Ch E: Essentials – Units, Measurement, and Problem Solving

E.2 The Units of Measurement

Understanding units and measurements is fundamental in chemistry, as they provide a standard way to express and compare quantities.

• Two Common Unit Systems: The SI (International System of Units) and the Imperial system (used mainly in the United States).

• Temperature Units: Celsius (°C), Kelvin (K), and Fahrenheit (°F).

• Metric Prefixes: Prefixes such as kilo- (103), centi- (10-2), milli- (10-3), etc., indicate multiples or fractions of base units.

• Typical Units:

  • Length: meter (m)

  • Mass: kilogram (kg)

  • Time: second (s)

  • Volume: liter (L) or cubic meter (m3)

  • Energy: joule (J)

• Importance of Units: Units ensure clarity and consistency in scientific communication and calculations.

• Temperature Conversions:

  • Celsius to Kelvin:

  • Celsius to Fahrenheit:

  • Fahrenheit to Celsius:

• Metric Prefix Conversions: Move the decimal point according to the power of ten associated with the prefix.

• Volume Conversions:

Example: Convert 250 mL to liters:

E.3 The Reliability of a Measurement and E.4 Significant Figures in Calculations

Precision, accuracy, and significant figures are essential for reporting and interpreting scientific data.

• Precision: How close repeated measurements are to each other.

• Accuracy: How close a measurement is to the true or accepted value.

• Random Error: Error that varies unpredictably; affects precision.

• Systematic Error: Error that is consistent and repeatable; affects accuracy.

• Significant Figure Rules:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros are significant only if there is a decimal point.

• Exact Numbers: Numbers with defined values (e.g., 1 dozen = 12) or counted values (e.g., 3 apples); have infinite significant figures.

• Significant Figures in Calculations:

  • Addition/Subtraction: Result has the same number of decimal places as the measurement with the fewest decimal places.

  • Multiplication/Division: Result has the same number of significant figures as the measurement with the fewest significant figures.

• Communicating Certainty: Scientists use significant figures to indicate the certainty of measurements.

• Multiple Operations: Carry extra digits through intermediate steps, round only at the end.

Example: (rounded to two significant figures)

E.5 Density

Density is a key property used to characterize substances and is defined as mass per unit volume.

• Density ():

• Intrinsic Property: Density does not depend on the amount of substance (intrinsic), unlike mass or volume (extrinsic).

• Determining Density: Measure mass and volume, then use the formula above.

Example: If a block has a mass of 50 g and a volume of 20 mL,

E.7 Converting Between Units

Unit conversions are performed using conversion factors, which are ratios that express how many of one unit are equal to another unit.

• Conversion Factor: A ratio derived from the equality between two different units (e.g., gives ).

• Distinguishing: A conversion factor is a defined relationship; a measurement is an observed value.

• Purpose: To express quantities in desired or standard units for comparison or calculation.

• How to Convert: Multiply the original quantity by the appropriate conversion factor(s).

Example: Convert 5.0 inches to centimeters:

Ch 1: Atoms

1.1 A Particulate View of the World: Structure Determines Properties

Chemistry studies matter and its transformations, focusing on the relationship between structure and properties.

• Chemistry: The study of matter, its properties, and the changes it undergoes.

• Matter: Anything that has mass and occupies space.

• Composition of Matter: Made up of atoms and molecules.

• Atom: The smallest unit of an element that retains its properties (e.g., a hydrogen atom).

• Molecule: Two or more atoms bonded together (e.g., H2O).

• Explaining Properties: The structure and arrangement of atoms and molecules determine the properties of matter.

• Classifying Matter: Matter can be classified by its physical state and composition.

Example: Water (H2O) is a molecule composed of two hydrogen atoms and one oxygen atom.

1.2 Classifying Matter: A Particulate View

Matter exists in different states and can be classified based on its composition and uniformity.

• States of Matter:

  • Solid: Definite shape and volume (e.g., ice)

  • Liquid: Definite volume, takes shape of container (e.g., water)

  • Gas: No definite shape or volume (e.g., steam)

• Classification by Composition:

  • Pure Substance: Composed of only one type of particle (element or compound)

  • Element: Cannot be broken down into simpler substances (e.g., O2)

  • Compound: Composed of two or more elements in fixed proportions (e.g., CO2)

  • Mixture: Physical combination of two or more substances

  • Heterogeneous Mixture: Non-uniform composition (e.g., salad)

  • Homogeneous Mixture (Solution): Uniform composition (e.g., saltwater)

• Differences: Mixtures can be separated by physical means; pure substances cannot.

Example: Air is a homogeneous mixture; sand and iron filings form a heterogeneous mixture.

1.3 The Scientific Approach to Knowledge

The scientific method is a systematic approach to understanding the natural world through observation and experimentation.

• Scientific Law: A statement based on repeated experimental observations that describes a phenomenon (e.g., Law of Conservation of Mass).

