Chapter 1 Notes: Chemistry: The Central Science

1.1 The Study of Chemistry

• Chemistry is the study of matter and the changes that matter undergoes.

• Matter is anything that has mass and occupies space.

• All matter consists of atoms of a relatively small number of elements; the properties of matter depend on which elements are present and how the atoms are arranged.

• Matter exists in different forms, taking on various chemical compositions and structures.

1.2 Classification of Matter

• Key classifications: substances vs mixtures

• Substance: matter with a definite composition and distinct properties

  • Examples: salt (NaCl), iron (Fe), water (H₂O), mercury (Hg), carbon dioxide (CO₂), oxygen (O₂)

  • Substances can be either elements or compounds

• States of matter: solids, liquids, and gases; condensed phase vs fluids

• Three major classifications of substances:

  • Elements: substances that cannot be separated into simpler substances by chemical means

  • Examples: Fe, Hg, O₂

  • Compounds: substances formed from two or more elements chemically united in fixed proportions; cannot be separated into simpler substances by physical means

  • Examples: NaCl, H₂O, CO₂

  • Mixtures: combinations of two or more substances in which the substances retain their distinct identities

  • Homogeneous mixtures: uniform composition (e.g., sugar in water)

  • Heterogeneous mixtures: non-uniform composition (e.g., sand with iron filings)

• Quick definitions:

  • Substances can be elements or compounds (pure substances)

  • Mixtures consist of two or more substances (not chemically bonded)

Subtle points & examples

• A substance has a definite composition and distinct properties; examples listed above.

• All substances can, in principle, exist as a solid, a liquid, and a gas (three physical states).

• Condensed phase vs fluids:

  • Solids and liquids are condensed phases; liquids and gases are fluids.

Homogeneous vs Heterogeneous details

• Homogeneous: uniform composition; components are distributed uniformly; can be separated physically (e.g., sugar in water)

• Heterogeneous: non-uniform composition; components can be visually distinguished (e.g., sand and iron filings)

1.3 Scientific Measurement

• SI base units discussed: Mass and Temperature (with mass measured in kilograms, temperature in kelvin)

• Derived units: Volume (L, dm³) and Density (g/cm³, g/mL)

• Key relationships:

  • Mass measures amount of matter in an object/sample

  • Temperature scales: Celsius and Kelvin; Kelvin is the absolute scale with absolute zero at 0 K; 1 °C = 1 K in magnitude

  • Temperature relationships:

  • $K = °C + 273.15$

• Volume and Density:

  • Volume often expressed in liters (L) or cubic meters (m³); 1 L = 1 dm³ and 1 dm = 0.1 m; thus 1 L = 1000 cm³

  • Density: $d = rac{m}{V}$; common density units include $1 ext{ g/cm}^3 = 1 ext{ g/mL} = 1000 ext{ kg/m}^3$

Base units and practical conversions

• Mass: base unit is kilogram (kg); 1 kg = 1000 g = 1 × 10³ g

• Temperature: base unit is kelvin (K); 0 K = absolute zero

• Temperature conversion examples:

  • Convert 36°C and 37°C to Kelvin:

  • $36^{<br>m °C} + 273.15 = 309.15 \, ext{K}$

  • $37^{<br>m °C} + 273.15 = 310.15 \, ext{K}$

  • Temperature range: 1°C range corresponds to 1 K range

Sample Problem 1.1 (Temperature conversion)

• Problem: Express 36°C, 37°C, and the range in Kelvin

• Strategy: Use $K = °C + 273.15$; convert each value and the range (difference in °C equals difference in K)

• Solution (given): 36°C → 309 K, 37°C → 310 K; range = 1 K

1.3 Scientific Measurement (continued)

• Temperature conversion formula between Celsius and Fahrenheit:

  • $T<em>F = rac{9}{5} T</em>C + 32$

  • $T<em>C = rac{5}{9}(T</em>F - 32)$

• Sample Problem 1.2: Convert 39°C to Fahrenheit

  • Strategy: Use Fahrenheit formula

  • Solution: $T_F = rac{9}{5} imes 39 + 32 = 102.2^ ext{°F}$

Derived units: Volume and Density in practice

• Volume: from the cube of a decimeter

  • 1 L = 1 dm³; 1 dm = 0.1 m; thus 1 L = 1000 cm³

• Density units: consistent with mass and volume units; examples include g/cm³ and g/mL

