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Chapter 1: Matter, Measurement, and Math – General Chemistry Study Notes

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Matter and Chemistry

Definitions and Fundamental Concepts

Chemistry is the science that seeks to understand how matter behaves by studying the properties and interactions of atoms and molecules. Matter is anything that occupies space and has mass. The properties of matter are determined by the properties of its constituent atoms and molecules.

  • Atom: The smallest identifiable unit of an element; a submicroscopic particle that is the fundamental building block of matter.

  • Molecule: Two or more atoms joined chemically in a specific geometric arrangement; the smallest identifiable unit of a compound.

Water molecule structureHydrogen peroxide molecule structure

Example: Water (H2O) is a molecule composed of two hydrogen atoms and one oxygen atom. Hydrogen peroxide (H2O2) is a molecule with two hydrogen atoms and two oxygen atoms, demonstrating how different arrangements and ratios of atoms create different substances.

Classification of Matter

States of Matter

Matter exists in three primary states: solid, liquid, and gas. Each state is characterized by the arrangement and movement of atoms or molecules.

  • Solid: Atoms or molecules are packed closely together in fixed positions, resulting in a definite shape and volume. Solids can be crystalline (long-range repeating order, e.g., diamond, NaCl) or amorphous (no long-range order, e.g., glass, plastic).

  • Liquid: Atoms or molecules are close together but can move past one another, resulting in a definite volume but no fixed shape.

  • Gas: Atoms or molecules are far apart and move freely, resulting in no fixed shape or volume. Gases are compressible.

Diamond structure (crystalline solid)Graphite structureCompressibility of solids and gases

Example: Diamond is a crystalline solid with a regular three-dimensional pattern, while graphite is an amorphous solid with layers of carbon atoms.

Classification by Composition

Matter can be classified as a pure substance or a mixture based on its composition.

  • Element: A pure substance that cannot be chemically broken down; composed of individual atoms.

  • Compound: A pure substance composed of two or more different elements in fixed, definite proportions; can be broken down into elements.

  • Mixture: A combination of two or more pure substances that can be separated by physical means. Mixtures can be homogeneous (uniform throughout) or heterogeneous (not uniform).

Classification of matter: elements, compounds, mixtures

Example: Pure water is a compound, helium is an element, wet sand is a heterogeneous mixture, and tea with sugar is a homogeneous mixture.

Physical and Chemical Properties & Changes

Physical Properties and Changes

Physical properties can be observed without changing the composition of the substance (e.g., odor, color, appearance, taste, boiling and melting point, solubility, density). Physical changes do not alter the composition of matter (e.g., changes of state, appearance, dissolving).

Physical change: dry ice sublimationPhysical change: sugar dissolving

Example: Dry ice (solid CO2) sublimates to gaseous CO2 without changing its chemical composition. Sugar dissolving in water is a physical change.

Chemical Properties and Changes

Chemical properties can only be observed by changing the composition of the substance (e.g., flammability, corrosiveness, toxicity). Chemical changes (reactions) alter the composition of matter (e.g., burning, rusting, bleaching).

  • Law of Conservation of Mass: In a chemical reaction, mass is neither created nor destroyed; mass is conserved.

Chemical change: propane burningChemical change: iron rusting

Example: Burning propane produces carbon dioxide and water, changing the chemical composition. Iron rusting forms iron oxide.

Energy in Chemistry

Types of Energy

Physical and chemical changes involve energy transformations. Energy is the capacity to do work. Types include:

  • Kinetic energy: Energy of motion.

  • Thermal energy: Related to temperature; arises from the motion of atoms or molecules.

  • Potential energy: Energy due to position or composition (e.g., gravitational, chemical).

Law of Conservation of Energy: Energy is conserved during a change; it cannot be created or destroyed, only converted or transferred.

