IV

Measurements, SI Units, and SIG Figs

Meniscus Reading and Volume Measurement

  • Read liquid levels at the bottom of the meniscus for accuracy, preventing parallax error.

  • Record measurements to include all known digits plus one estimated digit.

  • Rounding:

    • Apply significant figure rules. Trailing zeros can be ambiguous; use a decimal point for clarity (e.g., "100." has 3 sig-figs). Follow "nearest-even" (banker's rounding) or instructor's specific rule.

  • Significant Figures & Calculations:

    • Round multiplication/division results to the fewest significant figures of inputs. Round addition/subtracting results to the fewest decimal places. Carry extra sig-figs through intermediate steps, rounding only the final result.

  • Always retain units; conversions: 1_\text{L} = 1000_\text{mL}, 1_\text{cm}^3 = 1_\text{mL}.

  • SI Units: Base units include: Mass (kg), Length (m), Volume (L or \text{m}^3), Temperature (K), Time (s).

  • Prefixes: Giga (10^9), Mega (10^6), Kilo (10^3), Centi (10^{-2}), Milli (10^{-3}), Micro (10^{-6}), Nano (10^{-9}), Pico (10^{-12}), Femto (10^{-15}).

Properties: Intensive vs. Extensive

  • Intensive Properties: Independent of material amount (e.g., melting point, density).

  • Extensive Properties: Depend on material amount (e.g., mass, volume).

  • Density (\rho = \frac{m}{V}) is intensive; its SI unit is \text{kg} / \text{m}^3.

Density and a Worked Example

  • Density is constant for a given substance under specific temperature/pressure.

  • Example: Volume of 100 g aluminum (\rho_\text{Al} = 2.7\ \text{g/mL}) is \approx 37.0\ \text{mL}.

  • Water density is approx. 1\ \text{g/mL}.

Dimensional Analysis and Unit Conversions

  • Dimensional analysis uses conversion factors to change units.

  • Temperature Conversions:

    • C = (F - 32) \cdot \frac{5}{9}

    • K = C + 273.15

    • K = (F - 32) \cdot \frac{5}{9} + 273.15

  • Use parentheses correctly in calculations.

Temperature, Absolute Zero, and Benchmarks

  • Absolute Zero: Theoretical lowest temperature (0\ \text{K}, -273.15^\circ\mathrm{C}) where molecular motion ceases; practically unreachable.

  • Benchmarks (at 1 atm): Ice melting point: 0^\circ\mathrm{C}; Water boiling point: 100^\circ\mathrm{C}.

Measurement Precision and Accuracy: Graphical Intuition

  • Precision: Consistency of repeated measurements.

  • Accuracy: Closeness to the true value.

  • Goal: Achieve both (clustered and on-target).

    • Systematic Errors: Affect accuracy (consistent bias, e.g., miscalibrated instrument).

    • Random Errors: Affect precision (unpredictable variation).

Summary of Key Points to Remember for the Exam

  • Sig Figs & Rounding: Apply rules for all calculations; carry extra sig-figs.

  • Units & SI: Carry units; know SI base units and prefixes; perform common conversions.

  • Density & Dimensional Analysis: Use \rho = \frac{m}{V} and master unit conversions.

  • Intensive vs. Extensive: Distinguish properties.

  • Measurement & Tools: Read meniscus properly; recognize precision limits; use calculator brackets.

  • Relevance: Measurement, sig-figs, and unit handling are fundamental to chemistry.