Chapter 2. Atomic Structure, Isotopes, Mass Spectrometry, and Chemical Nomenclature

Learning Objectives

• Explain key observations and experiments that led to the atomic description of matter.

• Define the structural parts of an atom, including subatomic particles: protons, electrons, and neutrons.

• Identify ions and isotopes, and explain the fundamental differences between them.

• Perform quantitative calculations involving isotopic mass and relative elemental abundances.

• Identify common ionic charges from an element's position on the periodic table.

• Write chemical formulas from compound names, and systematically determine names from chemical formulas for:

  • Ionic compounds

  • Ionic compounds with transition metals (variable oxidation states)

  • Molecular (covalent) compounds

  • Acids (binary and oxyacids)

  • Common chemical species

• Identify prefix conventions associated with carbon chain lengths in organic molecules.

Fundamental Atomic Theory and Chemical Laws

Law of Conservation of Matter

• Mass is neither created nor destroyed during a chemical process.

• Chemical reactions merely rearrange or relocate atoms.

• This law restricts the possible outcomes of chemical reactions and provides the foundation for stoichiometry.

Law of Multiple Proportions

• When two elements combine to form a series of distinct compounds, the ratios of the masses of the second element that combine with a fixed mass of the first element can always be reduced to small whole numbers.

• Chemical combination occurs through whole numbers of discrete atomic units.

Mass Combination Ratios and Volumetric Relationships

• Nature only allows certain combinations of masses

• Oxygen and hydrogen react predominantly in an $8:1$ mass ratio to form water ($\text{H}_2\text{O}$):   $\frac{16\,\text{g oxygen}}{2\,\text{g hydrogen}} = \frac{8\,\text{g oxygen}}{1\,\text{g hydrogen}}$

• Water ($\text{H}_2\text{O}$) consists of $2\,\text{mol}$ of hydrogen ($1\,\text{g}$ per mole) and $1\,\text{mol}$ of oxygen ($16\,\text{g}$ per mole).

• Hydrogen and oxygen can also combine to form hydrogen peroxide ($\text{H}_2\text{O}_2$):   $\frac{32\,\text{g oxygen}}{2\,\text{g hydrogen}} = \frac{16\,\text{g oxygen}}{1\,\text{g hydrogen}}$

• Comparing the oxygen mass per $1\,\text{g}$ of hydrogen between $\text{H}_2\text{O}_2$ ($16\,\text{g}$) and $\text{H}_2\text{O}$ ($8\,\text{g}$) yields a simple whole-number ratio of $2:1$.

• Volumetric Gas Behavior:

  • $2$ volumes of hydrogen gas react with $1$ volume of oxygen gas to yield $2$ volumes of water vapor.

  • Under identical temperature and pressure conditions, equal volumes of gas contain equal numbers of particles.

Subatomic Structure of the Atom

Subatomic Particles

• Protons ($\text{p}^+$): Positively charged subatomic particles located densely within the atomic nucleus.

• Neutrons ($\text{n}^0$): Electrically neutral subatomic particles located densely within the atomic nucleus.

• Electrons ($\text{e}^-$): Negatively charged subatomic particles occupying the space outside the nucleus.

• Nucleus: The central part of an atom, composed of protons and neutrons, containing most of the atom's mass.

• Electron Cloud: The region around the nucleus where electrons are likely to be found, defined by probability distributions.

Historical Experiments

• Millikan's Oil Drop Experiment: Measured the magnitude of the fundamental electric charge of an electron.

• Rutherford Gold Foil Experiment: Demonstrated that the atom contains an extremely dense, positively charged central nucleus containing protons ($\text{p}^+$) and neutrons ($\text{n}^0$), surrounded mostly by empty space.

Atomic Mass Units

• Because atomic masses are exceptionally small, standard mass units like grams are impractical.

• Atomic Mass Unit ($\text{amu}$), also designated as Dalton ($\text{Da}$) or unified atomic mass unit ($\text{u}$):   $1\,\text{amu} = 1.6606 \times 10^{-24}\,\text{g}$

Atomic Symbols, Isotopes, and Ions

Atomic Notation

Chemical species are represented using the standard notation: ${}_Z^A\text{X}^c$

• $\text{X}$: Chemical symbol of the element.

