CG

Chapter 1: Matter, Measurement, and Problem Solving

Matter, Measurement, and Problem Solving

  • Matter is anything that occupies space (volume) and has mass.
  • The properties of matter are determined by the atoms and molecules within the matter.
  • Examples:
    • Water molecule
    • Oxygen atom
    • Hydrogen peroxide molecule (O₂H₂? actually H₂O₂) with oxygen atoms
  • Core definitions:
    • Atom: the smallest particle of an element; retains its unique chemical characteristics; building blocks of all matter.
    • Molecule: a collection of atoms chemically bonded together in fixed proportions and fixed arrangement.
    • Chemistry: science that seeks to understand the behavior of matter by studying the behavior of atoms and molecules.

The Scientific Approach

  • Hypothesis: a tentative explanation for a set of observations.
  • Scientific Law: a statement that summarizes past observations and predicts future ones (the "what").
  • Scientific Theory: a general explanation of widely observed phenomena that has been extensively tested (the "why").
  • Process (simplified):
    • Observations → Experiments → (confirm or revise) Hypothesis → (confirm or revise) Theory → (confirm or revise) Law as applicable.

Example: Law vs. Theory

  • Law of Conservation of Mass (Lavoisier): in a chemical reaction, matter is neither created nor destroyed; total mass stays constant.

  • Dalton's Atomic Theory: matter is composed of small, indestructible particles called atoms; during a chemical reaction, particles are rearranged, not created/destroyed; total mass is constant.

  • Practical takeaway: Law describes what happens; Theory explains why it happens.

  • Practice Question (incorrect statement):

    • A) A hypothesis is an unproven explanation for a set of observations.
    • B) Atoms are the building blocks of all matter.
    • C) Once a scientific theory has been proven, it cannot be modified. ← INCORRECT
    • D) A scientific law summarizes many observations, but does not explain why they occur.
    • E) Molecules contain specific numbers of atoms bound together in a fixed arrangement.

States of Matter

  • States:
    • Gas: shape and volume are variable (no fixed shape or volume)
    • Solid: fixed shape and fixed volume
    • Liquid: fixed volume, changeable shape
  • Visual cues: (a) no chemical bonds broken; (b) gas expands/contracts with container; (c) solids maintain shape; (d) liquids take container shape but keep volume

Crystalline vs. Amorphous Solids

  • Crystalline solid: atoms/molecules arranged in patterns with long-range, repeating order. Examples: diamond, salt, sugar.
  • Amorphous solid: no long-range, repeating order. Examples: glass, most plastics.
  • Crystalline Solid example: Diamond (C, s, diamond).

Classes of Matter

  1. Pure Substance: consists of only one chemical substance
    • Element: simplest matter; only one kind of atom (one symbol from periodic table)
    • Compound: two or more elements bonded in a fixed composition (e.g., H₂O)
  2. Mixture: two or more chemicals
    • Homogeneous: uniform composition
    • Heterogeneous: non-uniform composition
  • Examples:
    • Helium (element, pure substance)
    • Pure water (compound, pure substance)
    • Wet sand (mixture, heterogeneous)
    • Tea with sugar (mixture, homogeneous)

Separating Mixtures (based on physical properties; no chemical bonds broken)

  • Filtration (gravity filtration): filter paper traps solids; liquid passes through.
    • Example setup: funnel, filter paper, stirring rod; collect liquid in a receiving vessel.
  • Distillation: separates liquids based on boiling points; most volatile component boils first and is condensed to a pure liquid.
    • Components: distillation flask, condenser, receiving vessel; cooling water circulates through condenser.
  • Chromatography (paper chromatography): separation based on interactions with stationary and mobile phases (start and ongoing progress shown in slides).
  • Summary of separation types: Distillation, Filtration, Chromatography (depending on properties like solubility and volatility).

Practice: Classification (recap)

  • Black coffee = homogeneous mixture (ok)
  • Copper = element (ok)
  • A pencil = could be a mixture? Typically wood/graphite; treated as heterogeneous in some contexts; note common answer: element or mixture depending on focus
  • Air in a room = homogeneous mixture (ok)
  • Methane gas (CH₄) = compound (ok)
  • Glucose = compound (ok)

Physical vs Chemical Properties

  • Physical properties: observed without changing identity of substance; no bonds broken.

