General Chemistry Exam 1 Study Guide: Essentials, Atoms, and Quantum-Mechanical Model

Essentials: Units, Measurement, and Problem Solving

SI Units and Prefixes

The International System of Units (SI) is the standard for scientific measurements. Understanding SI units and their prefixes is essential for accurate calculations and conversions in chemistry.

• Base SI Units: Meter (m), Kilogram (kg), Second (s), Kelvin (K), Mole (mol), Ampere (A), Candela (cd)

• Common Prefixes: kilo- (103), centi- (10-2), milli- (10-3), micro- (10-6), nano- (10-9)

• Temperature Conversions: $T(^{ ext{o}}F) = 1.8 imes T(^{ ext{o}}C) + 32$

• Volume Conversions: 1 L = 1.034 qt

Symbol	M	k	h	da	d	c	m	μ	n
Power of 10	6	3	2	1	-1	-2	-3	-6	-9

Significant Figures and Accuracy

• Significant Figures: Digits in a measurement that are known with certainty plus one estimated digit.

• Precision vs. Accuracy: Precision refers to the reproducibility of measurements; accuracy refers to how close a measurement is to the true value.

Density

• Definition: Density is mass per unit volume.

• Formula: $\text{Density} = \frac{m}{V}$

• Example: Water has a density of approximately 1.00 g/mL at room temperature.

Unit Conversions and Dimensional Analysis

• Dimensional Analysis: A method to convert one unit to another using conversion factors.

• Example: Converting 10 cm to meters: $10 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 0.1 \text{ m}$

Atoms

States of Matter

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

• Solid: Definite shape and volume

• Liquid: Definite volume, shape of container

• Gas: No definite shape or volume

Elements, Compounds, and Mixtures

• Element: Pure substance consisting of one type of atom

• Compound: Substance composed of two or more elements chemically combined

• Mixture: Physical blend of two or more substances

Atomic Theory and Structure

• Dalton's Atomic Theory: All matter is composed of atoms; atoms of the same element are identical; atoms combine in simple whole-number ratios.

• Subatomic Particles: Protons (+), Neutrons (0), Electrons (-)

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

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

• Mass Number (A): Sum of protons and neutrons

• Average Atomic Mass: Weighted average of isotopic masses

Moles and Avogadro's Number

• Mole: The amount of substance containing as many entities as there are atoms in 12 g of carbon-12

• Avogadro's Number: $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$

• Example: 1 mole of H2O contains $6.022 \times 10^{23}$ molecules

The Quantum-Mechanical Model of the Atom

Wave Nature of Light

Light exhibits both wave-like and particle-like properties. Understanding its behavior is crucial for quantum mechanics.

• Electromagnetic Radiation: Includes radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma rays

• Key Properties: Frequency ($\nu$), Wavelength ($\lambda$), Energy ($E$)

• Speed of Light: $c = 3.00 \times 10^8 \text{ m/s}$

• Frequency-Wavelength Relationship: $c = \lambda \nu$

Energy of a Photon

• Formula: $E = h \nu$

• Planck's Constant: $h = 6.626 \times 10^{-34} \text{ J} \cdot \text{s}$

• Example: Calculate the energy of a photon with frequency $5.0 \times 10^{14} \text{ Hz}$: $E = (6.626 \times 10^{-34}) \times (5.0 \times 10^{14}) = 3.31 \times 10^{-19} \text{ J}$

Electromagnetic Spectrum

• Order (increasing energy): Radio < Microwave < Infrared < Visible < Ultraviolet < X-ray < Gamma ray

• Visible Light: Wavelengths from about 400 nm (violet) to 700 nm (red)

Atomic Spectra and Quantization

• Line Spectra: Atoms emit light at specific wavelengths, indicating quantized energy levels

• Bohr Model: Electrons orbit the nucleus in quantized energy levels

• Energy Level Formula: $E_n = -2.18 \times 10^{-18} \left( \frac{1}{n^2} \right)$ (for hydrogen atom, $n = 1, 2, 3, ...$)

Quantum Numbers

• Principal Quantum Number ($n$): Indicates energy level (shell)

• Angular Momentum Quantum Number ($l$): Indicates subshell (shape of orbital)

• Magnetic Quantum Number ($m_l$): Orientation of orbital

• Spin Quantum Number ($m_s$): Electron spin direction (+1/2 or -1/2)

• Allowed Combinations: $l$ ranges from 0 to $n-1$; $m_l$ ranges from $-l$ to $+l$

Hydrogen Atom and Atomic Orbitals

• Schrödinger Equation: Describes the probability distribution of electrons

• Shapes of Orbitals: s (spherical), p (dumbbell), d (cloverleaf), f (complex)

• Nodes: Regions where the probability of finding an electron is zero

• Phase: Refers to the sign of the wave function in different regions of space

Additional info:

• Students should be familiar with the rules for quantum number combinations and the physical meaning of each quantum number.

• Understanding the historical context of atomic models (Dalton, Thomson, Rutherford, Bohr) is helpful for conceptual questions.