Atoms and the Periodic Table Study Guide

Organization of the Periodic Table

• Definition of the Periodic Table: A chart in which elements having similar chemical and physical properties are grouped together.
• Periods: The horizontal rows of the periodic table. Elements are arranged in periods in order of increasing atomic number.
• Groups: The vertical columns of the periodic table.
• Classification by Type:
  • Metals: These are defined as good conductors of heat and electricity.
  • Nonmetals: These are defined as poor conductors of heat or electricity.
  • Metalloids: These elements exhibit intermediate properties between those of metals and nonmetals.

Classification of Elements by Group

• Group 1A Elements: These are known as the alkaline metals. They include Lithium ($Li$), Sodium ($Na$), Potassium ($K$), Rubidium ($Rb$), Cesium ($Cs$), and Francium ($Fr$).
• Group 2A Elements: These are known as the alkaline earth metals. They include Beryllium ($Be$), Magnesium ($Mg$), Calcium ($Ca$), Strontium ($Sr$), Barium ($Ba$), and Radium ($Ra$).
• Group 6A Elements: These are known as the chalcogens. They include Oxygen ($O$), Sulfur ($S$), Selenium ($Se$), Tellurium ($Te$), and Polonium ($Po$).
• Group 7A Elements: These are known as the halogens. They include Fluorine ($F$), Chlorine ($Cl$), Bromine ($Br$), Iodine ($I$), and Astatine ($At$).
• Group 8A Elements: These are known as the noble gases. They include Helium ($He$), Neon ($Ne$), Argon ($Ar$), Krypton ($Kr$), Xenon ($Xe$), and Radon ($Rn$).
• Transition Elements: These include Groups 1B and 3B through 8B. They are also referred to as transition metals.

Fundamental Definitions and Molar Concepts

• The Mole: The mole is defined as the amount of a substance that contains as many elementary entities (atoms, molecules, or other particles) as there are atoms in exactly $12\,g$ of carbon-12.
• Avogadro’s Number ($N_A$): This is the experimentally determined number of entities in one mole.
  • Unrounded value: $N_A = 6.0221415 \times 10^{23}$
  • Standard rounded value: $6.022 \times 10^{23}$
  • Reference Comparison: $1\text{ mole} = 6.022 \times 10^{23}$, similar to how $1\text{ dozen} = 12$ or $1\text{ gross} = 144$.
• Molar Mass: The mass in grams of one mole of a substance.
  • By definition, the mass of a mole of carbon-12 is exactly $12\,g$.
  • Mass of 1 carbon-12 atom = exactly $12\,amu$.
  • Mass of 1 mole of carbon-12 = exactly $12\,g$.
  • Standard unit: Units are typically expressed in grams per mole ($g/mol$ or $g\,mol^{-1}$) to facilitate unit cancellation during chemical calculations.
• Interconverting Mass, Moles, and Atoms:
  • Mass to Moles: Molar mass is the conversion factor used to move from mass to moles or vice versa.
  • Moles to Atoms: Avogadro’s constant ($N_A$) is the conversion factor used to move from moles to the number of atoms.

Requirements for Element Knowledge

• Naming and Symbols: Students are expected to know the names and symbols for the first 36 elements of the periodic table.
• Latin Root Symbols: The following 10 elements possess symbols derived from their Latin names:
  • Sodium ($Na$)
  • Potassium ($K$)
  • Silver ($Ag$)
  • Copper ($Cu$)
  • Tin ($Sn$)
  • Antimony ($Sb$)
  • Tungsten ($W$)
  • Gold ($Au$)
  • Mercury ($Hg$)
  • Lead ($Pb$)
• Molecular Elements: Several elements exist naturally as diatomic molecules ($X_2$):
  • Hydrogen ($H_2$)
  • Nitrogen ($N_2$)
  • Oxygen ($O_2$)
  • Fluorine ($F_2$)
  • Chlorine ($Cl_2$)
  • Bromine ($Br_2$)
  • Iodine ($I_2$)
• Diatomic Mnemonics:
  • "I Bring Cookies For Our New Home"
  • "Have No Fear Of Ice Cold Beer"

The Atomic Theory and Scientific Principles

• Atom: The smallest identifiable unit of an element.
• Element: A substance that cannot be broken down into two or more simpler substances by any means. Examples include gold, oxygen, and helium.
• Separation Analogy: A collection of atoms can be separated into smaller numbers of atoms. However, if an individual atom is separated into smaller pieces (subatomic particles), those pieces are no longer that element.
• Dalton’s Atomic Theory:
  1. Elements are composed of small indivisible, indestructible particles called atoms.
  2. All atoms of a given element are identical and have the same mass and properties.
  3. Atoms of a given element are different from atoms of other elements.
  4. Compounds are formed by combinations of atoms of two or more elements.
  5. Chemical reactions involve the rearrangement of atoms; matter is neither created nor destroyed during a reaction.
• Definition of a Scientific Theory:
  • The best available explanation of existing evidence/data/observations.
  • Explains "how" and/or "why" a phenomenon occurs.
  • Makes testable predictions.
  • Is falsifiable (can be proven false by experimentation).
  • May change over time as new evidence is discovered.