• Theory: A well-substantiated explanation of some aspect of the natural world.

• Scientific Approach: Involves observation, hypothesis, experimentation, and revision.

• Empirical: Based on observation and experiment, not opinion or belief.

• Difference: Laws describe what happens; theories explain why it happens.

Example: The Law of Conservation of Mass states that mass is neither created nor destroyed in a chemical reaction.

1.5 Modern Atomic Theory and the Laws that Led to It

Modern atomic theory is based on several fundamental laws, including the Law of Conservation of Mass.

• Law of Conservation of Mass: In a chemical reaction, mass is conserved; the total mass of reactants equals the total mass of products.

• Application: If 10 g of hydrogen reacts with 80 g of oxygen, the total mass of water produced is 90 g.

1.7–1.9 The Structure of an Atom and Subatomic Particles

Atoms are composed of subatomic particles: protons, neutrons, and electrons, each with distinct properties and locations.

• Protons: Positively charged, found in the nucleus, relative mass ≈ 1 amu.

• Neutrons: Neutral, found in the nucleus, relative mass ≈ 1 amu.

• Electrons: Negatively charged, found outside the nucleus, relative mass ≈ 1/1836 amu.

• Atomic Number (Z): Number of protons; defines the element; shown as subscript in atomic symbol (e.g., ).

• Defining Particle: The number of protons determines the element.

• Cation: Positively charged ion (fewer electrons than protons).

• Anion: Negatively charged ion (more electrons than protons).

• Mass Number (A): Total number of protons and neutrons:

• Isotope: Atoms of the same element with different numbers of neutrons.

• Natural Abundance: The relative proportion of each isotope in a natural sample.

• Mass Spectrometer: Instrument used to separate and measure isotopes.

• Mass Spectrum: Graph showing the relative abundance of isotopes.

• Calculating Subatomic Particles:

  • Protons = atomic number (Z)

  • Neutrons = mass number (A) – atomic number (Z)

  • Electrons = protons (for neutral atom); adjust for charge in ions

• Average Atomic Mass: Weighted average of all isotopes:

Example: Chlorine has two main isotopes: (75.78%) and (24.22%). Average atomic mass = amu.

1.10 Atoms and the Mole: How Many Particles?

The mole is a counting unit in chemistry, linking the microscopic world of atoms to measurable quantities.

• Mole (mol): Amount of substance containing particles (Avogadro’s number).

• Molar Mass: Mass of one mole of a substance (g/mol); found on the periodic table.

• Using Avogadro’s Number: Converts between number of particles and moles.

• Conversions:

  • Number of atoms moles:

  • Mass moles:

• Different Elements: Each element has a unique molar mass due to different atomic masses.

Example: How many atoms in 2.0 mol of carbon?

Ch 2/3: Atomic Electronic Structure

Coulomb’s Law

Coulomb’s law describes the force between charged particles and is fundamental to understanding atomic structure and periodic trends.

• Two Driving Forces: Attraction and repulsion between charged particles.

• Attraction/Repulsion: Protons (+) and electrons (–) attract; like charges repel.

• Coulomb’s Law Equation:

  • = force, = constant, and = charges, = distance between charges

• Ionization Energy: Energy required to remove an electron from an atom; always positive.

• Potential Energy: As proton and electron get closer, potential energy becomes more negative (more stable).

• Explanation: Coulomb’s law explains why opposite charges attract and like charges repel; greater charge or smaller distance increases force.

• Ionization Energy and Potential Energy: As potential energy becomes more negative, more energy is required to remove an electron (higher ionization energy).

• Helium vs. Hydrogen: Helium’s nucleus has twice the charge of hydrogen, so the force (and ionization energy) is about double for electrons at the same distance.

Shell Model and Periodic Trends

The shell model explains the arrangement of electrons in atoms and the resulting periodic trends in properties such as ionization energy and atomic size.

• Ionization Energy Trends:

  • Increases across a period (left to right)

  • Decreases down a group (top to bottom)

• Atomic Size Trends:

  • Decreases across a period

  • Increases down a group

• Shielding: Inner electrons shield outer electrons from the full charge of the nucleus.

• Effective Nuclear Charge (): Net positive charge experienced by valence electrons:

  • = atomic number, = number of core electrons

• Reactivity: Elements with low ionization energy (e.g., alkali metals) are more reactive; high ionization energy (e.g., noble gases) are less reactive.

• Explanation of Trends:

  • Across a period: Increased nuclear charge pulls electrons closer, increasing ionization energy and decreasing atomic size.

  • Down a group: Additional shells increase distance and shielding, decreasing ionization energy and increasing atomic size.

• Shell Model Evidence: Sudden jumps in ionization energy suggest electrons are organized in shells.

Example: Sodium (Na) has a lower ionization energy than chlorine (Cl) because its valence electron is farther from the nucleus and more shielded.

Additional info: The shell model and periodic trends are foundational for understanding chemical reactivity and bonding, which are explored in later chapters.