Introductory Chemistry: Measurement, Matter, and Energy

Chapter 1: The Chemical World

Scientific Method

The scientific method is a systematic approach used by scientists to explore observations, answer questions, and solve problems. It ensures that scientific inquiry is logical, repeatable, and based on evidence.

• Observations: Gathering information using the senses or instruments. Observations can be qualitative (descriptive) or quantitative (measured).

• Hypotheses: A tentative explanation or prediction that can be tested by experiments.

• Laws: Statements that summarize a large number of observations and predict future events (e.g., the law of conservation of mass).

• Theories: Well-substantiated explanations of some aspect of the natural world that can incorporate laws, hypotheses, and facts.

Example: The law of conservation of mass was developed after repeated observations that mass is conserved in chemical reactions.

Law of Conservation of Mass

The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction.

• Equation:

$\text{Total mass of reactants} = \text{Total mass of products}$

Example: If 10 g of hydrogen reacts with 80 g of oxygen, the total mass of water produced will be 90 g.

Chapter 2: Measurement and Problem Solving

Scientific Notation

Scientific notation expresses very large or very small numbers in the form $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer.

• Example: 0.00056 = $5.6 \times 10^{-4}$; 123,000 = $1.23 \times 10^{5}$

Reading Measurements and Estimated Value

When reading a measurement, always record all certain digits plus one estimated digit (the last digit).

• Example: If a ruler shows 2.4 cm, and you estimate between marks, you might record 2.45 cm.

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one estimated digit.

• How to count significant figures:

  • 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.

• How many figures to keep in a calculation:

  • For multiplication/division: The result should have as many significant figures as the measurement with the fewest significant figures.

  • For addition/subtraction: The result should have as many decimal places as the measurement with the fewest decimal places.

• Rules for rounding: If the digit to be dropped is less than 5, leave the last digit unchanged. If it is 5 or greater, increase the last digit by one.

Example: 2.345 × 1.2 = 2.814 → 2.8 (2 sig figs)

SI Units for Various Quantities

The International System of Units (SI) is the standard system for scientific measurements.

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

Using Prefixes with Units

Prefixes indicate multiples or fractions of SI units.

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

Dimensional Analysis (Unit Conversion)

Dimensional analysis uses conversion factors to change units.

• One-step conversion: Multiply by a conversion factor (e.g., $1 \text{ in} = 2.54 \text{ cm}$).

• Multi-step conversion: Use several conversion factors in sequence.

• Units raised to a power: Square or cube both the number and the unit (e.g., $1 \text{ m}^2 = (100 \text{ cm})^2 = 10,000 \text{ cm}^2$).

Example: Convert 5.0 m to cm: $5.0 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 500 \text{ cm}$

Density

Density is the mass per unit volume of a substance.

• Formula:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Using density as a conversion factor: Density can be used to convert between mass and volume.

Example: If density = $2.70 \text{ g/cm}^3$ and mass = 54.0 g, then volume = $\frac{54.0 \text{ g}}{2.70 \text{ g/cm}^3} = 20.0 \text{ cm}^3$

Chapter 3: Matter and Energy

Matter: Atoms and Molecules

Matter is anything that has mass and occupies space. It is composed of atoms (the smallest unit of an element) and molecules (two or more atoms bonded together).

States of Matter

Matter exists in three primary states: solid, liquid, and gas.

• Solids: Definite shape and volume. Particles are closely packed. Can be crystalline (ordered structure, e.g., salt) or amorphous (no long-range order, e.g., glass).

• Liquids: Definite volume but no definite shape. Particles are close but can move past each other.

• Gases: No definite shape or volume. Particles are far apart and move freely.

Classifying Matter

• Pure Substances: Have a fixed composition. Can be:

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

  • Compounds: Composed of two or more elements chemically combined (e.g., H2O).

• Mixtures: Physical combinations of two or more substances. Can be:

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

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

Physical and Chemical Properties

• Physical properties: Can be observed without changing the substance's identity (e.g., color, melting point).

• Chemical properties: Describe a substance's ability to undergo chemical changes (e.g., flammability).

Physical and Chemical Changes

• Physical changes: Do not alter the chemical composition (e.g., melting, boiling).

• Chemical changes: Result in new substances (e.g., rusting of iron).

Law of Conservation of Mass

Mass is conserved in both physical and chemical changes.

Law of Conservation of Energy

Energy cannot be created or destroyed, only transformed from one form to another.

• Equation:

$\text{Total energy before} = \text{Total energy after}$

Kinetic and Potential Energy

• Kinetic energy: Energy of motion.

• Potential energy: Stored energy due to position or composition.

Conversion of Energy Units

• Joule (J): SI unit of energy.

• Calorie (cal): Common unit in chemistry. $1 \text{ cal} = 4.184 \text{ J}$

Endothermic and Exothermic Reactions

• Endothermic: Absorb energy from surroundings (e.g., melting ice).

• Exothermic: Release energy to surroundings (e.g., combustion).

Converting Between Temperature Scales

• Celsius to Kelvin: $K = ^\circ C + 273.15$

• Celsius to Fahrenheit: $^\circ F = (^\circ C \times \frac{9}{5}) + 32$

• Fahrenheit to Celsius: $^\circ C = (^\circ F - 32) \times \frac{5}{9}$

Specific Heat Capacity

Specific heat capacity (c) is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C.

• Equation:

$q = m \times c \times \Delta T$

• Where $q$ = heat (J), $m$ = mass (g), $c$ = specific heat (J/g·°C), $\Delta T$ = change in temperature (°C).

Relating Heat Energy to Temperature Changes

Heat energy causes temperature changes according to the specific heat capacity of the substance.

Example: How much heat is needed to raise 50 g of water by 10°C? (c = 4.18 J/g·°C)

$q = 50 \text{ g} \times 4.18 \text{ J/g·°C} \times 10 \text{°C} = 2090 \text{ J}$

Additional info: Where content was brief or listed, academic context and examples were added for clarity and completeness.