Unit 1 Review Notes: Classification of Matter and Measurement
Classification of Matter
Matter: anything with mass and occupies space; composed of atoms.
States of matter and their properties:
Solid: Definite shape and volume; particles fixed, closely packed, strong intermolecular forces, incompressible.
Liquid: Indefinite shape, definite volume; particles closely packed but flow, weaker intermolecular forces, nearly incompressible.
Gas: Indefinite shape and volume; particles far apart, move freely, negligible intermolecular forces, highly compressible and expansible.
Pure substances: elements and compounds
Elements: Cannot be decomposed chemically. Defined by atomic number (protons).
Examples:
Hydrogen gas: $H_2$
Oxygen gas: $O_2$
Iron: $Fe$
Key concept: simplest form of matter, unique atom type; all atoms have same protons.
Matter: anything with mass and occupies space; composed of atoms.
States of Matter
Solid: Definite shape/volume, fixed particles, strong forces, incompressible.
Liquid: Indefinite shape, definite volume, flowing particles, weaker forces, nearly incompressible.
Gas: Indefinite shape/volume, far apart particles, negligible forces, highly compressible/expansible.
Pure Substances
Elements: Cannot be chemically decomposed. Defined by atomic number (protons). Simplest form (e.g., $H_2$, $Fe$).
Compounds: Two or more different elements chemically combined in fixed proportions. Decomposed by chemical changes. Properties differ from constituent elements (e.g., $H_2O$, $NaCl$).
Elements vs. Compounds: Elements are single atom types; compounds are multiple elements bonded. Conversion requires chemical change.
Mixtures
Combinations of 2+ pure substances, each retaining identity; separated by physical means.
Heterogeneous: Non-uniform, visibly distinct components (e.g., granite, salad).
Homogeneous (Solutions): Uniform composition, evenly distributed components (e.g., air, salt water).
Separation of Mixtures
Evaporation: Separates soluble solid from liquid (solvent vaporizes).
Distillation: Separates liquid components by boiling point differences.
Filtration: Separates insoluble solid from liquid (solid retained).
Chromatography: Separates components based on differential distribution.
Physical vs. Chemical Changes
Physical: Change in form/appearance; no new substance formed; identity remains (e.g., melting, boiling).
Chemical: Rearrangement of atoms, forms new substances with different properties; often irreversible (e.g., rusting, combustion).
Measurement and Significant Figures
Qualitative: Descriptive, non-numerical (e.g., color).
Quantitative: Numerical measurements with magnitude, unit, and uncertainty (e.g., mass, length).
Components of Measurement: Numerical value, unit, inherent uncertainty.
Accuracy: Closeness to true value. Precision: Reproducibility of measurements.
Errors: Systematic (consistent bias, minimized by calibration), Random (unpredictable, minimized by repetition).
Significant Figures (Sig Figs): Digits known with certainty + one estimated digit; communicate precision.
Identification Rules: Non-zeros are significant. Zeros between non-zeros are significant. Leading zeros are not significant. Trailing zeros are significant only if a decimal point is present.
Calculation Rules:
Multiplication/Division: Result has sig figs equal to factor with fewest.
Addition/Subtraction: Result has decimal places equal to measurement with fewest.
Scientific Notation: $a \times 10^n$ ($1 \leq a < 10$), clearly indicates sig figs.
Units and Conversions
Metric Prefixes: (pico $10^{-12}$ to mega $10^6$).
Base SI Units: length ($m$), mass ($kg$), time ($s$), current ($A$), temperature ($K$), amount ($mol$), luminous intensity ($cd$).
Dimensional Analysis: Problem-solving for unit conversion by treating units algebraically. Steps: Identify units, gather conversion factors, construct chain, cancel units, perform arithmetic, report result.
Example: \text{2.5 hours} \times \frac{\text{60 minutes}}{\text{1 hour}} \times \frac{\text{60 seconds}}{\text{1 minute}} = \text{9000 seconds} ($9.0 \times 10^3\text{ seconds}$).
