Unit 1: Matter and Measurement - Study Notes

Safety

  • Purpose: Understand and apply lab safety rules and procedures for chemistry labs to protect yourself and others.
  • General conduct: follow all instructor directions, never work alone in the lab unless allowed, keep workspace organized, and clean up after activities.
  • Personal protective equipment (PPE): wear safety goggles, lab coat/apron, and closed-toe shoes; tie back long hair; remove loose jewelry; avoid loose clothing near open flames or hot surfaces.
  • Handling chemicals: read labels and Safety Data Sheets (SDS) for hazards; never pipette by mouth; use proper glassware handling; label all containers clearly; dispose of chemical waste in proper containers following guidelines.
  • Apparatus and procedures: know locations and use of safety shower/eyewash, fire extinguisher, fire blanket, and emergency exit; understand how to handle spills, broken glass, and chemical exposure.
  • Safe practices: no eating/drinking in the lab; minimize splashes and spills; wash hands after handling chemicals; report accidents or near-misses promptly.
  • Environmental and ethical considerations: practice proper waste disposal, minimize waste when possible, and report any equipment malfunctions to maintain safety and integrity of experiments.
  • Practical implications: safety rules reduce risk, improve data quality, and support ethical scientific conduct.

Metrics

  • Objective: Determine the mass, volume, and density of a substance using both laboratory skills and mathematical calculations.
  • Basic metric units and symbols:
    • Mass: m in grams, symbol: g
    • Volume: V in liters or milliliters, symbol: L or mL
    • Density: \rho or d in g/L or g/mL or g/cm^3
  • Basic metric prefixes and meanings (and symbols):
    • kilo: 10^3, symbol: k (e.g., 1\,k\text{g} = 1000\,g)
    • deci: 10^{-1}, symbol: d
    • centi: 10^{-2}, symbol: c
    • milli: 10^{-3}, symbol: m
    • micro: 10^{-6}, symbol: \mu
    • nano: 10^{-9}, symbol: n
  • Dimensional analysis: method to convert between units by multiplying by appropriate conversion factors to cancel units and isolate the desired unit.
  • Common example usages: converting grams to kilograms, mL to L, etc.
  • Practice expectations: set up unit factors, verify unit cancellation, and end with the desired unit.

Dimensional Analysis

  • Definition: A systematic method for converting between units using equality relationships between units.
  • Steps:
    • Identify given quantity and desired unit.
    • Write one or more conversion factors that relate the units (e.g., 1\,\text{kg} = 1000\,\text{g}, 1\,\text{L} = 1000\,\text{mL}).
    • Multiply the quantity by conversion factors so that units cancel appropriately.
    • Simplify to obtain the final value with appropriate units.
  • Importance: ensures dimensional consistency and accuracy in calculations across different unit systems.
  • Example outline: convert 2500\,\text{mL} to liters by applying conversion factor 1\,\text{L}/1000\,\text{mL} to obtain 2.50\,\text{L}.

Significant Digits

  • Definition: Significant digits (sig figs) are the digits that carry meaningful information about the precision of a measurement.
  • What counts as significant:
    • All nonzero digits are significant.
    • Zeros between nonzero digits are significant (captive zeros).
    • Trailing zeros are significant if there is a decimal point.
    • Leading zeros are not significant.
  • How to determine the number of significant digits in a measurement or device:
    • Read the instrument’s smallest mark and consider how precisely you can estimate beyond the mark.
  • Rounding to a specified number of significant digits:
    • Round according to the specified sig figs, preserving the scaling of the number.
  • Rules for calculations:
    • Multiplication/Division: the result has the same number of significant digits as the measurement with the fewest significant digits. \text{sig figs} = \min(\text{sig figs of factors})
    • Addition/Subtraction: the result should be rounded to the least precise decimal place (i.e., the same number of digits to the right of the decimal point as the measurement with the fewest decimal places).
  • Examples:
    • Multiplication: 12.11(3.2) = 39.952\Rightarrow 40.\text{ (2 or 3 sig figs depending on context, often 3)}
    • Addition: 12.11 + 3.2 = 15.31\Rightarrow 15.3\text{ if rounded to one decimal place}

Scientific Notation

  • Purpose: Express very large or very small numbers compactly and perform calculations more easily.
  • Conversion between regular notation and scientific notation:
    • Regular to scientific: move decimal point so that there is one nonzero digit to the left, multiply by 10^n where n is the number of places moved.
    • Scientific notation to regular: multiply the coefficient by 10^n and adjust the decimal place.
  • Calculations using numbers in scientific notation:
    • Multiply coefficients and add exponents for powers of 10.
    • Divide coefficients and subtract exponents for powers of 10.
  • Example: 4.50\times 10^3 and 3.20\times 10^{-2}; product is 4.50\times 3.20\times 10^{3-2} = 14.40\times 10^{1} = 1.440\times 10^2 after normalization.

