Chapter 2: Measurement, Units, and Calculations

Scientific Notation and Decimal Form

Scientific notation is a method for expressing very large or very small numbers in a compact form. It is commonly used in chemistry to simplify calculations and represent measurements.

• Scientific Notation: A number is written as , where and is an integer.

• Conversion: To convert to scientific notation, move the decimal point so only one nonzero digit remains to the left. To convert back, move the decimal point places (right for positive , left for negative ).

• Example: ;

Significant Figures (Sig Figs)

Significant figures indicate the precision of a measured or calculated quantity. Correctly counting and rounding sig figs is essential for reporting scientific data.

• Counting Sig Figs: 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.

• Rounding: Round to the required number of sig figs based on the context or calculation.

• Example: 0.00450 has three sig figs; 1200 has two sig figs (unless written as 1.2 × 103).

Sig Fig Rules in Calculations

Different operations require different rules for determining the number of significant figures in the result.

• Addition/Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

• Multiplication/Division: The result should have the same number of sig figs as the measurement with the fewest sig figs.

• Example: (rounded to two sig figs)

SI Prefixes and Units

The International System of Units (SI) uses prefixes to indicate powers of ten for base units.

• Common SI Prefixes: kilo- (), centi- (), milli- (), micro- (), nano- ()

• Example: 1 kilometer (km) = meters (m)

Unit Conversions and Dimensional Analysis

Dimensional analysis is a systematic method for converting between units using conversion factors.

• One-Step Conversion: Multiply by the appropriate conversion factor.

• Multi-Step Conversion: Set up a chain of conversion factors so that units cancel appropriately.

• Example: Convert 25 cm to meters:

Density Calculations

Density is a physical property defined as mass per unit volume.

• Formula:

• Units: Commonly g/cm3 or kg/m3

• Example: If a block has a mass of 50 g and a volume of 20 cm3,

Chapter 3: Matter and Energy

Classification of Matter

Matter can be classified by its physical state and composition.

• States: Solid, liquid, gas

• Composition: Pure substances (elements, compounds) and mixtures (homogeneous, heterogeneous)

• Example: Air is a homogeneous mixture; water is a compound.

Physical and Chemical Properties and Changes

Properties and changes in matter are categorized as physical or chemical.

• Physical Properties: Observed without changing composition (e.g., melting point, density)

• Chemical Properties: Describe ability to undergo chemical change (e.g., flammability)

• Physical Change: Change in state or appearance, not composition (e.g., melting ice)

• Chemical Change: Produces new substances (e.g., rusting iron)

Energy Conversions

Energy can be converted between different units using conversion factors.

• Common Units: Joules (J), calories (cal)

• Conversion:

• Example: Convert 100 cal to joules:

SI Standard Units

The SI system defines standard units for scientific measurements.

• Length: meter (m)

• Mass: kilogram (kg)

• Time: second (s)

• Temperature: kelvin (K)

• Amount of substance: mole (mol)

Heat Capacity and Specific Heat

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

• Units: J/g°C

• Formula: where = heat (J), = mass (g), = specific heat (J/g°C), = change in temperature (°C)

• Example: Calculate heat required to raise 10 g of water by 5°C ( J/g°C): J

Chapter 4: Atomic Structure and the Periodic Table

Structure of the Atom

An atom consists of a nucleus (protons and neutrons) surrounded by electrons.

• Protons: Positively charged particles in the nucleus

• Neutrons: Neutral particles in the nucleus

• Electrons: Negatively charged particles in orbitals around the nucleus

Atomic Number, Mass Number, and Atomic Mass

These terms describe the composition and mass of atoms.

• Atomic Number (Z): Number of protons in the nucleus

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

• Atomic Mass: Weighted average mass of all isotopes of an element (in atomic mass units, amu)

• Example: Carbon-12 has 6 protons and 6 neutrons;

Isotopes

Isotopes are atoms of the same element with different numbers of neutrons.

• Example: and are isotopes of carbon

• Atomic Mass Calculation:

The Periodic Table: Organization and Groups

The periodic table arranges elements by increasing atomic number and groups elements with similar properties.

• Metals: Left and center; good conductors, malleable

• Nonmetals: Right side; poor conductors, brittle

• Main Group Elements: Groups 1, 2, 13–18

• Transition Elements: Groups 3–12

• Groups: Halogens (Group 17), Noble Gases (Group 18), Alkali Metals (Group 1), Alkaline Earth Metals (Group 2)

Cations and Anions

Cations and anions are ions formed by loss or gain of electrons.

• Cation: Positively charged ion (loss of electrons)

• Anion: Negatively charged ion (gain of electrons)

• Calculating Protons and Electrons: For a cation, electrons = atomic number – charge; for an anion, electrons = atomic number + charge

• Example: Na+ has 11 protons and 10 electrons; Cl– has 17 protons and 18 electrons

Additional info: Some details, such as specific conversion charts and formulas, were inferred based on standard introductory chemistry curriculum.