Temperature Scales: Fahrenheit (F), Celsius (C), Kelvin (K). Conversion formulas:
F = \frac{9}{5}C + 32
K = C + 273.15
Derived Concepts
Density: Mass per unit volume (intensive property). \rho = \frac{m}{V} Units: $\mathrm{g/cm^3}$. Water displacement for volume.
Key Takeaways
Accurate measurements are fundamental. Sig figs ensure honest precision. Dimensional analysis is a universal tool.
Reporting uncertainty and proper calibration promote scientific integrity and valid results.
Quick Reference
Density: \rho = \frac{m}{V}
Temperature: F = \frac{9}{5}C + 32, K = C + 273.15
Sig Figs: Rules for identification, multiplication/division, addition/subtraction.
Metric Prefixes: ($p = 10^{-12}$ to $M = 10^6$).
Base SI Units: $m, kg, s, A, K, mol, cd$.
Decomposed into simpler substances only by chemical changes.
Examples:
Water: $H_2O$
Sodium chloride: $NaCl$
Key concept: properties different from constituent elements; formation/decomposition involves chemical bonds (chemical changes).
How elements and compounds differ
Elements = pure substances of one atom type; simplest forms of matter with chemical identity.
Compounds = pure substances of two+ different elements chemically bonded in fixed ratios; unique properties, can be chemically decomposed.
Changes: Element to compound (or vice versa) requires a chemical change (rearrangement of atoms, breaking/forming bonds).
Example: $2H2 (g) + O2 (g) \rightarrow 2H_2O (l)$
Mixtures: heterogeneous vs homogeneous
Mixtures: Combinations of two+ pure substances, each retaining identity; separated by physical means.
Heterogeneous mixtures: Non-uniform composition; visibly distinct components; properties vary.
Examples: granite, salad, sand in water.
Homogeneous mixtures (solutions): Uniform composition and appearance; components evenly distributed; single phase.
Examples: air, salt water, sugar dissolved in water.
Separation of mixtures (how to separate)
Evaporation: Separates soluble solid from liquid by heating (solvent vaporizes, solute remains).
Distillation: Separates liquid components by boiling point differences. Volatile liquid vaporizes, condenses (distillate).
Filtration: Separates insoluble solid from liquid using a filter medium (solid retained, liquid passes).
Chromatography: Separates components based on differential distribution between stationary and mobile phases.
Methods for separation of mixtures: description and use cases
Evaporation: Recovers solid solute from volatile solvent.
Distillation: Separates liquids with different boiling points or volatile liquid from non-volatile solid.
Filtration: Separates undissolved solids from liquids.
Chromatography: Separates complex mixtures based on component affinities for stationary phase.
Physical changes vs chemical changes
Physical changes (no new substance formed): Change in form/appearance, not chemical composition. Identity remains.
Examples: melting ice, boiling water, dissolving sugar, cutting paper.
Chemical changes (new substances formed): Rearrangement of molecules/ions, forms new substances with different properties; often irreversible.
Examples: rusting iron ($4Fe (s) + 3O2 (g) \rightarrow 2Fe2O3 (s)$), combustion of methane ($CH4 (g) + 2O2 (g) \rightarrow CO2 (g) + 2H_2O (g)$), digestion.
Measurement and Significant Figures (sig. figs.)
Qualitative vs quantitative measurements
Qualitative: Descriptive, non-numerical observations (e.g., color, texture, odor).
Quantitative: Numerical measurements with magnitude and unit (e.g., mass, length, temperature); have uncertainty.
Two components of every measurement
Numerical value (magnitude).
Unit (e.g., g, m, s). Measurement also carries inherent uncertainty.
Accuracy vs precision
Accuracy: Closeness of measurement to true value (minimal systematic error).
Precision: Reproducibility of repeated measurements (low random error).
Instrument limitations and errors
Systematic error: Consistent bias (e.g., faulty equipment); minimized by calibration.
Random error: Unpredictable fluctuations; minimized by repeated measurements and averaging.
Significant figures (sig figs) and why we use them
Significant figures: Digits known with certainty + one estimated digit; communicate measurement precision.
Rules for identifying sig figs:
Non-zero digits are significant.
Zeros between non-zero digits are significant.
Leading zeros are never significant.
