General Chemistry Exam 1 Study Guide: Principles, Concepts, and Problem-Solving Skills

Exam Preparation and Study Strategies

Overview of Exam Content

This study guide covers material from Chapters 1, 2, and 1e of the textbook Principles of Chemistry. The exam will assess your understanding of key concepts, problem-solving skills, and the ability to apply formulas and scientific reasoning. Spheres are frequently used in all fields of science, so you should start learning and committing these to memory now, as they will be used throughout this course.

• Key Concepts: Focus on definitions, relationships, and applications.

• Problem-Solving: Practice with example problems and exercises from the textbook.

• Self-Assessment: Use end-of-chapter questions to test your understanding.

Classification of Matter

Distinguishing Matter by Mass vs. Weight

Understanding the difference between mass and weight is fundamental in chemistry. Mass is a measure of the amount of matter in an object, while weight is the force exerted by gravity on that mass.

• Mass: Measured in kilograms (kg) or grams (g).

• Weight: Measured in newtons (N); depends on gravitational acceleration.

• Example Problem: Where will a glass of milk have the greatest mass? Answer: The mass remains the same everywhere, but the weight varies with gravity.

States of Matter and Their Characteristics

Matter exists in different states: solid, liquid, and gas. Each state has distinct properties.

• Solids: Definite shape and volume.

• Liquids: Definite volume, indefinite shape.

• Gases: Indefinite shape and volume.

• Ability to classify: Recognize differences between states based on particle arrangement and energy.

Pure Substances vs. Mixtures

Chemical substances can be classified as pure substances or mixtures. Pure substances have uniform composition, while mixtures contain two or more substances physically combined.

• Elements: Cannot be broken down into simpler substances.

• Compounds: Composed of two or more elements chemically combined.

• Mixtures: Can be homogeneous (uniform) or heterogeneous (non-uniform).

• Example Problem: Classify the following as pure substances or mixtures: 1. Sweet tea 2. Carbon dioxide 3. Aluminum 4. Vegetable soup

Measurement and Units

Unit Conversions

Converting between units is essential for solving chemistry problems. Use conversion factors to change from one unit to another.

• Example Problems: Convert 0.020 kg/m3 to kg/L. Convert 1.76 inches to cm. Convert 4.00 m2 to ft2.

• Formula: $\text{Value in new units} = \text{Value in old units} \times \text{Conversion factor}$

Temperature Scales

Temperature can be measured in Fahrenheit, Celsius, or Kelvin. Converting between these scales is a common task.

• Formulas: $T_{\text{C}} = \frac{5}{9}(T_{\text{F}} - 32)$ $T_{\text{K}} = T_{\text{C}} + 273.15$

• Example Problem: If the temperature is 47 K, what is the temperature in Fahrenheit?

SI Prefix Multipliers

SI units use prefixes to indicate powers of ten. Understanding and converting these is important for scientific calculations.

• Common Prefixes: kilo (k, $10^3$), centi (c, $10^{-2}$), milli (m, $10^{-3}$), micro ($\mu$, $10^{-6}$)

• Example Problem: Convert 983 m into km.

Density and Measurement Accuracy

Density Calculations

Density is defined as mass per unit volume. It is used to identify substances and solve various problems.

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

• Example Problem: The density of iron is 7.78 g/cm3. What is the radius in cm of a sphere of iron that has a mass of 3.5 pounds?

Accuracy and Precision

Accuracy refers to how close a measurement is to the true value, while precision refers to how close repeated measurements are to each other.

• Random Errors: Affect precision.

• Systematic Errors: Affect accuracy.

• Example Problem: Evaluate precision and accuracy in a data set.

Significant Figures and Uncertainty

Understanding Significant Figures

Significant figures indicate the precision of a measurement. The number of significant figures reflects the uncertainty in the measurement.

• Rules: All nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros are significant if there is a decimal point.

• Example Problem: How many significant figures are in 0.00210 km?

Reporting Calculations with Significant Figures

When performing calculations, the result should be reported with the correct number of significant figures.

• Multiplication/Division: Use the least number of significant figures.

• Addition/Subtraction: Use the least number of decimal places.

• Example Problem: Perform the following calculation and report the result: $9.15 / 4.970$

Atoms, Elements, Molecules, and Compounds

Chemical Structure and Classification

Atoms are the basic units of matter. Elements consist of one type of atom, while compounds are made of two or more elements chemically bonded.

• Ions: Atoms or molecules with a net electric charge due to loss or gain of electrons.

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

• Example Problem: Classify each of the following as an atom, ion, molecule, or compound.

Subatomic Particles

Atoms are composed of protons, neutrons, and electrons. Protons and neutrons are found in the nucleus, while electrons orbit the nucleus.

• Proton: Positive charge, mass ≈ 1 amu.

• Neutron: No charge, mass ≈ 1 amu.

• Electron: Negative charge, mass ≈ 0.0005 amu.