• $Z$: Atomic Number = total number of protons in the nucleus (defines element identity).

• $A$: Mass Number = total number of protons + total number of neutrons ($A = Z + \text{neutrons}$).

• $c$: Net Charge = number of protons minus number of electrons ($c = \text{protons} - \text{electrons}$).

Comparative Data for Isotopic and Ionic Species

Definitions of Key Terms

• Isotopes: Atoms of the same element containing identical numbers of protons ($Z$) but different numbers of neutrons, resulting in different mass numbers ($A$). Examples include ${}_6^{12}\text{C}$ vs. ${}_6^{13}\text{C}$ and ${}_1^1\text{H}$ vs. ${}_1^2\text{H}$.

• Ions: Charged chemical species formed when a neutral atom gains or loses electrons.

  • Cation: Positively charged ion resulting from electron loss (contains more $\text{p}^+$ than $\text{e}^-$).

  • Anion: Negatively charged ion resulting from electron gain (contains more $\text{e}^-$ than $\text{p}^+$).

• Ion Charge Determination: The net charge exponent is calculated as:   $\text{Charge} = \text{number of protons} - \text{number of electrons}$

Isotopic Mass Calculations

Average Atomic Mass

• Elements found in nature usually exist as mixtures of two or more stable isotopes.

• The atomic mass reported on the periodic table represents a weighted average of isotopic masses based on natural fractional abundances:   $\text{Average Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})$

Sample Calculation: Silicon

Silicon possesses three naturally occurring isotopes:

• ${}^{28}\text{Si}$: $92.23\%$ relative abundance ($0.9223$ fraction), isotopic mass = $27.9769\,\text{amu}$

• ${}^{29}\text{Si}$: $4.67\%$ relative abundance ($0.0467$ fraction), isotopic mass = $28.9765\,\text{amu}$

• ${}^{30}\text{Si}$: $3.10\%$ relative abundance ($0.0310$ fraction), isotopic mass = $29.9738\,\text{amu}$

Computation: $\text{Average Atomic Mass} = (0.9223 \times 27.9769\,\text{amu}) + (0.0467 \times 28.9765\,\text{amu}) + (0.0310 \times 29.9738\,\text{amu})$ $\text{Average Atomic Mass} = 25.80310023\,\text{amu} + 1.35320255\,\text{amu} + 0.9291878\,\text{amu} = 28.08549058\,\text{amu} \approx 28.09\,\text{amu}$

Mass Spectrometry and Molecular Mass Determination

Principles of Mass Spectrometry

Mass spectrometers measure the precise molecular masses and isotopic distributions of substances.

1. Sample Vaporization & Ionization: The sample is vaporized and irradiated with an electron beam, knocking off electrons to form positive ions.

2. Deflection via Electromagnet: An adjustable electromagnet exerts a magnetic field on the moving ion beam.

3. Mass-to-Charge Separation: Ions are separated based on their mass-to-charge ratio ($m/Z$):

   • Ions with an $m/Z$ ratio that is too large bend too little.

   • Ions with an $m/Z$ ratio that is too small bend too much.

   • Only ions with the specific, tuned $m/Z$ ratio follow the trajectory into the detector.

4. Data Output: A plot of relative signal intensity versus $m/Z$ produces a mass spectrum.

Mass Spectra Analysis Examples

• Acetylene ($\text{C}_2\text{H}_2$): Features a radical molecular cation peak $\text{M}^{+\bullet}$ at $m/Z = 26\,\text{amu}$.

• Benzene ($\text{C}_6\text{H}_6$): Features a dominant molecular ion peak $\text{M}^{+\bullet}$ at $m/Z = 78\,\text{amu}$, with fragmentation peaks appearing at $m/Z = 15, 26, 39, 50, 51, 63$

Molecular Formula Determination

Determining a compound's true molecular formula requires two pieces of analytical data:

1. Empirical Formula (EF): Derived from mass percentage composition.

2. Molecular Mass: Derived from mass spectrometry data.

$\text{Molecular Formula} = (\text{Empirical Formula}) \times \left( \frac{\text{Molecular Mass}}{\text{Empirical Formula Mass}} \right)$

• Acetylene Example:

  • Empirical Formula: $\text{CH}$ (mass = $13\,\text{amu}$)