Trailing zeros are significant only if a decimal point is present.
Rules for sig figs in calculations:
Multiplication/division: Result has same number of sig figs as factor with fewest sig figs.
Example: $(3.72 \text{ cm}) \times (2.0 \text{ cm}) = 7.4 \text{ cm}^2$.
Addition/subtraction: Result has same number of decimal places as measurement with fewest decimal places.
Example: $12.11 \text{ g} + 0.034 \text{ g} = 12.14 \text{ g}$.
Scientific notation
Standardized form $a \times 10^n$ ($1 \leq a < 10$); clearly indicates sig figs. Useful for very large/small numbers.
Example: $0.00340 = 3.40 \times 10^{-3}$; $60,200 = 6.020 \times 10^4$.
Metric prefixes (from pico to mega) and their abbreviations
Pico: $10^{-12}$, $p$
Nano: $10^{-9}$, $n$
Micro: $10^{-6}$, $\mu$
Milli: $10^{-3}$, $m$
Centi: $10^{-2}$, $c$
Deci: $10^{-1}$, $d$
Base unit
Kilo: $10^3$, $k$
Mega: $10^6$, $M$
Base SI units
Seven fundamental units:
meter: length, $m$
kilogram: mass, $kg$
second: time, $s$
ampere: electric current, $A$
kelvin: temperature, $K$
mole: amount of substance, $mol$
candela: luminous intensity, $cd$
Dimensional analysis (philosophy and steps)
Philosophy: Problem-solving technique for unit conversion, treating units like algebraic variables.
Practical steps:
Identify Start and Target Units.
Gather Equivalence Statements (conversion factors).
Construct Conversion Factor Chain (cancel unwanted units).
Cancel Units.
Perform Arithmetic.
Report Result with correct sig figs and units.
Example: Convert $2.5$ hours to seconds: \text{2.5 hours} \times \frac{\text{60 minutes}}{\text{1 hour}} \times \frac{\text{60 seconds}}{\text{1 minute}} = \text{9000 seconds} (or $9.0 \times 10^3\text{ seconds}$).
Temperature scales and conversions
Fahrenheit (F), Celsius (C), Kelvin (K).
Conversion formulas:
$F = \frac{9}{5}C + 32$
$K = C + 273.15$
$C = \frac{5}{9}(F - 32)$
$K = \frac{5}{9}(F - 32) + 273.15$
Density and volume measurement
Density: Intensive physical property; mass per unit volume. \rho = \frac{m}{V} Units: $\mathrm{g/cm^3}$, $\mathrm{g/mL}$, $\mathrm{g/L}$ ($1\text{ cm}^3 = 1\text{ mL}$).
Water displacement: Determines irregular object volume by measuring displaced water volume.
Example: Object mass $56.7\text{ g}$, displaces $23.0\text{ mL}$ water; $\rho = \frac{56.7\text{ g}}{23.0\text{ mL}} \approx 2.47\text{ g/mL}$.
Connections to foundational principles and real-world relevance
Accurate measurements are fundamental to science and tech.
Sig figs ensure honest reporting of precision.
Dimensional analysis is a universal tool for unit conversions and error checking.
Ethical, philosophical, and practical implications
Reporting uncertainty promotes scientific integrity.
Proper calibration ensures valid results.
Clear data presentation avoids miscommunication.
Quick reference formulas and concepts recap
Density: \rho = \frac{m}{V}
Temperature conversions:
F = \frac{9}{5}C + 32
K = C + 273.15
C = \frac{5}{9}(F - 32)
K = \frac{5}{9}(F - 32) + 273.15
Sig figs rules: identification, multiplication/division, addition/subtraction.
Metric prefixes: $p (10^{-12})$, $n (10^{-9})$, $\mu (10^{-6})$, $m (10^{-3})$, $c (10^{-2})$, $d (10^{-1})$, base, $da (10^{1})$, $h (10^{2})$, $k (10^{3})$, $M (10^{6})$.
Base SI units: $m$ (length), $kg$ (mass), $s$ (time), $A$ (current), $K$ (temp), $mol$ (amount), $cd$ (intensity).