• Example Problem: Which of the following statements about subatomic particles are false?

The Periodic Table and Atomic Structure

Periodic Table Information

Each element on the periodic table is identified by its chemical name, symbol, atomic number, and atomic mass.

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

• Atomic Mass: Weighted average mass of all isotopes.

• Example Problem: What element has 53 protons, 61 neutrons, and 54 electrons?

Isotopes and Ions

Isotopes are atoms of the same element with different numbers of neutrons. Ions are atoms or molecules that have gained or lost electrons.

• Example Problem: Write the chemical symbol for an ion with 28 neutrons and 19 electrons.

Calculating Atomic Mass and Isotope Abundance

The average atomic mass is calculated using the masses and natural abundances of isotopes.

• Formula: $\text{Average atomic mass} = \sum (\text{isotope mass} \times \text{fractional abundance})$

• Example Problem: What is the atomic mass for carbon that would appear on a periodic table?

The Mole and Avogadro's Number

Concept of the Mole

The mole is a counting unit in chemistry, representing $6.022 \times 10^{23}$ entities (Avogadro's number).

• Formula: $\text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}}$

• Example Problem: How many sulfur molecules are there in 3.8 moles of sulfur dioxide, SO2?

Electromagnetic Radiation and Atomic Spectra

Properties of Electromagnetic Radiation

Electromagnetic radiation includes visible light, ultraviolet, infrared, X-rays, and gamma rays. It is characterized by wavelength, frequency, and energy.

• Formula: $c = \lambda \nu$ (where $c$ is the speed of light, $\lambda$ is wavelength, $\nu$ is frequency)

• Formula: $E = h \nu$ (where $E$ is energy, $h$ is Planck's constant)

• Example Problem: A laser emits green light with a wavelength of 515 nm. What is the frequency of this light?

Electromagnetic Spectrum

The electromagnetic spectrum ranges from radio waves (longest wavelength, lowest energy) to gamma rays (shortest wavelength, highest energy).

• Order: Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma ray

• Example Problem: Which region of the electromagnetic spectrum contains the least amount of energy?

Photoelectric Effect and Atomic Emission

The photoelectric effect demonstrates that light can eject electrons from a metal surface if the light's frequency exceeds a threshold value.

• Example Problem: What is the minimum energy required to dislodge electrons from sodium metal?

Atomic Spectra and Electron Transitions

Atoms emit or absorb light at specific wavelengths when electrons transition between energy levels.

• Formula: $E = -R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$ (Rydberg formula for hydrogen atom)

• Example Problem: Which of the following electron transitions in hydrogen atom emits a photon of the largest energy?

Quantum Mechanics and Atomic Structure

Wave-Particle Duality

Electrons exhibit both wave-like and particle-like properties. The de Broglie wavelength relates a particle's momentum to its wavelength.

• Formula: $\lambda = \frac{h}{mv}$

• Example Problem: An electron has a de Broglie wavelength of 225 nm. What is its speed?

Heisenberg Uncertainty Principle

The uncertainty principle states that it is impossible to simultaneously know both the position and momentum of a particle with absolute precision.

• Formula: $\Delta x \Delta p \geq \frac{h}{4\pi}$

• Example Problem: If the uncertainty in a bullet's velocity is 5.0 m/s, what is the uncertainty in its position?

Quantum Numbers and Electron Orbitals

Quantum numbers describe the properties of atomic orbitals and the electrons in them.

• Principal quantum number (n): Energy level

• Angular momentum quantum number (l): Shape of orbital

• Magnetic quantum number (ml): Orientation of orbital

• Spin quantum number (ms): Spin direction

• Example Problem: Indicate how many electrons can share each of the following sets of quantum numbers.

Electron Probability Density and Orbital Shapes

Electron probability density describes where electrons are likely to be found. Orbitals have characteristic shapes (spherical for s, dumbbell for p, etc.).

• Example Problem: Make a sketch of a 3d orbital and indicate the number of nodes.

Summary Table: Key Concepts and Formulas

Concept	Key Formula	Example Application
Density	$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$	Calculate mass or volume given density
Temperature Conversion	$T_{\text{K}} = T_{\text{C}} + 273.15$	Convert Celsius to Kelvin
Average Atomic Mass	$\sum (\text{isotope mass} \times \text{fractional abundance})$	Calculate atomic mass from isotopic data
Speed of Light	$c = \lambda \nu$	Find frequency or wavelength of light
Energy of Photon	$E = h \nu$	Calculate energy from frequency
de Broglie Wavelength	$\lambda = \frac{h}{mv}$	Find wavelength of a moving particle
Heisenberg Uncertainty	$\Delta x \Delta p \geq \frac{h}{4\pi}$	Calculate uncertainty in position or momentum

Additional info: Some context and explanations have been expanded for clarity and completeness, including definitions, formulas, and example problems. This guide is designed to be self-contained and suitable for exam preparation in a General Chemistry college course.