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

Introduction to Chemistry

The Central Idea of Chemistry

Chemistry is the science that seeks to understand the behavior of matter by studying the properties and behavior of atoms and molecules. The fundamental principle is that the properties of matter are determined by the properties of molecules and atoms. For example, the properties of water molecules determine how water behaves, and the properties of sugar molecules determine how sugar behaves.

• Matter is anything that occupies space and has mass.

• Understanding matter at the molecular level enables unprecedented control over materials and their properties.

Atoms and Molecules

Definitions and Structure

Atoms are the submicroscopic particles that constitute the fundamental building blocks of ordinary matter. Free atoms are rare in nature; instead, they bind together in specific geometrical arrangements to form molecules.

• Molecules are groups of two or more atoms held together by chemical bonds.

• Example: Carbon monoxide (CO) is a molecule composed of one carbon atom and one oxygen atom held together by a chemical bond.

• Small differences in atoms and molecules can result in large differences in the substances they compose. For example, graphite and diamond are both made of carbon atoms (allotropes of carbon), but their atomic arrangements differ, leading to different properties.

Allotropes are different structural forms of the same element in the same physical state (e.g., graphite and diamond for carbon).

The Scientific Method

Process and Components

The scientific method is an empirical process for understanding nature by observing its behavior and conducting experiments to test ideas. It is the foundation of scientific inquiry in chemistry.

• Observation: Gathering data about the characteristics or behavior of nature.

• Hypothesis: A tentative interpretation or explanation of the observations. A good hypothesis is falsifiable and can be tested by experiments.

• Experimentation: Testing hypotheses through controlled experiments.

• Scientific Law: A brief statement that summarizes past observations and predicts future ones (e.g., Law of Conservation of Mass: "In a chemical reaction, matter is neither created nor destroyed").

• Theory: A model that explains why nature behaves as it does, based on well-established hypotheses. Theories are also tested by experiments.

Comparison Table: Law vs. Theory

Aspect	Law	Theory
Describes	What nature does	Why nature does it
Basis	Summarizes observations	Explains underlying reasons
Testability	Can be tested by experiments	Can be tested by experiments

Classification of Matter

States of Matter

Matter can be classified by its physical state: solid, liquid, or gas. The state depends on the arrangement and movement of atoms or molecules.

• Solid: Atoms or molecules are packed closely in fixed locations. Solids have a fixed volume and rigid shape. They can be crystalline (ordered structure, e.g., diamond, table salt) or amorphous (no long-range order, e.g., glass, plastic).

• Liquid: Atoms or molecules are close but can move past each other. Liquids have a fixed volume but not a fixed shape; they flow to assume the shape of their container (e.g., water, alcohol).

• Gas: Atoms or molecules are far apart and move freely. Gases are compressible and assume both the shape and volume of their container (e.g., air, oxygen gas).

Composition of Matter

Matter can also be classified by its composition as a pure substance or a mixture.

• Pure Substance: Made up of only one component with invariant composition. Can be an element (cannot be broken down into simpler substances, e.g., helium) or a compound (composed of two or more elements in fixed proportions, e.g., water).

• Mixture: Composed of two or more components in variable proportions. Can be heterogeneous (composition varies from one region to another, e.g., sand and water) or homogeneous (uniform composition throughout, e.g., sweetened tea).

Classification Table:

Type	Definition	Example
Element	Cannot be chemically broken down	Helium (He)
Compound	Composed of two or more elements	Water (H2O)
Heterogeneous Mixture	Non-uniform composition	Sand and water
Homogeneous Mixture	Uniform composition	Saltwater

Separation of Mixtures

Mixtures can be separated by exploiting differences in physical or chemical properties:

• Decanting: Pouring off a liquid from a solid-liquid mixture (e.g., sand and water).

• Filtration: Separating an insoluble solid from a liquid using filter paper.

• Distillation: Separating components of a homogeneous liquid mixture by boiling off the more volatile component.

