Analytical Chemistry Tutoring

Analytical chemistry asks a practical question: how much of something is in this sample, and how sure are you? So the course mixes chemistry, statistics, and lab technique. Quantitative analysis covers sampling, error, titrations, and equilibrium. Instrumental analysis covers the machines, such as spectrophotometers, gas and liquid chromatographs, mass spectrometers, and electrodes. STEM Tutor 360's one-on-one analytical chemistry tutoring helps with the calculations behind each method and with writing up lab results the way your instructor expects.

Many students find the statistics the unfamiliar part. Standard deviation, confidence intervals, and propagation of uncertainty show up on every lab report and most exams, and the rules for significant figures are stricter than in earlier courses. Sessions work on your own data sets and past lab write-ups, so you practice the techniques on the kind of numbers you will report.

A typical analytical chemistry problem, worked

Five iron standards (1.00, 2.00, 3.00, 4.00, and 5.00 mg/L) are developed with 1,10-phenanthroline and read at 510 nm in a 1.00 cm cell. The absorbances are 0.201, 0.398, 0.603, 0.794, and 0.997. A water sample, diluted tenfold before color development, reads 0.512. What is the iron concentration in the original sample?

Beer's law says $A = \varepsilon b c$, so absorbance should be a straight line in concentration. A least-squares fit gives $A = 0.1988\, c + 0.0022$, with $R^{2} = 0.9999$. Solve for the diluted sample: $c = \dfrac{0.512 - 0.0022}{0.1988} = 2.56\ \text{mg/L}$. That lies inside the standards, so interpolation is valid. Undo the dilution: $2.56 \times 10 = 25.6\ \text{mg/L}$ of iron in the original sample.

Two checks finish the job. The slope gives $\varepsilon$: $0.1988\ \text{L/(mg cm)} \times 55.85\ \text{g/mol} \times 1000\ \text{mg/g} = 1.11 \times 10^{4}\ \text{L/(mol cm)}$, close to the value usually quoted for this complex. And the regression statistics put the uncertainty in the diluted result near 0.02 mg/L (one standard deviation), so the report reads $25.6 \pm 0.2\ \text{mg/L}$.

Lab reports and data treatment

• Report a mean with its standard deviation and the number of replicates, with significant figures that match the uncertainty.
• Propagate uncertainty by the right rule: absolute uncertainties in quadrature for sums and differences, relative uncertainties in quadrature for products and quotients.
• Test outliers with a stated method, such as a Q test or Grubbs test, and report what you removed.
• Show the regression statistics and the calibration range, and note where the unknown falls inside it.
• Compare your result with a reference value or a second method using a t-test.

Where students usually get stuck

• Mixing up accuracy (closeness to the true value) and precision (agreement among replicates).
• Using one propagation rule for a calculation that has both addition and multiplication.
• Back titrations, and knowing when to work in moles instead of concentrations.
• Extrapolating past the calibration range, or forcing the line through zero without a reason.
• Chromatography calculations: retention factor, plate number, and resolution.