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Chapter 1 Notes (Chemistry, Matter, and Measurement)

1.1 What Is Chemistry?

  • Chemistry is the study of matter: what it consists of, its properties, and how it changes.

  • Matter: anything that has mass and occupies space.

  • Science: process of learning about the natural universe by observing, testing, and building models.

  • Chemistry is a central science; overlaps with biology, geology, etc.; mathematics is the language of science.

  • The scientific method: a general, organized process for answering questions. Core concepts:

    • Hypothesis: a testable idea to explain how the natural universe works.

    • Hypothesis vs theory: a theory is a broad, well-supported statement describing a large set of observations/data.

    • Experiments test the hypothesis; results may support, refine, or falsify it.

  • Example focus: how quantities and measurements are essential in science and everyday life to avoid errors.

1.2 The Classification of Matter

  • Physical properties: describe matter (size, shape, color, mass).

  • Chemical properties: describe how matter changes its chemical structure or composition (e.g., flammability).

  • Substance: matter with uniform properties throughout.

  • Two types of substances:

    • Element: cannot be broken down into simpler substances (e.g., Aluminum).

    • Compound: can be broken down into simpler substances (e.g., Water H$_2$O).

  • Mixture: physical combination of two or more substances retaining their identities.

    • Heterogeneous mixtures: components are visibly different (e.g., dirt).

    • Homogeneous mixtures (solutions): uniform composition (e.g., saltwater, air).

  • Atoms and molecules: basic units; atoms are the smallest unit of an element; molecules are the smallest unit of a compound.

  • Phases of matter: solid (definite shape and volume), liquid (definite volume, takes shape of container), gas (neither definite shape nor volume).

  • Phase changes: physical changes between phases (e.g., melting, boiling, sublimation).

1.3 Measurements

  • Quantity = number + unit; both parts are necessary for clarity.

  • Examples: distance reported as 5 km or 12 miles; without a unit, information is incomplete.

  • Important concepts:

    • Units define the scale; numbers define how much.

    • Measurements express properties of matter, used in all sciences.

  • Common terms:

    • Mass, length, time, temperature, amount, etc., are measured quantities.

1.4 Expressing Numbers: Scientific Notation

  • Scientific notation expresses very large or very small numbers compactly.

  • Form: a \times 10^{n} where 1 \leq a < 10 and n is an integer.

  • Rules of form: move decimal so that the coefficient a is between 1 and 10.

  • Examples:

    • 1,500,000 = 1.5 \times 10^{6}

    • 67,000,000,000 = 6.7 \times 10^{10}

  • Convention: only one nonzero digit before the decimal point in the coefficient.

1.5 Expressing Numbers: Significant Figures

  • Significant figures (sig figs): all digits known with certainty plus the first estimated digit.

  • Rules for significant figures:

    • Nonzero digits are significant.

    • Captive zeros (zeros between nonzero digits) are significant.

    • Leading zeros are not significant.

    • Trailing zeros are significant only if the number contains a decimal point.

  • Rounding rules (final result):

    • For addition/subtraction: align decimals and keep the rightmost place where all numbers have digits; round accordingly.

    • For multiplication/division: round to the fewest significant figures among the inputs.

  • Scientific notation clarifies significant figures by listing them explicitly.

1.6 The International System of Units (SI)

  • SI base units (seven):

    • length: ext{m} (meter)

    • mass: ext{kg} (kilogram)

    • time: ext{s} (second)

    • amount: ext{mol} (mole)

    • temperature: ext{K} (kelvin)

    • electrical current: ext{A} (ampere)

    • luminous intensity: ext{cd} (candela)

  • Chemistry commonly uses five base units: ext{m}, ext{kg}, ext{mole}, ext{second}, ext{K}; Celsius is also widely used for temperature.

  • Prefixes (multipliers): e.g.,

    • giga- 10^{9}, mega- 10^{6}, kilo- 10^{3}, centi- 10^{-2}, milli- 10^{-3}, micro- 10^{-6}, nano- 10^{-9}, etc.

  • Derived SI units: combinations of base units (e.g., area ext{m}^2, volume ext{m}^3, density \frac{m}{V}, energy joule ext{J}).

  • Important non-SI units used in chemistry: liter (L) ≈ 1.06 quarts; 1 L = 1000 mL = 1000 cm$^3$; 1 cal = 4.184 J.

  • Relationship between temperature scales: K = ^ ext{o}C + 273.

  • The kilogram is defined by a physical artifact kept in France.

1.7 Converting Units

  • Conversions use conversion factors: a fraction that equates two equivalent quantities expressed in different units.

  • Key idea: multiply by a conversion factor that cancels the original unit and introduces the new unit.

  • Example: convert 3.55 m to cm:

    • 3.55 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 355 \text{ cm}

  • Exact numbers (from definitions or counting) have infinite significant figures and do not limit final precision.

  • Steps for unit-conversion problems:

    • Write the given quantity.

    • Choose a conversion factor that cancels the original unit.

    • Multiply and simplify; express final answer with appropriate significant figures.

1.8 End-of-Chapter Material (Key Takeaways)

  • Chemistry describes matter and its behavior; matter is described by physical and chemical properties.

  • Substances can be elements, compounds, or mixtures (heterogeneous or homogeneous).

  • Measurements express quantities as a number with a unit; proper communication requires both.

  • Scientific notation and significant figures are essential tools for handling large/small numbers and measurement precision.

  • SI units and prefixes standardize communication in science; conversions use cancellation to switch units.

  • Derived units (e.g., volume, density, energy) are built from base SI units; density relates mass to volume via \rho = \frac{m}{V}.