Accuracy and Precision

  • Definitions:
    • Accuracy: Closeness of a measurement to the true value.
    • Precision: Reproducibility of measurements (how close repeated measurements are to each other).
  • Relationship:
    • You can have high precision but low accuracy (consistently off from true value).
    • You can have high accuracy but low precision (close on average to true value but variable results).
    • Ideal experiments aim for both high accuracy and high precision.
  • Percent error:
    • Formula: \text{percent error} = \left|\frac{v{\text{exp}} - v{\text{true}}}{v_{\text{true}}}\right| \times 100\%
    • Use: evaluate accuracy of a measurement or procedure.
  • Relative precision of lab equipment:
    • Based on the instrument’s smallest scale division (e.g., a balance with (0.01\,\text{g}) precision has a certain relative precision).
  • Practical implications: report uncertainties, assess data quality, and guide improvements in measurement techniques.

Percent Error and Uncertainty (Practical Assessment)

  • When to use percent error:
    • Compare measured values to accepted/true values.
    • Identify systematic vs random errors.
  • Interpreting results:
    • Small percent error indicates good agreement with the true value.
    • Large percent error suggests measurement issues or procedure flaws.
  • Limitations:
    • Some true values may be uncertain themselves; consider uncertainty ranges.

Classification of Matter

  • Matter can be classified by composition:
    • Pure substances: elements and compounds.
    • Mixtures: combinations of two or more substances.
  • Pure substances:
    • Elements: cannot be decomposed by ordinary chemical means (e.g., Fe, O₂).
    • Compounds: substances that can be broken down into simpler substances by chemical means (e.g., H₂O, NaCl).
  • Mixtures:
    • Homogeneous mixtures: uniform composition throughout (solutions) (e.g., saltwater).
    • Heterogeneous mixtures: nonuniform composition (e.g., oil and water).
  • Property and change distinctions:
    • Chemical properties: describe a substance’s ability to undergo chemical changes (e.g., reactivity with acids, flammability).
    • Physical properties: observed without changing composition (e.g., color, density, melting point).
    • Chemical changes: results in new substances (e.g., combustion, oxidation).
    • Physical changes: no new substances formed (e.g., phase change, dissolving).

Phases of Matter

  • Basic properties by phase:
    • Solid: definite shape and volume; particles vibrate in place.
    • Liquid: definite volume, no definite shape; particles slide past each other.
    • Gas: no definite shape or volume; particles move freely and fill space.
  • Warming curve:
    • A graph of temperature vs. time as a substance is heated; plateaus indicate phase changes where energy goes into changing phase rather than raising temperature.
    • Phases and phase changes to label on the curve: melting (fusion), freezing, vaporization (boiling), condensation, sublimation (solid to gas), and deposition (gas to solid).
  • Phase change processes:
    • Melting (fusion): solid to liquid.
    • Vaporization (boiling): liquid to gas.
    • Sublimation: solid to gas.
    • Condensation: gas to liquid.
    • Freezing: liquid to solid.
    • Deposition: gas to solid.
  • Energy calculations for phase changes and heating:
    • Specific heat capacity: q = m c \Delta T
    • Heat of fusion: q{\text{fusion}} = m Lf
    • Heat of vaporization: q{\text{vaporization}} = m Lv
    • Total energy for heating and phase changes across a temperature range with potential phase changes:
    • If heating from initial temperature $Ti$ to final temperature $Tf$ with possible phase changes, compute piecewise:
      • Heating solid: q = m c{s} (T{m} - Ti) up to melting point $Tm$.
      • Fusion: q = m Lf at $Tm$ (if melting occurs).
      • Heating liquid: q = m c{l} (Tf - T{m}) up to boiling point $T{b}$.
      • Vaporization: q = m Lv at $Tb$ (if vaporization occurs).
      • Heating gas: q = m c{g} (Tf - T_{b}) if heating above boiling point.
  • Practical notes:
    • Specific heat values ($c$) depend on the phase and substance.
    • Latent heats ($Lf$, $Lv$) are properties of the substance and require data tables.
    • Energy calculations use consistent units (e.g., J, g, K or °C with appropriate conversions).

Connections and Implications

  • Connections to foundational principles:
    • Measurement accuracy and precision underpin all experimental data and error analysis.
    • Dimensional analysis ensures unit consistency across experiments and computations.
    • Understanding phases and energy transfer is essential in thermodynamics and materials science.
  • Real-world relevance:
    • Lab safety and measurement accuracy impact scientific integrity in research and industry.
    • Proper use of significant figures and uncertainty reporting affects decision-making in engineering and environmental science.

Ethics and Practical Implications

  • Scientific integrity: report measurements honestly, include uncertainty, and acknowledge limitations.
  • Waste handling and environmental responsibility: proper disposal and minimization of hazardous waste.
  • Safety as a core ethical responsibility: maintaining a safe working environment protects researchers and the community.
  • Practical implications: accurate data collection improves reproducibility, reliability of conclusions, and public trust in science.