5.1 Analytical Measurements: Apparatus, Units, Concentration, Sampling, and Sample Preparation

5.1 Analytical Measurements: Apparatus, Units, Concentration, Sampling, and Sample Preparation

Quick Answer: Analytical area A (10 items) covers basic concepts: instruments and apparatus, laboratory safety and disposal (Section 1.3), units, and stoichiometric, concentration, dilution, and aliquot calculations. Area B adds sampling and sample preparation, significant figures, and standards organizations. These calculations sit inside almost every quantitative question, so practise them until they are automatic.

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Weighing and Volumetric Apparatus

The Analytical Balance

• A standard analytical balance reads to 0.1 mg; semimicro balances read to 0.01 mg.
• Weighing by difference (weigh the container, transfer the sample, reweigh) avoids exposing hygroscopic solids and cancels constant balance errors.
• Dry primary standards in an oven (typically 105-110 C) and cool them in a desiccator before weighing. Never weigh warm objects: convection currents make them read light.
• A buoyancy correction matters for low-density samples: $W = W' + W'\left(\frac{d_{air}}{d_{obj}} - \frac{d_{air}}{d_{wts}}\right)$, with $d_{air} \approx 0.0012$ g/mL and $d_{wts} = 8.0$ g/mL for steel weights.

Volumetric Glassware

Read the bottom of the meniscus at eye level to avoid parallax. Rinse pipets and burettes with the solution they will hold, never with water alone. Calibrate glassware by weighing the water it delivers: at 25 C, 1.0000 g of water weighed in air with steel weights corresponds to 1.0040 mL.

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Units and Concentration

The SI has seven base units: metre, kilogram, second, ampere, kelvin, mole, and candela. Since 2019 all seven are defined by fixed constants.

Concentrated reagent molarity:

$M = \frac{\rho\ (\text{g/mL}) \times 1000 \times w}{\text{molar mass}}$

For 37.2% HCl with density 1.19 g/mL, $M = \frac{1.19 \times 1000 \times 0.372}{36.46} = 12.1$ M. Concentrated $H_2SO_4$ (96%, 1.84 g/mL) is 18.0 M.

Unit conversion: 2.5 ppm Fe in water is 2.5 mg/L, which equals $\frac{2.5 \times 10^{-3}}{55.845} = 4.5 \times 10^{-5}$ M.

Dilutions and Aliquots

$C_1V_1 = C_2V_2$

For serial dilutions, multiply the dilution factors: three successive 1-to-10 dilutions give 1-to-1000.

Worked aliquot problem: A 0.4000 g iron ore sample is dissolved, reduced to $Fe^{2+}$, and diluted to 250.0 mL. A 25.00 mL aliquot needs 12.40 mL of 0.004000 M $KMnO_4$ ($MnO_4^- + 5Fe^{2+} + 8H^+ \rightarrow Mn^{2+} + 5Fe^{3+} + 4H_2O$).

• mol $MnO_4^-$ $= 0.01240 \times 0.004000 = 4.960 \times 10^{-5}$
• mol $Fe$ in the aliquot $= 5 \times 4.960 \times 10^{-5} = 2.480 \times 10^{-4}$
• mol $Fe$ in the sample $= 2.480 \times 10^{-4} \times \frac{250.0}{25.00} = 2.480 \times 10^{-3}$
• %Fe $= \frac{2.480 \times 10^{-3} \times 55.845}{0.4000} \times 100 = 34.62\%$

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Significant Figures

• Addition and subtraction: keep the fewest decimal places: $12.11 + 0.3 = 12.4$.
• Multiplication and division: keep the fewest significant figures: $3.141 \times 2.1 = 6.6$.
• Logarithms: the digits after the decimal point in the log equal the significant figures in the number. $[H^+] = 4.3 \times 10^{-5}$ M (two figures) gives pH 4.37; going back, pH 4.37 gives $[H^+] = 4.3 \times 10^{-5}$ M.
• Exact numbers (stoichiometric coefficients, defined conversions) do not limit significant figures. Round only at the end, carrying at least one extra digit through intermediate steps.

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Sampling

An analysis can be no better than its sample. The sampling chain runs from the population (lot) to a gross sample, then a laboratory sample, and finally the test portion actually analysed.

• Random sampling gives every portion an equal chance of selection. Systematic (grid or time-interval) sampling is practical but can miss periodic variation. Composite samples average a lot; discrete samples reveal its variability.
• Heterogeneous solids are reduced by coning and quartering or with a riffle splitter, and ground to a uniform particle size.
• Variance adds: $s_{overall}^2 = s_{sampling}^2 + s_{method}^2$. With 3% sampling and 1% method standard deviations, the overall value is $\sqrt{9 + 1} = 3.2\%$. Halving the method error to 0.5% only lowers it to 3.0%, so collecting better samples is the priority.
• The number of samples needed for a target error $e$ is approximately $n = \frac{t^2 s_s^2}{e^2}$.
• Preserve samples appropriately: acidify water to pH below 2 for metals, refrigerate for nutrients and BOD, and avoid contamination from containers.

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Sample Preparation and Dissolution

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Standards Organizations and Accreditation

• International: ISO (standards, including ISO/IEC 17025 for testing and calibration laboratories); IUPAC (nomenclature and terminology); BIPM (the SI); NIST (Standard Reference Materials); AOAC INTERNATIONAL (official food and agricultural methods); ASTM International; APHA, AWWA, and WEF (Standard Methods for the Examination of Water and Wastewater); the USP (pharmaceutical monographs); US EPA methods; and Eurachem/CITAC guides on method validation and measurement uncertainty.
• Philippines: the DTI Philippine Accreditation Bureau (PAB) accredits laboratories to ISO/IEC 17025. The DTI Bureau of Philippine Standards issues Philippine National Standards (PNS). The National Metrology Laboratory at DOST-ITDI maintains national measurement standards.
• Certified reference materials (CRMs) with traceable certified values are used to establish accuracy and metrological traceability; Section 1.3 covers the quality system.