• Sample Problem 1.3 (Density of ice):

  • Given: A cube with side 2.0 cm has mass 7.36 g

  • Volume: $V = (2.0\text{ cm})^3 = 8.0\text{ cm}^3$

  • Density: $d = \frac{m}{V} = \frac{7.36\text{ g}}{8.0\text{ cm}^3} = 0.92\text{ g/cm}^3$

  • For 23.0 g of ice at 0°C: $V = \frac{m}{d} = \frac{23.0\text{ g}}{0.92\text{ g/cm}^3} \approx 25\text{ cm}^3$

1.4 The Properties of Matter

• Physical properties: observed or measured without changing the identity of a substance

  • Examples: boiling/melting points, density, color, odor, conductivity

  • Physical changes: e.g., melting of ice to water is reversible by cooling; melting point is a physical property

• Chemical properties: observed through chemical changes; involve internal structure changes and are not reversible by simple physical means

  • Example: hydrogen burning in oxygen to form water; after reaction, hydrogen gas no longer exists as hydrogen under the same conditions

  • Chemical properties cannot be determined just by touch/appearance; require altering composition

• Distinguishing changes:

  • Physical change: identity remains; e.g., melting, freezing, dissolving

  • Chemical change: new substances formed; not easily reversible by physical means

• Extensive vs Intensive properties:

  • Extensive: depend on amount of matter (e.g., mass, volume)

  • Intensive: do not depend on amount of matter (e.g., density, temperature)

Examples and key points

• Melting point is an example of a physical property

• Burning of gasoline, souring of milk, combustion of sugar are chemical properties/changes

1.5 Uncertainty in Measurement

• Two types of numbers: exact vs inexact

  • Exact numbers: defined values (e.g., 1 in = 2.54 cm, 1 kg = 1000 g, 1 dozen = 12)

  • Inexact numbers: numbers obtained by measurement

• Significant figures (SF): reflect uncertainty in inexact numbers

• Rules for SFs:
  1) All nonzero digits are significant
  2) Zeros between nonzero digits are significant
  3) Leading zeros are not significant
  4) Trailing zeros are significant if the number contains a decimal point
  5) Trailing zeros in a number without a decimal point may be ambiguous; scientific notation helps

• Expressing ambiguity: use scientific notation to indicate precision clearly, e.g., $1.3 \times 10^2$ vs $1.30 \times 10^2$

Sample Problems on SFs

• Problem 1.5: Determine SFs in numbers:

  • (a) 443 cm → 3 SFs

  • (b) 15.03 g → 4 SFs

  • (c) 0.0356 kg → 3 SFs

  • (d) 3.000 × 10^3 L → 4 SFs

  • (e) 50 mL → ambiguous (1 or 2 SFs)

  • (f) 0.9550 m → 4 SFs

• Solutions rounded accordingly; emphasis on counting significant figures in measurement values

• Significance determination strategy: nonzero digits are significant; zeros have rules described above

Scientific notation to avoid ambiguity

• Example: 1.3 × 10^2 (2 SF) vs 1.30 × 10^2 (3 SF)

Calculations with Significant Figures

• Addition/Subtraction: result limited by the number with the fewest digits to the right of the decimal point

  • Example: 102.50 + 0.231 → 102.73 (two digits after decimal must be preserved to match the least precise operand)

• Multiplication/Division: result limited by the number with the fewest SFs among operands

  • Example: 1.4 × 8.011 = 11.2154 → 11.22 (3 SFs in 1.4? This example in notes shows rounding to 3 SFs; check context)

• Exact numbers do not limit SFs in calculations

• In multistep calculations, keep extra digits during intermediate steps to reduce rounding error

Sample Problem 1.6: Calculations with SFs

• (a) 317.5 mL + 0.675 mL → 318.2 mL (4 SFs? Final needs to match decimal places; fewest digits to the right of decimal is 1 in 317.5; so 1 decimal place)

• (b) 47.80 L − 2.075 L → 45.725 L → 45.73 L

• (c) 13.5 g ÷ 45.18 L → 0.299 g/L (3 SFs)

