General Chemistry I: Atomic Structure, Units, Periodic Table, and Measurement

Atomic Structure and Electron Configurations

Anomalous Electron Configurations

Certain elements exhibit electron configurations that deviate from the expected order due to increased stability associated with half-filled or fully filled subshells. These are known as anomalous electron configurations.

• Examples: Cr, Cu, Nb, Tc, Ru, Rh, Pd, Ag, Pt, Au

• For example, chromium (Cr) is expected to have the configuration [Ar] 4s2 3d4, but instead it is [Ar] 4s1 3d5.

• This occurs because half-filled (d5) and fully filled (d10) subshells are particularly stable.

Application: Understanding these exceptions is important for predicting chemical behavior and bonding.

Fundamental Constants and Unit Conversions

SI Units and Conversion Factors

Accurate measurement and conversion between units are essential in chemistry. Below are some common conversion factors and constants:

• 1 kg = 2.2046 lb

• 16 oz = 1 lb

• 1 m = 3.2808 ft

• 1 km = 0.6214 mi

• 1 gal = 3.78 L

Temperature Conversions

• $T(K) = T(^{\circ}C) + 273.15$

• $T(^{\circ}F) = \frac{9}{5} \times T(^{\circ}C) + 32$

Physical Constants

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

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

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

Wavelength and Energy Relationships

• Wavenumber: $\tilde{\nu} = \frac{1}{\lambda}$

• Rydberg equation for hydrogen spectral lines: $\frac{1}{\lambda} = R_\infty \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$ where $R_\infty = 1.097 \times 10^7 \ \text{m}^{-1}$

Dipole Moment

• Dipole moment ($\mu$) = charge ($Q$) × distance

• Charge of one electron: $1.60 \times 10^{-19}$ C

• 1 Debye (D) = $3.336 \times 10^{-30}$ C·m

The Periodic Table of the Elements

Organization and Groups

The periodic table arranges elements by increasing atomic number and groups elements with similar chemical properties into columns called groups or families.

• Main groups: Groups 1A–8A (1, 2, 13–18)

• Transition metals: Groups 3–12

• Lanthanides and actinides: F-block elements, often shown below the main table

Example: Alkali metals (Group 1) are highly reactive metals, while noble gases (Group 18) are inert.

Measurement, Precision, and Significant Figures

Accuracy vs. Precision

• Accuracy: How close a measurement is to the true value.

• Precision: How close repeated measurements are to each other.

Example: A set of darts clustered together but far from the bullseye is precise but not accurate.

Significant Figures

• Significant figures reflect the precision of a measured or calculated quantity.

• Rules:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros after a decimal point are significant.

Example: 0.00450 has three significant figures.

Dimensional Analysis and Problem Solving

Density Calculations

• Density ($d$): $d = \frac{\text{mass}}{\text{volume}}$

• Used to convert between mass and volume.

Example: If the density of chloroform is 1.4832 g/mL, the volume for 102.5 g is $\frac{102.5\ \text{g}}{1.4832\ \text{g/mL}} = 69.11\ \text{mL}$.

Unit Conversions

• Use conversion factors to change units (e.g., pounds to kilograms, micrometers to meters).

• Set up conversion so units cancel appropriately.

Example: 1 μm = $1 \times 10^{-6}$ m.

Atomic Structure and Quantum Numbers

Quantum Numbers

• Principal quantum number ($n$): Indicates the energy level (shell).

• Angular momentum quantum number ($l$): Indicates the subshell (s, p, d, f).

• Magnetic quantum number ($m_l$): Orientation of the orbital.

• Spin quantum number ($m_s$): Electron spin (+1/2 or -1/2).

Example: For a 4d orbital, $n = 4$, $l = 2$.

Orbital Diagrams and Electron Configurations

• Use the Aufbau principle, Hund's rule, and Pauli exclusion principle to fill orbitals.

• Some elements (see above) have anomalous configurations for extra stability.

Example: Nickel (Ni, Z=28): [Ar] 4s2 3d8

Periodic Trends and Properties

Atomic and Ionic Radii

• Atomic radius generally decreases across a period and increases down a group.

• Cations are smaller than their parent atoms; anions are larger.

Example: Sr2+ (215 pm) > Ca2+ (197 pm) > Br- (114 pm)

Classification of Elements

• Metals: Shiny, good conductors, malleable, ductile.

• Nonmetals: Dull, poor conductors, brittle.

• Metalloids: Properties intermediate between metals and nonmetals.

Example: Silicon is a metalloid.

Waves and Electromagnetic Spectrum

Electromagnetic Spectrum

• Order of increasing energy: microwave < infrared < visible < ultraviolet

• Wavelength and frequency are inversely related: $c = \lambda \nu$

Example: Ultraviolet light has higher energy and shorter wavelength than visible light.

Wave Properties

• Amplitude: Height of the wave.

• Wavelength ($\lambda$): Distance between peaks.

• Frequency ($\nu$): Number of cycles per second.

Sample Table: Periodic Trends (Inferred from Questions)

Element	Smallest	Second Smallest	Second Largest	Largest
Ca, Se, Kr, K	Kr	Se	Ca	K

Additional info: Table inferred from periodic trend question; actual values depend on atomic/ionic radii.

Sample Table: Unit Conversions

Quantity	Conversion
Mass	1 kg = 2.2046 lb
Length	1 m = 3.2808 ft
Volume	1 gal = 3.78 L

Applications and Problem Types

• Density and volume calculations

• Significant figures in calculations

• Temperature conversions between Celsius, Fahrenheit, and Kelvin

• Classification of elements based on properties

• Identification of periodic table groups and trends

• Electron configuration and orbital diagrams

• Quantum numbers and their allowed values

• Energy ordering of electromagnetic spectrum regions

• Calculation of LD50 and other applied chemistry problems