Discovery and Evolution of Atomic Structure

• Cathode Ray Tube Experiments (Late 1800s): Scientists studied radiation (emission/transmission of energy as waves) using evacuated glass tubes containing two metal plates.
  • The Cathode: The negatively charged plate.
  • The Anode: The positively charged plate.
  • A high-voltage source causes the cathode to emit an invisible ray drawn to the anode. The ray is revealed when it strikes a phosphor-coated surface.
• J. J. Thomson (1856–1940):
  • Observed that cathode rays were repelled by negative charges and attracted to positive charges.
  • Proposed the rays were a stream of negatively charged particles called electrons.
  • Since atoms are neutrally charged, he proposed there must be a balancing positive charge.
  • Plum Pudding Model: Proposed the atom is a sphere of positively charged matter with negatively charged electrons embedded uniformly within it.
• Ernest Rutherford:
  • Used alpha ($\alpha$) particles to probe atomic structure.
  • Nuclear Model: Proposed that the positive charge is concentrated in a central core called the nucleus.
  • The nucleus accounts for most of the atom's mass and is extremely dense.
• Planetary Model: Includes electrons orbiting the nucleus. A historical note specifies that in a strict planetary model, an electron would lose energy and spiral into the nucleus, indicating a need for refined models.

Properties of Subatomic Particles

• Protons: Positively charged particles located in the nucleus.
• Neutrons: Electronically neutral particles located in the nucleus. They are slightly larger than protons.
• Electrons: Negatively charged particles distributed around the nucleus.

Table 2.1: Masses and Charges of Subatomic Particles

Atomic Identifiers and Isotopes

• Atomic Number ($Z$): The number of protons in the nucleus of an atom. In a neutral atom, this is also equal to the number of electrons. The atomic number determines the identity of the element.
• Mass Number ($A$): The total number of protons and neutrons in the nucleus.
• Nucleons: A collective term for protons and neutrons.
• Isotopes: Atoms that have the same atomic number ($Z$) but different mass numbers ($A$) due to varying numbers of neutrons.
  • Isotopes of the same element exhibit very similar chemical properties, forming the same types of compounds with similar reactivity.

Average Atomic Mass and Mass Spectrometry

• Atomic Mass Unit ($amu$): Defined as $1/12$ the mass of a carbon-12 atom.
• Average Atomic Mass: Represents the average mass of the naturally occurring mixture of isotopes for an element.
• Calculations (Example Carbon):
  • Isotope $^{12}C$: Isotopic mass = $12.00000\,amu$, Natural abundance = $98.93\%$.
  • Isotope $^{13}C$: Isotopic mass = $13.003355\,amu$, Natural abundance = $1.07\%$.
  • $\text{Average mass} = (0.9893) \times (12.00000\,amu) + (0.0107) \times (13.003355\,amu) = 12.01\,amu$.
• Mass Spectrometry: The most direct and accurate method for determining atomic and molecular masses using a mass spectrometer.

Questions & Discussion

• Question: Determine the number of $C$ atoms in $0.515\,g$ of carbon.
• Question: What is the mass of $1.0000\text{ mole}$ of silver atoms?
  • Answer choices: $6.022 \times 10^{23}\,g$, $107.87\,g$, $1.0000\,g$, $197.97\,g$, $23.520\,g$.
• Question: Which has more atoms: $1.01\,g$ of hydrogen atoms or $39.95\,g$ of argon?
  • Answer: Neither (both represent approximately $1\text{ mole}$ of atoms).
• Question: Which has more atoms: $1.01\,g$ of hydrogen gas ($H_2$) or $39.95\,g$ of argon?
  • Answer: Neither (molecular hydrogen mass is $2.02\,g/mol$, so $1.01\,g$ is $0.5\text{ moles}$ of $H_2$ molecules, which equals $1\text{ mole}$ of $H$ atoms).
• Question: How many atoms are in $5.60\,g$ of iron?
  • Calculated: $\frac{5.60\,g}{55.85\,g/mol} \times 6.022 \times 10^{23} \approx 6.04 \times 10^{22}\text{ Fe atoms}$.
• Question: A jeweler has a sample of Gold ($Au$) containing $3.01 \times 10^{22}$ atoms. What is the mass?
  • Calculated: $\frac{3.01 \times 10^{22}}{6.022 \times 10^{23}} \times 196.97\,g/mol \approx 9.85\,g$.
• Question: A hiker uses a portable oxygen canister ($O_2$) containing $18.7\,g$ of oxygen gas. How many oxygen atoms are present?
  • Calculated: $\frac{18.7\,g}{32.00\,g/mol} \times 2 \times 6.022 \times 10^{23} \approx 7.03 \times 10^{23}\text{ atoms}$.
• Question: A chlorine isotope has a mass number of $37$. How many neutrons does it have?
  • Answer: $37 - 17 = 20\text{ neutrons}$.
• Question: How many neutrons does $^{42}_{20}Ca$ have?
  • Answer: $42 - 20 = 22\text{ neutrons}$.
• Question: How many electrons does $^{42}_{20}Ca^{2+}$ have?
  • Answer: $20 - 2 = 18\text{ electrons}$.
• Question: Statements check for $^{90}_{37}Rb^{+}$.
  1. Has 90 protons (False, has 37).
  2. Has 90 neutrons (False, has $90 - 37 = 53$).
  3. Has 37 electrons (False, has $37 - 1 = 36$ for the cation).
• Question: Copper is $69.17\%$ $Cu-63$ ($62.9396\,amu$) and the rest is $Cu-65$ ($64.9278\,amu$). What is the average atomic mass?
  • Answer: $63.55\,amu$.
• Question: Chlorine has isotopes $Cl-35$ and $Cl-37$. Based on the periodic table ($35.45\,amu$), which is more abundant?
  • Answer: Chlorine-35 is more abundant.