Analytical Chemistry
Analytical Chemistry on the ACS exam rewards quantitative reasoning: how a measurement is calibrated, how uncertainty and detection limits are reported, how mixtures are separated, and how spectroscopic and electrochemical signals become concentrations. Expect calculation-heavy items rather than descriptive recall.
Calibration and figures of merit
- Linear calibration: S = mC + b. Sensitivity is m; the intercept b should be statistically indistinguishable from a blank response.
- Limit of detection LOD = 3s/m and limit of quantitation LOQ = 10s/m, where s is the standard deviation of replicate blank measurements.
- Standard addition: used when matrix suppression or enhancement prevents external calibration; plot S vs. added concentration and take the negative x-intercept as the original concentration.
- Internal standards compensate for variable injection volume or detector drift; calibrate the analyte/internal-standard signal ratio rather than the raw signal.
Separations
- Retention factor k' = (tR − t0)/t0; selectivity α = k2'/k1'; efficiency N = 16(tR/w)^2; resolution R = 2(tR2 − tR1)/(w1 + w2). Baseline resolution requires R ≈ 1.5.
- van Deemter: H = A + B/u + Cu. A is eddy diffusion (reduced by small particles), B is longitudinal diffusion (worse at low flow), C is mass transfer (worse at high flow); the curve minimum gives the optimum flow.
- For multiple extractions the fraction remaining is (Vaq/(Vaq + D·Vorg))^n, so several small portions remove more analyte than one large portion.
Spectroscopy and electrochemistry
- Beer's law A = εbc holds only for dilute, non-interacting solutions; negative deviations arise at high concentration, from stray light, and from polychromatic radiation.
- Nernst equation at 25 °C: E = E° − (0.05916/n) log Q, with ΔG° = −nFE°.
Worked example
A blank measured ten times gives s = 0.0021 absorbance units, and the calibration slope is m = 1.24 × 10^4 M^−1. Then LOD = 3s/m = 3(0.0021)/(1.24 × 10^4) = 5.1 × 10^−7 M, and LOQ = 10s/m = 1.7 × 10^−6 M. If the sample was diluted tenfold before measurement, the method LOD referred to the original sample is 5.1 × 10^−6 M.
Traps
- Using 2s or 1s instead of 3s for the LOD, or reporting LOD in absorbance units instead of concentration.
- Forgetting a dilution factor, or mixing ε units (L mol^−1 cm^−1) with path length in cm.
- Plugging half-height peak widths into resolution formulas written for baseline widths.
- Reading the standard-addition x-intercept without changing its sign.
- Assuming S/N = 3 is a natural constant rather than a convention.