General Chemistry Exam 1 Study Guide: Atomic Structure and Amount of Substance

Section 1: Atomic Structure

Introduction

This section covers the fundamental concepts of atomic structure, including the composition of atoms, isotopes, atomic mass, electron configuration, and the interpretation of mass spectrometry data. Mastery of these topics is essential for understanding the behavior of elements and their interactions in chemical reactions.

Structure of the Atom

• Atoms are composed of protons (positively charged), neutrons (neutral), and electrons (negatively charged).

• The nucleus contains protons and neutrons, while electrons occupy regions around the nucleus called orbitals.

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

• Mass number (A): Total number of protons and neutrons in the nucleus.

• Isotopes: Atoms of the same element (same Z) with different numbers of neutrons (different A).

Atomic Mass and Isotopes

• Relative atomic mass (Ar): The weighted average mass of the atoms in a naturally occurring sample of the element, relative to 1/12 the mass of a carbon-12 atom.

• Relative isotopic mass: The mass of a specific isotope relative to 1/12 the mass of a carbon-12 atom.

• Relative atomic mass calculation: $A_r = \sum (\text{isotopic mass} \times \text{fractional abundance})$

• Relative molecular mass (Mr): The sum of the relative atomic masses of the atoms in a molecule.

• Relative formula mass: Used for ionic compounds; sum of the relative atomic masses of the ions in the formula unit.

Mass Spectrometry

• Mass spectrometer: Instrument used to determine the relative masses and abundances of isotopes.

• Key steps: ionization, acceleration, deflection, and detection.

• Mass spectra can be used to identify elements and calculate relative atomic masses.

• Interpreting mass spectra: Each peak corresponds to an isotope; the height (intensity) indicates relative abundance.

Electron Arrangement and Energy Levels

• Electrons are arranged in energy levels (shells) around the nucleus.

• Each shell is divided into sub-shells (s, p, d, f).

• Each sub-shell contains orbitals, which can each hold up to 2 electrons.

• Electron configurations can be written using sub-shell notation (e.g., 1s2 2s2 2p6), or shown in orbital box diagrams and energy level diagrams.

• Order of filling: Aufbau principle, Pauli exclusion principle, Hund's rule.

• First 36 elements: Know their electron configurations.

Ionization Energy

• Ionization energy: The energy required to remove one mole of electrons from one mole of gaseous atoms.

• First ionization energy: $\text{X}(g) \rightarrow \text{X}^+(g) + e^-$

• Factors affecting ionization energy:

  • Nuclear charge (number of protons)

  • Distance of electrons from the nucleus (atomic radius)

  • Shielding by inner electrons

• Trends:

  • Down a group: Ionization energy decreases (increased atomic radius and shielding)

  • Across a period: Ionization energy increases (increased nuclear charge, same shielding)

• Successive ionization energies: Each subsequent electron removed requires more energy.

• Ionization energies provide evidence for shell and sub-shell structure.

Summary Table: Subatomic Particles

Particle	Relative Mass	Relative Charge	Location
Proton	1	+1	Nucleus
Neutron	1	0	Nucleus
Electron	1/1836	-1	Orbitals around nucleus

Section 2: Amount of Substance

Introduction

This section focuses on the quantitative aspects of chemistry, including the mole concept, Avogadro's constant, calculations involving moles, solutions, gases, and chemical equations. Understanding these concepts is crucial for solving stoichiometric problems and analyzing chemical reactions.

The Mole and Avogadro's Constant

• Mole (mol): The amount of substance containing as many particles (atoms, molecules, ions) as there are atoms in 12 g of carbon-12.

• Avogadro's constant (NA): $6.022 \times 10^{23}$ particles per mole.

• Number of particles = moles $\times$ Avogadro's constant.

Calculating Moles and Mass

• To calculate moles from mass: $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar mass (g mol}^{-1})}$

• To calculate mass from moles: $\text{Mass (g)} = \text{Moles} \times \text{Molar mass (g mol}^{-1})$

• For solutions: $\text{Moles} = \text{Concentration (mol dm}^{-3}) \times \text{Volume (dm}^3)$

Ideal Gas Equation

• The ideal gas equation relates pressure, volume, temperature, and moles of a gas:

$\text{pV} = \text{nRT}$

• p = pressure (Pa), V = volume (m3), n = moles, R = gas constant ($8.314 \text{ J mol}^{-1} \text{K}^{-1}$), T = temperature (K).

• Convert units as necessary (e.g., °C to K: $T(\text{K}) = T(°\text{C}) + 273.15$).

Chemical Equations and Stoichiometry

• Write and balance full and ionic equations for reactions.

• Use state symbols: (s), (l), (g), (aq).

• Calculate the mass of a reactant or product from a balanced equation.

• Calculate the volume of gas produced or consumed using the ideal gas equation or molar volume at standard conditions.

Empirical and Molecular Formulas

• Empirical formula: Simplest whole-number ratio of atoms in a compound.

• Molecular formula: Actual number of atoms of each element in a molecule.

• To determine empirical formula from percentage composition:

  1. Convert percentages to masses (assume 100 g sample).

  2. Divide by atomic masses to get moles.

  3. Divide by smallest number of moles to get ratio.

• Molecular formula = (empirical formula)n, where n is an integer.

Atom Economy and Percentage Yield

• Percentage yield: $\text{Percentage yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100$

• Atom economy: $\text{Atom economy} = \frac{\text{Molar mass of desired product}}{\text{Total molar mass of products}} \times 100$

• High atom economy is desirable for economic and environmental reasons.

Summary Table: Key Equations

Equation	Purpose
$\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}$	Calculate moles from mass
$\text{Moles} = \text{Concentration} \times \text{Volume}$	Calculate moles in solution
$\text{pV} = \text{nRT}$	Ideal gas equation
$\text{Percentage yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100$	Calculate reaction yield
$\text{Atom economy} = \frac{\text{Molar mass of desired product}}{\text{Total molar mass of products}} \times 100$	Calculate atom economy

Additional info:

• High atom economy and yield are important for sustainable chemical manufacturing.

• Understanding the mole concept is foundational for all quantitative chemistry calculations.