Chapter 1: Math Skills for Chemistry

Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a concise form, which is essential in chemistry for handling measurements and calculations.

• Definition: A number is written as the product of a coefficient (between 1 and 10) and a power of ten.

• Example: 0.00056 = ; 120,000 =

• Application: Used for reporting measurements, calculations, and conversions in chemistry.

Chapter 2: Chemistry and Measurements

Units of Measurement

Chemistry relies on standardized units for mass, volume, length, time, and temperature. The Metric and SI (International System) units are commonly used.

• Mass: gram (g), kilogram (kg)

• Volume: liter (L), milliliter (mL)

• Length: meter (m), centimeter (cm)

• Time: second (s)

• Temperature: Celsius (°C), Kelvin (K)

Measured Numbers and Estimation

• Measured Numbers: Always estimate the last digit when recording a measurement. This digit is uncertain.

• Example: If a ruler shows 2.4 cm, the '4' is estimated.

Significant Figures

Significant figures (sig figs) indicate the precision of a measured or calculated quantity.

• Rules:

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

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

• Rounding: If the digit to be dropped is less than 5, round down; if 5 or above, round up.

Exact Numbers

• Definition: Numbers that are counted or defined, not measured, and have infinite significant figures (e.g., 1 dozen = 12).

SI Units and Prefixes

• Common Prefixes:

  • kilo (k):

  • centi (c):

  • milli (m):

• Other prefixes include mega, deca, micro, etc. (No need to memorize all).

Equalities and Conversion Factors

• Equalities: Show the relationship between two units (e.g., ).

• Conversion Factors: Fractions derived from equalities used to convert between units.

• Example: To convert 5 m to cm:

Density and Specific Gravity

• Density: The mass of a substance per unit volume.

• Specific Gravity: The ratio of the density of a substance to the density of water (unitless).

• Density as a Conversion Factor: Used to convert between mass and volume.

• Example: If density of ethanol is , then has

Practice with Unit Conversions

• Practice converting between units using conversion factors and significant figures.

Chapter 3: Matter and Energy

States of Matter and Their Properties

• Solid: Definite shape and volume; particles are closely packed.

• Liquid: Definite volume, no definite shape; particles are less tightly packed than solids.

• Gas: No definite shape or volume; particles are far apart and move freely.

Classification of Matter

• Pure Substance: Has a fixed composition (element or compound).

• Mixture: Physical blend of two or more substances.

• Element: Substance made of one type of atom (e.g., O2).

• Compound: Substance made of two or more elements chemically combined (e.g., H2O).

• Atom: Smallest unit of an element.

• Molecule: Two or more atoms bonded together.

Physical and Chemical Properties and Changes

• Physical Properties: Observed without changing the substance (e.g., color, melting point).

• Chemical Properties: Describe how a substance reacts (e.g., flammability).

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

• Chemical Change: Substance is transformed into a new substance (e.g., rusting iron).

Temperature and Units

• Celsius (°C), Kelvin (K), Fahrenheit (°F): Common temperature scales.

• Conversion:

Energy: Kinetic and Potential

• Kinetic Energy: Energy of motion.

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

Units of Energy and Conversions

• Joule (J): SI unit of energy.

• Calorie (cal): Common unit in food energy;

• Food Energy Values:

  • Carbohydrate:

  • Protein:

  • Fat:

Note: Round food energy calculations to the nearest tens place.

Chapter 4: Atoms and Elements

The Periodic Table: Periods and Groups

• Periods: Horizontal rows (numbered 1-7).

• Groups: Vertical columns (numbered 1-18).

• Special Groups:

  • Alkali metals (Group 1)

  • Alkaline earth metals (Group 2)

  • Halogens (Group 17)

  • Noble gases (Group 18)

• Main Group Elements: Groups 1, 2, and 13-18.

• Transition Elements: Groups 3-12.

Metals, Nonmetals, and Metalloids

• Metals: Shiny, good conductors, malleable (e.g., iron).

• Nonmetals: Dull, poor conductors, brittle (e.g., sulfur).

• Metalloids: Properties intermediate between metals and nonmetals (e.g., silicon).

Structure of the Atom

• Protons: Positively charged particles in the nucleus.

• Neutrons: Neutral particles in the nucleus.

• Electrons: Negatively charged particles orbiting the nucleus.

Atomic Number and Mass Number

• Atomic Number (Z): Number of protons in the nucleus; defines the element.

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

• Example: Carbon-12: Z = 6, A = 12

Isotopes and Symbols

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

• Symbol: , where X is the element symbol, A is mass number, Z is atomic number.

• Example: is an isotope of carbon.

Chapter 5: Nuclear Chemistry

Types of Radiation Emitted

• Alpha (α): Helium nuclei; low penetration.

• Beta (β): High-energy electrons; moderate penetration.

• Gamma (γ): High-energy electromagnetic waves; high penetration.

Nuclear Equations

• Writing and Balancing: Show the changes in the nucleus during radioactive decay. Both mass and atomic numbers must be balanced.

• Example:

  • Alpha decay:

  • Beta decay:

Half-Life

• Definition: The time required for half of a radioactive sample to decay.

• Key Point: Two half-lives do not equal one "full-life"; after each half-life, half of the remaining sample decays.

• Calculation:

  • After n half-lives, remaining amount =

• Example: If 100 g of a radioisotope has a half-life of 3 years, after 6 years (2 half-lives), g remains.

Practice Problems

• Practice writing nuclear equations and calculating half-lives for various isotopes.