Metric Prefixes

1.2 Scientific Measurement

• What can we measure to describe matter? What are the units used to describe these quantities?
• memorize the metric prefixes: nano-, micro-, milli-, centi-, deci-, kilo-, mega-, giga-
• Density is defined as:
  $\text{Density} = \frac{m}{V}$
• Practice problem (density): Suppose a nugget is believed to be gold. Mass = 163 g. It displaces water in a graduated cylinder from 50.0 mL to 58.5 mL, so the volume of the nugget is $V = 58.5\,\text{mL} - 50.0\,\text{mL} = 8.5\,\text{mL} = 8.5\,\text{cm}^3$
  Density = $\frac{163\,\text{g}}{8.5\,\text{cm}^3} = 19.176…\,\frac{\text{g}}{\text{cm}^3} \approx 19.2\,\frac{\text{g}}{\text{cm}^3}$
• Interpretation: A density near 19.3 g/cm³ is characteristic of gold, but the measurement alone does not prove the nugget is gold. Additional tests would be needed.

1.3 Uncertainty in Measurement (Significant Figures)

• Significant figures (sig figs): digits reported by a measurement, reflecting instrument precision.

• Rules (fill-in-the-blank style from slides):

  • Zeroes between two other significant figures are significant.
    Example: 103 has 3 sig figs.
  • Zeroes to the right of a decimal place are significant.
    Example: 2.50 has 3 sig figs.
  • Zeroes before the first non-zero digit are not significant.
    Example: 0.0013 has 2 significant digits (1 and 3).
  • Trailing zeroes in whole numbers (e.g., 13,000) require notation (e.g., scientific notation) to indicate whether they are significant.
  • Scientific notation helps indicate significant figures clearly.
    Example: Writing 1000. indicates four sig figs (the decimal point signals significance of trailing zeros).

• Addition/subtraction rule for sig figs:

  • The final result should be reported with the same number of digits to the right of the decimal point as the measured number with the fewest digits to the right of the decimal.
  • Example: $89.332 + 1.1 = 90.4$ (1 decimal place is the limiting decimal precision)

• Multiplication/division rule for sig figs:

  • The final result should have the same number of sig figs as the value with the fewest sig figs used in the calculation.
  • Example: $2.8 \times 4.5039 = 12.61092 \to \text{ (2 sig figs)} \Rightarrow 1.3\times 10^1$

• Practice problems (approach): Carry out operations as measurements would be calculated experimentally and express each answer in the correct units with the correct number of sig figs:

  • Example prompt: $7.310\ \text{km} \div 5.70\ \text{km} \ (3.26 \times 10^{-3}\ \text{mg}) - (7.88 \times 10^{-5}\ \text{mg})$
  • Example prompt: $\frac{7.8\ \text{m} - 0.34\ \text{m}}{1.15\text{s} + 0.82\text{s}}$
  • Note: The exact numerical results depend on applying the rule sets (sig figs for each operation and decimal alignment for addition/subtraction).

• Additional practice prompts (from slides):

  • Carry out the following operations and express with correct units and sig figs: 7.310 km ÷ 5.70 km, (3.26 × 10^{-3} mg), − (7.88 × 10^{-5} mg), (7.8 m − 0.34 m) / (1.15 s + 0.82 s)

1.4 Using Units and Solving Problems (Dimensional Analysis)

• Why units matter: Understanding units prevents mishaps (e.g., in multinational/naval contexts) and aids clear communication.
• Dimensional analysis / conversion factors (train track method): use conversion factors to cancel units and move between unit systems.
• Practice problem (unit conversions): How many nanometers are in 1 meter? → $1\ \text{m} = 10^9\ \text{nm}$
• Further practice:
  • How many meters are in a mile? (1 m = 3.28 ft) → 1 mile ≈ 1.609 km ≈ 1609 m
  • A storage container has a volume of 2.75 m³. Convert to cm³: $1\ \text{m}^3 = (100\ \text{cm})^3 = 10^6\ \text{cm}^3$ → $2.75\ \text{m}^3 = 2.75\times 10^6\ \text{cm}^3$
  • Airspeed: 290 km/h to mph (1 mile = 1.609 km) → 290 km/h ÷ 1.609 km per mile ≈ 180.35 mph
  • Jet-fuel mass: Tanks hold 360.0 gallons; density of JP-4 = 0.810 kg/L; convert volumes (gallon → L) and compute mass in g, then convert to pounds (1 lb = 453.592 g).