    • Examples: hardness, color, melting point, density (independent of chemical changes)

  • Chemical properties: tendency to undergo a chemical reaction with another substance (bonds must break)

    • Example: iron reacting with oxygen to form iron oxide (rust)

  • Practice: classify items as Physical or Chemical properties (examples given include diamond hardness, mercury liquid at room temperature, tarnish resistance of metals, glass shattering, aspirin as medicine, perfume odor, flammability of gasoline, salt dissolving in water).

Energy-Related Definitions

  • Energy: the capacity to do work.
  • Work: force acting through a distance, i.e., W = F imes d.
  • Types of Energy:
    • Kinetic Energy: energy associated with motion.
    • Thermal Energy: energy associated with the temperature of an object (all particle motions).
    • Potential Energy: energy associated with position (e.g., elevated position) or composition (reactivity).

The Law of Conservation of Energy

  • Energy can be converted from one form to another but cannot be created or destroyed.
  • Total energy in a closed system remains constant (First Law of Thermodynamics).
  • Example: high potential energy in a weight on a building can convert to kinetic energy as it falls; some energy may be harnessed to do work (e.g., car moving forward).

Important Ideas About Energy

  • Energy is conserved in physical and chemical changes.
  • Systems with high potential energy tend to lower their potential energy, releasing energy to surroundings.
  • Implication: energy flow drives changes toward more stable configurations.

Making Measurements

  • Accurate measurements are essential for good science.
  • Standardized units are needed to share data.
  • Proper error analysis is crucial.

SI Base Units

  • Length → meter (m)

  • Mass → kilogram (kg)

  • Time → second (s)

  • Temperature → kelvin (K)

  • Energy → joule (J)

  • Amount of substance → mole (mol)

  • Electric current → ampere (A)

  • Luminous intensity → candela (cd)

  • Base unit symbols: m, kg, s, K, J, mol, A, cd

Prefixes (SI)

  • tera (T) 10^12
  • giga (G) 10^9
  • mega (M) 10^6
  • kilo (k) 10^3
  • deci (d) 10^-1
  • centi (c) 10^-2
  • milli (m) 10^-3
  • micro (µ) 10^-6
  • nano (n) 10^-9
  • pico (p) 10^-12

Temperature Scales

  • Fahrenheit, Celsius, Kelvin scales are related by linear relationships.
  • Water phase changes illustrate scale points:
    • Water boils at 100 °C (373 K)
    • Water freezes at 0 °C (273 K)
  • Absolute zero is the temperature at which motion effectively stops.
    • 0 K corresponds to −273.15 °C and −459.67 °F.
  • Common reference points: 32 °F = 0 °C; 212 °F = 100 °C.

Changing Temperature Scales

  • Linear relationship: y = m x + b linking scales.
  • Celsius (°C) to Fahrenheit (°F):
    • TF = 1.8\,TC + 32
  • Celsius to Kelvin:
    • TK = TC + 273.15
  • Inverse relations (handy):
    • TC = \frac{5}{9} (TF - 32)
    • TC = TK - 273.15

Practice: Temperature/Units Concepts

  • Statement evaluation examples:
    • A truck at 50 mph has significant kinetic energy (true).
    • A freshly charged battery stores chemical potential energy (true).
    • Meters (m) and kilograms (kg) are base SI units (true).
    • A milligram (mg) is larger than a milligram (mg) (nonsense; ignore).
    • Absolute zero is the temperature at which water freezes (false; it's the temperature at which motion stops).

English–Metric Conversions (exactness)

  • 1 inch = 2.54 cm (exact)
  • 1 pound = 453.592 g (exact)
  • 1 gallon = 3.7854 L (exact)
  • 1 mL = 1 cm³ by definition
  • See standard conversion references in the course material

Derived Units: Volume & Density

  • Volume: V = (\text{unit of length})^3
  • Density: \rho = \frac{m}{V}; can be used as a conversion factor:
    • \rho = \frac{m}{V} \quad\text{or}\quad m = \rho V

Extensive vs. Intensive Properties

  • Extensive properties vary with the amount of substance:
    • Examples: length, mass, volume
  • Intensive properties do not depend on the amount of substance:
    • Examples: color, density, melting point

Precision and Accuracy (Measurement Quality)

  • Precision: repeatability of a set of measurements; how closely results agree with themselves.
  • Accuracy: agreement between a measurement and the true value.
  • Example notes show different students achieving varying precision/accuracy.

