.

Output: a mass spectrum showing peaks at characteristic $m/z$ values for the molecular ion (M⁺) and fragments.

Determining molecular mass: the highest peak (M⁺) gives molecular mass.

Isotope ratios: relative peak heights at $m/z$ corresponding to isotopes give isotopic abundance. Example: chlorine shows peaks at 35 and 37 with intensities ~3:1, giving relative atomic mass $\approx 35.5$.

6. IR (infrared) spectroscopy

IR identifies functional groups by characteristic absorption frequencies. The molecule absorbs IR at frequencies matching its bond vibrations.

Memorise key absorptions for IB SL:

Use the IB Data Booklet during the exam — these values are provided.

7. NMR (¹H NMR)

¹H NMR detects hydrogen environments in a molecule. Three pieces of information:

• Number of peaks: equals number of distinct H environments.
• Chemical shift (δ, ppm): tells what kind of environment (e.g. $\delta \approx 9-10$ for aldehyde H, $\delta \approx 0.9-1.7$ for alkyl H).
• Integration ratio: gives ratio of H atoms in each environment.

For HL only: splitting (n+1 rule) tells you how many neighbouring H's. Not in SL syllabus.

Common δ values (Data Booklet):

8. UV-Vis spectroscopy

UV-Vis measures absorption of UV/visible light by molecules with π or non-bonding electrons. The wavelength of maximum absorption (\lambda_\max) depends on the molecular electronic structure.

Beer-Lambert law: $$A=ϵcl$$ where $A$ is absorbance, $ϵ$ is molar absorptivity (dm³·mol⁻¹·cm⁻¹), $c$ is concentration, $l$ is path length.

Used to determine concentration in solution: prepare calibration curve $A$ vs $c$, then read off unknowns.

9. Worked Example

A student determines the molar mass of an unknown alcohol via mass spectrometry and IR. Mass spectrum shows a strong peak at $m/z=60$ with smaller peaks at 45 and 31. IR shows a broad absorption at 3300 cm⁻¹ and a strong peak at 1050 cm⁻¹.

(a) From the IR, what functional group is present? (b) From the M⁺ peak, what is the molecular mass? (c) Suggest a structure consistent with both the molecular mass and the IR.

Solution.

(a) Broad O–H stretch at 3200–3550 cm⁻¹ suggests an alcohol. Strong 1050 cm⁻¹ is consistent with C–O stretch of an alcohol. So the functional group is –OH (alcohol).

(b) M⁺ at 60 → molar mass = 60 g/mol.

(c) Possible alcohols at M = 60: propan-1-ol or propan-2-ol (both C₃H₇OH = 60). Either fits the data; would need the more detailed fragmentation pattern (45 = M – 15 = loss of CH₃; 31 = CH₂OH⁺) or NMR to distinguish.

10. Common Pitfalls

• Confusing absolute and percentage uncertainty: addition uses absolute; multiplication uses percentage.
• Reading IR backwards: the x-axis is wavenumber (cm⁻¹), not wavelength. Higher wavenumber = higher energy = stronger bond.
• NMR integration ≠ peak height: integration is the area under the peak, indicated by step heights or numbers in modern software.
• Beer-Lambert linearity: only valid for dilute solutions. At high concentration, deviations occur.

11. Practice Questions

1. A burette delivers $25.20\pm 0.05$ cm³ of acid. Mass of NaOH dissolved is $1.00\pm 0.01$ g. Calculate moles of NaOH and propagate the percentage uncertainty (M(NaOH) = 40.0).
2. An IR spectrum has peaks at 1715 cm⁻¹ and 3300 cm⁻¹ (broad). Suggest the functional group(s).
3. An NMR spectrum of an unknown C₃H₆O₂ shows two peaks: δ = 2.1 ppm (3H integration), δ = 11.5 ppm (1H integration). Suggest a structure.

12. Quick Reference Cheatsheet

• Sum/difference: absolute uncertainties add.
• Product/quotient: percentage uncertainties add.
• Power $x^n$: percentage uncertainty × n.
• $\Delta x$ analogue: half smallest division. Digital: smallest unit.
• IR key: O–H 3200–3550 (broad); C=O 1700–1750; aromatic C–H 3000–3100.
• NMR shift: alkyl 0.9–1.7; alkene 4.5–6.0; aromatic 6.5–8.0; aldehyde 9.4–10.
• Beer-Lambert: $A=ϵcl$.

13. What's Next

Measurement & Data Processing is the foundation of your IA. Use Ollie to step through any specific propagation calculation or to identify a compound from its mass spec / IR / NMR combined: "What molecule fits these spectra?"