Temperature and Measurement

Temperature Scales

Temperature measures the average kinetic energy of particles. Common scales:

  • Fahrenheit (°F)

  • Celsius (°C)

  • Kelvin (K): SI unit, absolute scale

Conversion formulas:

SI Base Units

Measurements are quantitative and require both a numeric value and a unit. The SI system is a base-10 metric system.

Quantity

Unit

Symbol

Length

Meter

m

Mass

Kilogram

kg

Time

Second

s

Temperature

Kelvin

K

Amount of substance

Mole

mol

Electric current

Ampere

A

Luminous intensity

Candela

cd

SI Base Units table

Metric Prefix Multipliers

Metric prefixes allow expression of large and small numbers conveniently.

Prefix

Symbol

Multiplier

giga

G

1,000,000,000

mega

M

1,000,000

kilo

k

1,000

centi

c

0.01

milli

m

0.001

micro

μ

0.000001

nano

n

0.000000001

pico

p

0.000000000001

SI Prefix Multipliers table

Density

Definition and Calculation

Density (d) is the ratio of a substance’s mass to its volume. It is an intensive property, independent of the amount of material.

  • Formula:

  • Units: g/cm3 or g/mL

Example: A ring with mass 4.53 g and volume 0.212 cm3 has a density of (rounded).

Substance

Density (g/cm3)

Water

1.00

Ice

0.917

Glass

2.48

Iron

7.86

Gold

19.3

Platinum

21.4

Density formulaDensity as a conversion factor

Measurements and Significant Figures

Significant Figures and Uncertainty

Significant figures reflect the precision of a measurement. The uncertainty is indicated in the last digit, which is estimated. More significant figures mean higher certainty.

  • All nonzero digits are significant.

  • Zeros between significant digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros after a decimal point are significant.

  • Exact numbers (counts, conversion factors) have unlimited significant figures.

Estimation in weighing (1 g markings)Estimation in weighing (0.1 g markings)

Calculating with Significant Figures

  • Multiplication and Division: The answer has the same number of significant figures as the factor with the fewest.

  • Addition and Subtraction: The answer has the same number of decimal places as the quantity with the fewest.

Example: (rounded to 2 significant figures).

Scientific Notation

Writing Numbers in Scientific Notation

Scientific notation expresses numbers as a decimal part (between 1 and 9.999...) and an exponential part (10n).

  • Example: 12,502,424 =

  • Example: 0.0000380 =

Precision and Accuracy

Definitions and Types of Error

Accuracy refers to how close a measured value is to the actual value. Precision refers to how close a series of measurements are to one another.

  • Random error: Equal probability of being too high or too low; can be averaged out.

  • Systematic error: Consistently too high or too low; cannot be averaged out.

Precision and accuracy comparisonPrecision and accuracy table

Solving Chemical Problems

Dimensional Analysis

Dimensional analysis uses units as a guide to solving problems. Units are multiplied, divided, and canceled like algebraic quantities. Always include units in calculations.

  • Conversion factor: Used to convert between units using equivalent quantities.

  • Strategy: Identify the starting point (given), the end point (what to find), and devise a way to get from start to end using conversion factors.

The Scientific Method

Process and Key Concepts

The scientific method is a systematic approach to learning based on observation and experimentation. It involves:

  • Observation and data collection

  • Forming a hypothesis (testable, falsifiable)

  • Designing and conducting experiments

  • Analyzing data and drawing conclusions

  • Reporting results and revising hypotheses

Law and Theory

Scientific Law vs. Theory

Scientific Law: A brief statement or equation summarizing repeated past observations and predicting future ones (e.g., Law of Conservation of Mass).

Scientific Theory: Combines well-established hypotheses and laws to provide a deeper explanation or model of some aspect of the physical world. Theories predict behavior beyond current laws and can be modified as new evidence arises.

Example: Dalton’s Atomic Theory explains the nature of atoms and their role in chemical reactions.

*Additional info: Academic context was added to clarify definitions, examples, and the application of concepts for self-contained study notes.*

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