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Chemistry Notes: Isotopes, Mass Spectrometry, and Formulas (Study Notes)

Isotope composition of chlorine

  • Chlorine has two main isotopes commonly discussed:
    • $^{35}$Cl with mass ≈ 35 amu
    • $^{37}$Cl with mass ≈ 37 amu
  • If we denote:
    • $x$ = fraction (or percent) of $^{35}$Cl
    • $y$ = fraction (or percent) of $^{37}$Cl
    • Mass balance: $y = 1 - x$
  • The average atomic mass of chlorine is given as about $35.4$ amu. Using the weighted average:
    • 35x + 37(1 - x) = 35.45 ext{ or } 35.4
    • Solve: $-2x = -1.55
      ightarrow x \, ext{≈}\, 0.775$ (≈ 77.5%) for $^{35}$Cl, and $y = 1 - x \, ext{≈}\, 0.225$ (≈ 22.5%) for $^{37}$Cl.
  • If the instructor uses a rounded average of $35.4$, the result is about 75–78% for $^{35}$Cl depending on the exact average used; the key idea is that chlorine is a mix of isotopes whose weighted average gives the observed atomic mass.
  • When looking at the periodic table and element masses:
    • Hydrogen: about $1.007$ amu
    • Carbon: about $12.01$ amu
    • Oxygen: about $16.00$ amu
    • Chlorine: about $35.4$ amu (average of isotopes)
    • These are average atomic masses, accounting for isotopic composition.

How isotopes are measured: mass spectrometry

  • Mass spectrometry can determine isotope abundances by separating ions in a magnetic field.
  • Process (brief):
    • Ions are formed from the sample and passed through a device with a magnetic field.
    • The path of an ion deflects depending on its mass-to-charge ratio; heavier ions bend less.
    • A detector records the deflection pattern, producing signals corresponding to different isotopes.
    • A computer analyzes the signal to give relative abundances of each isotope in the sample.
  • Connection to electrons: the same general device physics (deflection by magnetic field) is used to separate charged species; ionization is a prerequisite step.

Notation for chemical formulas and counting atoms

  • A formula lists the atoms present in a molecule and their counts using subscripts:
    • Example: one carbon atom and four hydrogen atoms → $
      \,\mathrm{CH_4}
      $ (CH with a subscript 4).
  • If the subscript is 1, it is omitted:
    • $\mathrm{CH_4}$ means 1 C and 4 H.
  • Subscripts indicate how many atoms of each element are in the molecule.
  • When a compound has only certain elements, only those elements appear in the formula (no extraneous elements).
  • Drawing representations: ball-and-stick or space-filling models can visualize the arrangement of atoms in space.
  • The visual models are tools; the chemical formula encodes composition, not the exact 3D geometry.

Diatomic and polyatomic representations for hydrogen

  • Hydrogen can be represented in multiple ways:
    • Atomic hydrogen: $\mathrm{H}$ (one hydrogen atom).
    • Molecular hydrogen, hydrogen gas: $\mathrm{H_2}$ (two hydrogens bonded together).
  • When a coefficient is placed in front of a formula, it denotes the number of discrete units (not necessarily bonded) of that formula:
    • $2\,\mathrm{H}$ means two hydrogen atoms not bonded.
    • $\mathrm{H_2}$ with a subscript 2 means one hydrogen molecule consisting of two bonded hydrogens.
    • $2\,\mathrm{H_2}$ means two hydrogen molecules (four hydrogen atoms in total, arranged as two H–H units).

Ionic compounds: formation and the empirical formula

  • Ionic bonding basics:
    • Metals tend to lose electrons to form positive ions (cations).
    • Nonmetals tend to gain electrons to form negative ions (anions).
    • Electrostatic attraction between oppositely charged ions holds the compound together.
  • Example: titanium and oxygen form titanium(IV) oxide.
    • Titanium (Ti) is a metal; oxygen (O) is a nonmetal.
    • Ti tends to lose electrons; O tends to gain electrons.
    • The resulting ions balance to form an ionic compound with a neutral overall charge.
    • The empirical formula for this ionic compound is $\mathrm{TiO_2}$, representing the smallest whole-number ratio of ions in the solid.
  • Polyatomic ions and formula units:
    • Calcium hydroxide contains the polyatomic ion $\mathrm{OH^-}$ and is written as $\mathrm{Ca(OH)_2}$.
    • The sulfate ion is $\mathrm{SO4^{2-}}$; compounds containing sulfate can be written with that group: for example, aluminum sulfate $\mathrm{Al2(SO4)3}$ (2 aluminum atoms and 3 sulfate groups).
  • Key takeaway: ionic formulas reflect the smallest whole-number ratio of ions in the crystal (empirical formula for ionic compounds).