1.5 Classification of Matter

• States of matter / phase transitions: classify substances by particulate view and label phase transitions in both directions (melting, freezing, vaporization, condensation, sublimation, deposition).

• Pure substance vs mixture:

  • Pure substance: fixed composition (element or compound).
  • Mixture: combination of substances; can be homogeneous or heterogeneous.
  • Homogeneous mixture: uniform composition throughout (solutions).
  • Heterogeneous mixture: non-uniform composition (e.g., sand in water).

• How to separate mixtures (conceptual): salt (NaCl) + water can be separated by distillation or evaporation; solid in water can be separated by filtration; iron shavings mixed with sand can be separated by magnetic separation and filtration.

• Chemical vs physical properties (classification):

  • Physical change or property: no change in chemical identity; e.g., phase changes, dissolution, melting.
  • Chemical change or property: chemical identity changes (new substances formed).

  Examples:

  • a) Liquid nitrogen boils at −196 °C → physical property (boiling point); process is a physical change.
  • b) Sugar dissolves in water → physical change (dissolution).
  • c) Gasoline burns in air → chemical change (combustion).
  • d) Gold melts at 1064 °C → physical change (melting point).
  • e) A copper compound is blue → physical property (color).

1.6 Intensive vs. Extensive Properties

• Real-world example: Gold (Au) is malleable, ductile, melts at 1064 °C, density 19.3 g/cm³, color distinct. These are intensive properties; they do not depend on the amount of gold.

• An example amount: a 1 cm × 1 cm × 1 cm cube of gold has mass 19.3 g; its density, melting point, color, and electrical/thermal properties are intensive.

• Extensive properties depend on the amount of substance (e.g., mass, volume, total USD value).

• Practice prompt (from slides): Consider a chocolate chip cookie. What are some intensive properties of the cookie? What are some extensive properties?

• Type of property definitions:

  • Extensive: depends on the amount of substance.
  • Intensive: does not depend on the amount of substance.

1.7 Review of Properties (concept classification exercise)

• You will classify the following as Physical Property, Chemical Property, Intensive Property, and/or Extensive Property. (Some terms may fit more than one category.)
  • Mixture; Pure Substance
  • The melting point of steel is 3000 °C
  • The mass of a block of dry ice is 2 kg
  • Water reacts violently with sodium
  • These items are revisited to reinforce the four property categories: Physical vs. Chemical, Intensive vs. Extensive, and whether something is a Mixture vs. Pure Substance.

1.8 Chapter Review: Important Definitions/Concepts and Important Equations

• Important Definitions/ Concepts (highlights):

  • Mass, volume, density, significant figures, accuracy vs precision, dimensional analysis, state of matter, phase transitions, pure substances, mixtures, homogeneous vs heterogeneous, chemical vs physical properties, intensive vs extensive properties.

• Important Equations (highlights):

  • Density: $\text{Density} = \frac{m}{V}$
  • Sig figs rules (general guidelines for addition/subtraction vs multiplication/division) described above.
  • Dimensional analysis relationships for unit conversions (train track method).

Note: The transcript includes many practice prompts intended to reinforce understanding. Use the rules and examples above to work through similar problems on your own for exam preparation. If you want, I can fill in worked solutions for specific practice items (e.g., the detailed steps for the multi-part calculation in the 7.310 km ÷ 5.70 km problem) in a follow-up.