GOB Chemistry Study Guide: Matter, Measurement, and Atomic Structure (Chapters 2–4)

Matter and Measurements

Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a concise form. It is commonly used in chemistry to handle measurements that span many orders of magnitude.

• Format: A number is written as a × 10n, where 1 ≤ a < 10 and n is an integer.

• Example (large number): 5,600,000 = $5.6 \times 10^{6}$

• Example (small number): 0.00034 = $3.4 \times 10^{-4}$

Significant Figures (Sig Figs)

Significant figures reflect the precision of a measured or calculated quantity. Correctly identifying and using significant figures is essential for reporting scientific data.

• Counting Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros after a decimal point are significant.

• Examples:

  • 0.00450 (3 sig figs)

  • 120.0 (4 sig figs)

  • 500 (1 sig fig, unless specified otherwise)

Mathematical Operations and Significant Figures

Rules for significant figures differ depending on the type of mathematical operation:

• 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 significant figures as the measurement with the fewest significant figures.

• Example: $2.34 \times 1.2 = 2.8$ (rounded to 2 sig figs)

Conversion Factors and Unit Conversions

Conversion factors are ratios used to express the same quantity in different units. They are essential for converting between units in chemistry.

• Example: 1 inch = 2.54 cm, so $\frac{2.54\ \text{cm}}{1\ \text{in}}$ is a conversion factor.

• Application: To convert 5 inches to centimeters: $5\ \text{in} \times \frac{2.54\ \text{cm}}{1\ \text{in}} = 12.7\ \text{cm}$

Metric Prefixes

Metric prefixes indicate multiples or fractions of base units. Knowing these prefixes is crucial for interpreting measurements.

• Kilo- (k): $10^{3}$

• Deci- (d): $10^{-1}$

• Centi- (c): $10^{-2}$

• Milli- (m): $10^{-3}$

• Nano- (n): $10^{-9}$

• Mega- (M): $10^{6}$

• Giga- (G): $10^{9}$

Dimensional Analysis (Factor-Label Method)

Dimensional analysis is a systematic approach to problem-solving that uses conversion factors to move from one unit to another.

• Steps:

  1. Identify the starting and desired units.

  2. Set up conversion factors so units cancel appropriately.

  3. Multiply through and check units.

• Example (Medication Dose): "You are to give ampicillin 25 mg/kg to a child with a mass of 67 lb. If stock on hand is 250 mg/capsule, how many capsules should be given?"

  • Convert 67 lb to kg: $67\ \text{lb} \times \frac{1\ \text{kg}}{2.205\ \text{lb}} = 30.4\ \text{kg}$

  • Calculate dose: $30.4\ \text{kg} \times 25\ \frac{\text{mg}}{\text{kg}} = 760\ \text{mg}$

  • Capsules needed: $\frac{760\ \text{mg}}{250\ \text{mg/capsule}} = 3.04$ capsules (round as appropriate)

Density

Density is a physical property defined as mass per unit volume. It can be used as a conversion factor between mass and volume.

• Formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Units: Commonly g/mL or g/cm3

• Application: If you know the density and mass, you can find the volume, and vice versa.

Atoms and the Periodic Table

Atoms: The Fundamental Units

An atom is the smallest unit of matter that retains the properties of an element. Atoms are the building blocks of all substances.

• Structure:

  • Nucleus: Contains protons (positive charge) and neutrons (neutral).

  • Electrons: Negatively charged particles that move around the nucleus in energy levels (shells).

• Examples: Hydrogen (H), Carbon (C), Oxygen (O)

Subatomic Particles

Atoms are composed of three main subatomic particles:

• Protons:

  • Charge: +1

  • Mass: ~1 atomic mass unit (amu)

  • Location: Nucleus

  • Determines atomic number and identity of the element

  • Example: Carbon has 6 protons (atomic number 6)

• Neutrons:

  • Charge: 0 (neutral)

  • Mass: ~1 amu

  • Location: Nucleus

  • Stabilizes nucleus; different numbers create isotopes (e.g., Carbon-12 vs. Carbon-14)

• Electrons:

  • Charge: -1

  • Mass: 1/1836 of a proton (almost negligible)

  • Location: Orbitals around nucleus

  • Involved in chemical bonding; number equals protons in a neutral atom

Calculating Subatomic Particles

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

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

• Number of Neutrons: $\text{Neutrons} = \text{Mass Number} - \text{Atomic Number}$

• Number of Electrons: Equal to protons in a neutral atom

Matter: Elements, Compounds, and Mixtures

Elements

An element is a pure substance made of only one type of atom. Elements are represented on the periodic table.

• Examples: Oxygen gas (O2), Gold (Au)

Molecules

Molecules are formed when two or more atoms bond together chemically. They can be made of the same element or different elements.

• Molecules of Elements: O2 (oxygen gas), N2 (nitrogen gas)

• Molecules of Compounds: H2O (water), CO2 (carbon dioxide)

• Properties: Molecules have properties different from their constituent atoms.

Compounds

A compound is a substance formed when atoms of two or more different elements combine in fixed proportions.

• Examples: Water (H2O), Carbon dioxide (CO2), Sodium chloride (NaCl)

• Key Point: Compounds have a definite ratio of atoms and new properties distinct from the elements that form them.

Mixtures

Mixtures are physical combinations of two or more substances where each retains its own properties. They can be separated by physical means.

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

• Heterogeneous Mixtures: Non-uniform composition (e.g., sand and water, salad)

Comparison Table: Compounds vs. Mixtures

Feature	Compound	Mixture
Type of Change	Chemical	Physical
Composition	Fixed ratio	Variable ratio
Properties	New, different from elements	Original properties retained
Separation	Chemical methods needed	Physical methods possible
Example	H2O, CO2, NaCl	Air, saltwater, salad

Hierarchy of Building Blocks

• Atom → makes up Element

• Atoms combine → form Molecules/Compounds

• Ions → charged versions of atoms/molecules

• Mixtures → physical blends of substances

Summary

• Understand how to use scientific notation and significant figures in measurements and calculations.

• Be able to convert between units using conversion factors and metric prefixes.

• Apply dimensional analysis to solve real-world problems, such as medication dosing.

• Know the structure of atoms and how to determine the number of subatomic particles.

• Distinguish between elements, compounds, and mixtures, and understand their properties and differences.