Covalent compounds: sharing electrons and formulas

  • Covalent (molecular) bonding occurs when nonmetals share electrons.
  • In covalent compounds, the molecular formula lists all atoms present in the molecule.
  • The empirical formula for a covalent compound is the smallest whole-number ratio of elements in the compound.
  • Benzene as an example:
    • Molecular formula: $\mathrm{C6H6}$ (six carbons, six hydrogens).
    • Empirical formula: the smallest whole-number ratio of carbons to hydrogens.
    • Calculation: dividing by the greatest common divisor of the subscripts (6 and 6) → $\mathrm{CH}$.
    • Transcript note: the speaker mentioned an empirical form resembling $\mathrm{COH_2}$, which would be an error for benzene; the correct empirical formula is $\mathrm{CH}$.
  • The order of elements in a formula does not affect its identity or meaning; different valid representations can exist depending on the chosen convention or focus (structure, symmetry, or naming).
  • The speaker also emphasized that knowing the molecular formula does not always uniquely determine the arrangement; sometimes the structure (which hydrogen atoms are bonded to which carbons) matters for properties and reactivity.

Hydrogen bonding and structural considerations in molecules

  • Hydrogen atoms attached to carbon or other atoms can be arranged in various structural motifs.
  • The speaker highlighted that, for a given molecular formula, there can be multiple ways to depict the arrangement, and sometimes it is important to discuss specific hydrogens (e.g., hydrogens attached to a particular carbon) to explain behavior or reactivity.
  • Visual models (ball-and-stick vs space-filling) help convey different aspects of molecular geometry and surface properties.

Connections and practical implications

  • Isotope composition affects the atomic mass and can be probed experimentally via mass spectrometry, which in turn informs about isotopic abundances and elemental composition.
  • The distinction between ionic and covalent bonding explains why some formulas are written as empirical formulas (for ionic compounds) versus full molecular formulas (for covalent compounds).
  • Polyatomic ions (e.g., OH^-, SO_4^{2-}) are commonly used building blocks in ionic compounds and affect naming, stoichiometry, and properties.
  • Understanding empirical formulas helps in determining simplest ratio formats, which is especially important in balancing charges and stoichiometry in reactions.
  • The ability to switch between different representations (molecular vs empirical, ball-and-stick vs space-filling) supports deeper understanding of structure–property relationships, reactivity, and materials design.

Key formulas and notations (recap with LaTeX)

  • Isotope balance example:
    • Weighted average mass equation: 35x + 37(1 - x) = 35.45 \, (\text{amu})
    • Solution: x \approx 0.775 \Rightarrow \text{77.5% }^{35}\mathrm{Cl}, \; \text{22.5% }^{37}\mathrm{Cl}
  • Atomic masses cited in context:
    • mH \approx 1.007\ \text{amu},\; mC \approx 12.01\ \text{amu},\; mO \approx 16.00\ \text{amu},\; m{Cl} \approx 35.4\ \text{amu}
  • Ionic compound example formula:
    • \mathrm{TiO_2}
    • Polyatomic ion hydroxide: \mathrm{OH^-}
    • Calcium hydroxide: \mathrm{Ca(OH)_2}
    • Aluminum sulfate: \mathrm{Al2(SO4)_3}
  • Covalent compound example:
    • Molecular benzene: \mathrm{C6H6}
    • Empirical formula of benzene: \mathrm{CH}
  • Hydrogen representations:
    • Atomic hydrogen: \mathrm{H}
    • Molecular hydrogen: \mathrm{H_2}
  • General note on subscripts and ordering: subscripts denote counts; the order of elements in a formula is flexible for representation purposes but does not change composition.

Quick study tips drawn from the transcript

  • Practice deriving the isotopic composition from an average atomic mass using the weighted-average formula.
  • Be able to distinguish between empirical formulas (ionic compounds) and molecular formulas (covalent compounds).
  • Memorize common ions and their roles in polyatomic ion groups (e.g., OH^-, SO_4^{2-}).
  • Practice converting a molecular formula to its empirical formula and recognize when the empirical formula represents the simplest ratio rather than the actual count in a given molecule.
  • Use ball-and-stick and space-filling models to reinforce understanding of structure, while recognizing that different representations emphasize different aspects of bonding and geometry.

Summary

  • Isotopes contribute to the average atomic mass; mass spectrometry can quantify isotope abundances by deflection in a magnetic field.
  • Chemical formulas indicate which atoms are present and in what counts; subscripts convey multiplicity; 1 is omitted.
  • Ionic compounds are best described by empirical formulas reflecting the simplest ion ratio; covalent compounds use molecular formulas to show actual atom counts.
  • Polyatomic ions are common building blocks, influencing formula writing and bonding.
  • Hydrogen can exist as atoms or as H_2 molecules; coefficients denote the number of units and whether they are bonded.
  • Different formula representations and models support a deeper understanding of structure, bonding, and reactivity, which are essential for problem-solving on exams.