• (d) 6.25 cm × 1.175 cm → 7.34 cm³ (3 SFs)

• (e) 5.46 × 10^3 g + 4.991 × 10^3 g → 5.537 × 10^3 g → 5.537 × 10^3 g

Sample Problem 1.7: Density of a gas in a container

• Empty container volume: 9.850 × 10^3 cm³; mass before filling: 124.6 g; after filling with gas: 126.5 g

• Mass of gas: 126.5 − 124.6 = 1.9 g

• Density: $d = \frac{m}{V} = \frac{1.9\text{ g}}{9.850 \times 10^3 \text{ cm}^3} \approx 1.93\times 10^{-3} \text{ g/cm}^3$

• Answer (to appropriate SFs): ≈ $1.9 \times 10^{-3}$ g/cm³ or 0.0019 g/cm³

1.6 Using Units and Solving Problems

Conversion Factors and Dimensional Analysis

• A conversion factor is a fraction in which the same quantity is expressed in two equivalent ways (equals 1).

  • Examples:

  • $1\,\text{in} = 2.54\,\text{cm}$

  • $1\,\text{ft} = 12\,\text{in}$

• Dimensional analysis (factor-label method): multiply by conversion factors to cancel units and reach the desired unit.

  • Example: $12.00\,\text{in} \times \frac{2.54\,\text{cm}}{1\,\text{in}} \times \frac{1\,\text{m}}{100\,\text{cm}} = 0.3048\,\text{m}$

Sample Problem 1.8 (FDA sodium intake to pounds)

• Given: dietary sodium ≤ 2400 mg/day; convert to pounds using 1 lb = 453.6 g and 1 g = 1000 mg

• Setup: 2400 mg × (1 g / 1000 mg) × (1 lb / 453.6 g)

• Solution: ≈ 0.005291 lb

Sample Problem 1.9 (Blood volume to cubic meters)

• Given: blood volume ≈ 5.2 L

• Convert L to cm³: 1 L = 1000 cm³; then cm³ to m³: 1 cm³ = 1 × 10^-6 m³

• Calculation: $5.2\,\text{L} \times 1000\,\frac{\text{cm}^3}{\text{L}} \times 1\times 10^{-6}\, \frac{\text{m}^3}{\text{cm}^3} = 5.2 \times 10^{-3}\, \text{m}^3$

Extra Dimensional Analysis Problem

• Example: A motor doing work, copper mass, and energy per mole; steps involve converting units (J, kJ), molar mass, and time to hours to determine duration

• Answer provided: 35 hours (illustrative of multi-step dimensional analysis and unit-tracking)

Key Formulas to Remember

• Mass, temperature, and volume basics

  • $m = \text{mass} \qquad 1\ \text{kg} = 1000\ \text{g}$

  • $K = °C + 273.15$

  • $K = °C + 273.15\quad\text{and}\quad 1^{\circ}\text{C} = 1\text{ K}$

• Temperature conversions

  • Fahrenheit: $T<em>F = \frac{9}{5} T</em>C + 32$

  • Celsius from Fahrenheit: $T<em>C = \frac{5}{9}(T</em>F - 32)$

• Volume and density

  • $V = \frac{m}{d}$

  • $d = \frac{m}{V}$

  • Common density units: l $1\text{ g/cm}^3 = 1\text{ g/mL} = 1000\ \text{kg/m}^3$

  • $1\ \text{L} = 1\ \text{dm}^3, \quad 1\text{ dm} = 0.1\text{ m}$

• Significance and measurement accuracy

  • Exact numbers: infinite SFs, do not limit results

  • SF rules (summary): nonzero digits are significant; zeros rules depend on position and decimal point

• Dimensional analysis examples

  • Conversion factor consistency: e.g., $1\text{ in} = 2.54\text{ cm}$ and $1\text{ ft} = 12\text{ in}$

  • Tracking units to cancel to the desired unit

Connections to broader themes

• How chemistry connects measurement, units, and interpretation of data to determine properties, states, and changes in matter

• The importance of the distinction between physical and chemical properties/changes for predicting behavior during reactions

• Real-world applications: energy, nutrition (sodium limits), health (body temperature), environmental science (density and buoyancy), and everyday problem-solving using dimensional analysis II