  • Molecular Mass: $26\,\text{amu}$

  • Multiplier: $\frac{26\,\text{amu}}{13\,\text{amu}} = 2$

  • Molecular Formula: $\text{C}_2\text{H}_2$

• Benzene Example:

  • Empirical Formula: $\text{CH}$ (mass = $13\,\text{amu}$)

  • Molecular Mass: $78\,\text{amu}$

  • Multiplier: $\frac{78\,\text{amu}}{13\,\text{amu}} = 6$

  • Molecular Formula: $\text{C}_6\text{H}_6$

Isotopically Enriched Mass Spectrum Case Study

Consider an oxygen gas sample ($\text{O}_2$) isotopically enriched to contain $50\%$ ${}^{16}\text{O}$ and $50\%$ ${}^{18}\text{O}$:

• Possible Diatomic Combinations:

  • ${}^{16}\text{O}{}^{16}\text{O}$: mass = $32\,\text{amu}$; probability = $0.50 \times 0.50 = 0.25$ ($25\%$)

  • ${}^{16}\text{O}{}^{18}\text{O}$ and ${}^{18}\text{O}{}^{16}\text{O}$: mass = $34\,\text{amu}$; probability = $2 \times (0.50 \times 0.50) = 0.50$ ($50\%$)

  • ${}^{18}\text{O}{}^{18}\text{O}$: mass = $36\,\text{amu}$; probability = $0.50 \times 0.50 = 0.25$ ($25\%$)

Mass Spectrum Characteristics

• Three distinct peaks at $m/Z = 32, 34, 36$ exhibiting a relative intensity ratio of $1:2:1$.

Periodic Table Organization and Common Ionic Charges

Standard Group Charges

Classification of Cations and Monatomic Anions

Type I Cations (Fixed Charge)

• Group 1A cations: $\text{Li}^+$, $\text{Na}^+$, $\text{K}^+$, $\text{Rb}^+$, $\text{Cs}^+$

• Group 2A cations: $\text{Mg}^{2+}$, $\text{Ca}^{2+}$, $\text{Sr}^{2+}$, $\text{Ba}^{2+}$

• Additional fixed charge metals: $\text{Al}^{3+}$, $\text{Ga}^{3+}$, $\text{Zn}^{2+}$, $\text{Ag}^+$, $\text{Cd}^{2+}$

Type II Cations (Variable Charge Transition & Post-Transition Metals)

• Chromium: $\text{Cr}^{2+}$, $\text{Cr}^{3+}$

Naming Chemical Compounds

Writing chemical formulas and systematically determining names for compounds involves understanding the different types of chemical species and their nomenclature standards.

1. Ionic Compounds

   • Metal with a nonmetal

   • Electron transferred from one atom to another and electrostatic attraction holds compound together

   • Ionic compounds consist of cations and anions.

   • The name of the cation is written first followed by the name of the anion.

   • Simple anions are named by changing the end of the element's name to 'ide'.

   • Formula for binary ionic compound represents the minimum number of each ion that when combined will provide equal numbers of positive and negative electrical charges (a neutral formula unit)

   • For example, sodium chloride (NaCl) is composed of sodium ions (Na⁺) and chloride ions (Cl⁻).

1. Ionic Compounds with Transition Metals (Variable Oxidation States)

   • Transition metals can have more than one oxidation states, so their charge must be indicated in the name.

   • This is done using Roman numerals.

   • For example, iron(III) chloride indicates that iron has a +3 charge (Fe³⁺) combined with chloride ions (Cl⁻), resulting in FeCl₃.

   • CuBr - Copper(I) Bromide

   • FeS - Iron(II) sulfide

   • PbO2 - Lead(IV) odixe

2. Ionic Compounds containing Polyatomic Ions

1. Molecular (Covalent) Compounds

   • Molecular compounds are formed between two nonmetals.

   • Greek prefixes are used to denote the number of atoms of each element in the compound.

   • For example, carbon dioxide (CO₂) consists of one carbon atom and two oxygen atoms.

2. Acids (Binary and Oxyacids)

   • Binary acids consist of hydrogen and a nonmetal.

   • The name usually starts with "hydro-" and ends with "-ic" (e.g., hydrochloric acid for HCl).

   • Oxyacids contain hydrogen, oxygen, and another element.