Physical and Chemical Properties and Changes

Properties

• Physical Property: A property that a substance displays without changing its composition (e.g., odor, color, melting point, density).

• Chemical Property: A property that a substance displays only by changing its composition via a chemical reaction (e.g., flammability, acidity, toxicity).

Changes

• Physical Change: Alters only the state or appearance, not composition (e.g., boiling water, melting ice).

• Chemical Change: Alters the composition of matter; atoms rearrange to form new substances (e.g., rusting of iron).

Energy in Chemistry

Types and Conservation

Energy is the capacity to do work. Work is defined as the action of a force through a distance.

• Kinetic Energy: Energy associated with motion.

• Thermal Energy: Energy associated with the temperature of an object (a type of kinetic energy).

• POTENTIAL ENERGY: Energy associated with position or composition.

• Chemical Energy: A form of potential energy stored in chemical bonds.

• Law of Conservation of Energy: Energy is neither created nor destroyed in a physical or chemical change.

Measurement and Units

SI Units

Measurements in chemistry use the International System of Units (SI), which is based on the metric system.

Quantity	SI Unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Amount of substance	mole	mol

• Meter (m): SI unit of length.

• Kilogram (kg): SI unit of mass. 1 kg = 2.20462 lb.

• Second (s): SI unit of time.

• Kelvin (K): SI unit of temperature. Absolute zero (0 K) is the lowest possible temperature.

Temperature Conversions:

• $^\circ C = \frac{5}{9} ( ^\circ F - 32 )$

• $K = ^\circ C + 273.15$

Derived Units and Density

• Volume: Measured in cubic meters (m3), liters (L), or milliliters (mL).

• Density: The ratio of a substance’s mass to its volume. $\text{Density} = \frac{\text{mass}}{\text{volume}}$

• Density is an intensive property (does not depend on amount), while mass and volume are extensive properties (depend on amount).

Prefix Multipliers

SI units use prefixes to indicate powers of ten. For example, kilo- (k) means $10^3$, milli- (m) means $10^{-3}$, and micro- ($\mu$) means $10^{-6}$.

Prefix	Symbol	Multiplier
kilo	k	$10^3$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$
nano	n	$10^{-9}$

Significant Figures and Measurement Precision

Rules for Significant Figures

• All nonzero digits are significant.

• Interior zeroes (between nonzero digits) are significant.

• Leading zeroes (to the left of the first nonzero digit) are not significant.

• Trailing zeroes after a decimal point are significant.

• Trailing zeroes before a decimal point (and after a nonzero number) are significant.

• Trailing zeroes before an implied decimal point are ambiguous; use scientific notation to clarify.

• Exact numbers (from counting or definitions) have unlimited significant figures.

Significant Figures in Calculations

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

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

• Rounding: Round down if the last digit dropped is four or less; round up if it is five or more. Only round the final answer in multistep calculations.

Precision and Accuracy

• Precision: How close a series of measurements are to one another.

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

• Random Error: Error with equal probability of being too high or too low.

• Systematic Error: Error that tends to be consistently too high or too low.

Problem Solving and Dimensional Analysis

Unit Conversions

Most chemistry problems involve converting between units using dimensional analysis. Units are treated algebraically and can be multiplied, divided, and canceled.

• Unit Equation: Statement of two equivalent quantities (e.g., 2.54 cm = 1 in).

• Conversion Factor: Fractional quantity derived from a unit equation (e.g., $\frac{2.54\,\text{cm}}{1\,\text{in}}$).

• For units raised to a power, raise both the number and the unit to that power (e.g., $(2.54\,\text{cm})^2 = (1\,\text{in})^2$).

General Formula for Dimensional Analysis:

• Information given $\times$ conversion factor(s) = information sought

• Example: $2\,\text{in} \times \frac{2.54\,\text{cm}}{1\,\text{in}} = 5.08\,\text{cm}$

Additional info: These notes provide a comprehensive overview of the foundational concepts in general chemistry, including matter, measurement, scientific method, classification of substances, properties and changes, energy, units, significant figures, and problem-solving strategies.