Sources of Error in Measurements

  • Random Errors: arise from limitations of reading the scale; affect precision.
  • Systematic Errors: arise from faulty instrumentation or poor experimental design; affect accuracy.
  • Examples: a thermometer consistently reading 2°C too low; a scale consistently underweights.

Experimental Measurements and Uncertainty

  • All measurements have some uncertainty.
  • The reported value includes all certain digits plus one uncertain digit (estimated).
  • Example format: 4.56\;\text{mL} (with the last digit estimated).

Significant Figures (SF)

  • Nonzero integers are significant.
  • Zeros rules:
    • Leading zeros are not significant (placeholders).
    • Interior zeros between nonzero digits are significant.
    • Trailing zeros to the right of a decimal point are significant.
    • Trailing zeros in a number without a decimal point may not be significant (ambiguous without notation).
  • Rule set (summary):
    1) A number is significant if it is not a zero, a zero between nonzero digits, a zero at the end of a decimal number, or all digits in a coefficient in scientific notation.
    2) Zeros are not significant if they are leading, or placeholders in a large number without a decimal point.
  • Examples given:
    • 4.5 g (2 SF)
    • 122.35 m (5 SF)
    • 205 m (3 SF)
    • 5.082 kg (4 SF)
      1. L (not recommended; example shows 50. L as a nonstandard form)
    • 25.0°C (3 SF)
    • 16.00 g (4 SF)
    • 4.0 × 10^5 m (2 SF)
    • 5.70 × 10^-3 g (3 SF)
    • 0.0004 lb (1 SF? actually 1 significant digit; examples may vary by context)
    • 0.075 m (2 SF)
    • 850 000 m (2 SF? depends on notation)
    • 1 250 000 g (5 SF if decimalized; otherwise ambiguous)
  • Practice: identify incorrect SF labeling in a list of measurements.

Exact Numbers

  • Exact numbers have an infinite number of significant figures.
  • Examples:
    • 1 inch = 2.54 cm (exact)
    • 1 km = 1000 m (exact)
    • 1 dozen = 12 items (exact)
    • 1 hour = 60 minutes (exact)
    • 1 H₂O molecule = 2 H atoms (counting exact)

SF Rules: Addition & Subtraction

  • Round the answer to the first uncertain digit column (from the left) in the calculation.
  • Example workflow shown in class notes (illustrative): keep the value with the least number of decimals, or align decimal places before rounding.
  • Example results in notes illustrate rounding to the appropriate decimal place.

SF Rules: Multiplication & Division

  • Round the final result to the same number of SF as the factor with the fewest SF.
  • Example: Cube volume with dimensions 34.49 cm (4 SF), 23.0 cm (3 SF), and 15 cm (2 SF).
    • Volume = 34.49 × 23.0 × 15 = 11,899.05 cm³ → rounded to 2 SF per the smallest factor → ≈ 1.2 \times 10^4\; \text{cm}^3

Practice: SF Calculations (selected problems)

  • Problem: 8.6 cm × 3.3 cm + 5.1 cm = ? (follow addition/subtraction and multiplication/division SF rules)
  • Problem: 103.92 g ÷ 2.94 × 10^3 g = ? (observe SF rules and units)
  • Problem: 0.3452 mL (target final value with correct SF)
  • Note: Do not round until the final answer; include units.

Conversion Factors and Dimensional Analysis

  • Conversion Factor: expresses a fixed relationship as a fraction in different units, e.g.

    • \frac{1 \text{ kg}}{1000 \text{ g}} = 1
    • Equivalently: \frac{1000 \text{ g}}{1 \text{ kg}}

  • Dimensional Analysis (Units Conversion): interchange units using fixed relationships; start with the given quantity and use factors to cancel units.

  • Key idea: write the conversion factor so that the starting units cancel in the numerator with the same units in the denominator.

  • Example: How many 8.0 oz patties can be made from 3.2 lb of hamburger?