   • The naming depends on the polyatomic ion: if it ends in "-ate," change it to "-ic"; if it ends in "-ite," change it to "-ous" (e.g., H₂SO₄ is sulfuric acid; H₂SO₃ is sulfurous acid).

3. Common Chemical Species

   • Certain chemical species have established names that must be learned (e.g., ammonia for NH₃, water for H₂O).

   • Understanding these can help with recognizing chemical compounds in different contexts.

Question 3: Atomic Symbol Validity

• Prompt: The atomic symbol ${}_{17}^{35.453}\text{Cl}$ is incorrect because:

  • A. The number of protons is incorrect

  • B. There are too many neutrons

  • C. The mass number should be a whole number

  • D. It is fine

• Correct Answer: C. The mass number should be a whole number

• Explanation: The superscript $A$ in ${}_Z^A\text{X}$ represents the mass number (count of protons + neutrons), which must be a whole integer, not an average atomic weight ($35.453$).

Question 4: Monatomic Cation Naming

• Prompt: The correct name for $\text{Ca}^{2+}$ is:

  • a) calcium

  • b) calcium(II) ion

  • c) calcium ion

  • d) calcium(I) ion

  • e) monocalcium ion

• Correct Answer: c) calcium ion

• Explanation: Calcium is a Group 2A alkali earth metal with a fixed charge of $2+$, so Roman numerals are not used.

Question 5: Transition Metal Cation Naming

• Prompt: The correct name for $\text{V}^{3+}$ is:

  • a) vanadide

  • b) vanadite ion

  • c) vanadium(III) ion

  • d) vanadium(V) ion

  • e) trivanadium ion

• Correct Answer: c) vanadium(III) ion

• Explanation: Vanadium is a transition metal with variable oxidation states; the $3+$ charge is specified by Roman numeral (III).

Question 6: Formula Writing

• Prompt: The formula for magnesium fluoride is:

  • A. $\text{MgF}$

  • B. $\text{MgF}_2$

  • C. $\text{Mg}_2\text{F}$

  • D. $\text{MgF}_4$

  • E. None of the above

• Correct Answer: B. $\text{MgF}_2$

• Explanation: Magnesium forms $\text{Mg}^{2+}$ and fluoride is $\text{F}^-$. Charge balance requires two $\text{F}^-$ per $\text{Mg}^{2+}$.

Question 7: Counting Atoms in Complex Formulas

• Prompt: $\text{Fe(CO)}_6\text{Cl}_3$ has:

  • A. $6$ carbon atoms and $3$ oxygen atoms

  • B. $1$ carbon atom and $6$ oxygen atoms

  • C. $6$ carbon atoms and $6$ oxygen atoms

  • D. $1$ carbon atom and $1$ oxygen atom

  • E. None of these

• Correct Answer: C. $6$ carbon atoms and $6$ oxygen atoms

• Explanation: Subscript $6$ outside the parentheses applies to both Carbon and Oxygen in the carbonyl ($\text{CO}$) ligands.

Question 8: Identifying Nomenclature Errors

• Prompt: Which of the following compounds is named incorrectly?

  • A. $\text{KNO}_3$ potassium nitrate

  • B. $\text{TiO}_2$ titanium(II) oxide

  • C. $\text{Sn(OH)}_4$ tin(IV) hydroxide

  • D. $\text{PBr}_5$ phosphorus pentabromide

  • E. $\text{CaSO}_4$ calcium sulfate

• Correct Answer: B. $\text{TiO}_2$ titanium(II) oxide

• Explanation: Oxide is $\text{O}^{2-}$. Two oxide ions equal a $4-$ charge. Titanium must be $\text{Ti}^{4+}$, so the correct systematic name is titanium(IV) oxide.

Question 9: Correct Naming Evaluation

• Prompt: Which of the following names is/are correct?

  1. sulfide, $\text{S}^{2-}$

  2. ammonium chloride, $\text{NH}_4\text{Cl}$

  3. hydrobromic acid, $\text{HBr}$

  4. barium oxide, $\text{BaO}$

  • a) all

  • b) none

  • c) 1, 2

  • d) 3, 4

  • e) 1, 3, 4

• Correct Answer: a) all

• Explanation: All four chemical names and formulas provided are correct.