    • 1 patty / 1 patty × 3.2 lb × 16 oz / 1 lb × ??? → 6.4 patties
    • Emphasizes starting with the unit that cannot be used as a conversion factor yet (the given unit).

Density, Mass, and Volume Examples

  • Example: Mass of a cube of lead with edge length 1.0 in, density 11.34 g/mL.

    • Convert 1.0 in to cm: 1 in = 2.54 cm, so V = (1.0 in)^3 = (2.54 cm)^3 = 16.39 cm³.
    • Density relation: 1 cm³ = 1 mL; mass = density × volume = 11.34 g/mL × 16.39 cm³ = 186 g (rounded to ~190 g).
    • Final results shown: approximately 186 g, rounded to 190 g.

  • Mass percent as a conversion factor:

    • If a ring contains 32.5% by mass Au, then:
    • \frac{32.5\;\text{g Au}}{100\;\text{g ring}}
    • Or equivalently: \frac{100\;\text{g ring}}{32.5\;\text{g Au}}\times \text{Au mass} depending on the direction of conversion.

Practice: Bronze Alloy Problem

  • Problem: Bronze alloy contains 78% by mass Cu. If the density of the alloy is 8.52 g/mL, what volume of bronze would contain 13.46 g of Cu?
    • Step 1: Convert Cu mass to total alloy mass using mass percent:
    • Cu mass = 0.78 × total mass ⇒ total mass = 13.46 g / 0.78 ≈ 17.256 g
    • Step 2: Convert total mass to volume using density:
    • Volume = mass / density ≈ 17.256 g / (8.52 g/mL) ≈ 2.026 mL
    • Answer (closest from options): 2.0\;\text{mL}

Interpreting Graphs

  • Example: Atmospheric CO₂ vs. Time (Y vs. X)
    • Read off (X, Y) pairs by selecting a value on either axis and reading the corresponding value on the other axis.
    • Slope (m) interpretation: when X is time, the slope represents the rate of change (change in CO₂ concentration per unit time).
  • Typical axes:
    • Y-axis: Carbon dioxide concentration (parts per million, ppm)
    • X-axis: Year (e.g., 1860, 1880, …, 2020)

Note on Practical Study Habits (Guidance from slides)

  • Always relate new material to foundational principles:
    • Conservation laws (mass, energy)
    • The nature of matter (atoms/molecules) and chemical vs physical changes
  • Use dimensional analysis to reduce unit errors and reinforce unit fluency.
  • Practice sorting properties into physical vs chemical, and properties that are extensive vs intensive.
  • Be mindful of significant figures when performing calculations, especially in lab reports and data interpretation.

Quick Reference Formulas and Concepts

  • Work: W = F\cdot d
  • Density: \rho = \frac{m}{V}, and m = \rho V
  • Volume: V = (\text{length})^3
  • Kinetic Energy: KE = \tfrac{1}{2} m v^2
  • Temperature conversions:
    • Celsius to Fahrenheit: TF = 1.8\,TC + 32
    • Celsius to Kelvin: TK = TC + 273.15
    • Fahrenheit to Celsius (inverse): TC = \tfrac{5}{9}(TF - 32)
    • Kelvin to Celsius (inverse): TC = TK - 273.15
  • Significance concepts:
    • Significant Figures: rules for counting, leading/trailing zeros, and decimal presence.
    • Exact numbers have infinite SF (e.g., defined constants like 1 inch = 2.54 cm).

Summary Takeaways

  • Matter’s properties arise from atoms and molecules; chemistry studies these interactions.
  • The scientific method uses hypotheses, laws, and theories that can be revised with new evidence.
  • Matter exists as pure substances or mixtures; mixtures can be separated by physical means.
  • Energy is conserved; different energy forms can transform into one another.
  • Measurements require standardized units, error analysis, and proper handling of uncertainty.
  • SI units, prefixes, and conversions enable consistent calculations across problems.
  • Significant figures govern precision in measurements and calculations; distinguish addition/subtraction vs multiplication/division rules.
  • Dimensional analysis is a powerful tool for unit consistency and problem solving.
  • Mass percent can serve as a conversion basis when dealing with compositions.
  • Graphs convey rates via slopes; practice reading coordinates and interpreting trends.