$N_A = 6.022 \times 10^{23}$ particles per mole

$n = \frac{m}{M}$

• n = moles, m = mass (g), M = molar mass (g/mol)

Sum of atomic masses from periodic table: $M = \sum (\text{atomic mass} \times \text{number of atoms})$

Example: $H_2O = 2(1.008) + 15.999 = 18.015$ g/mol

$N = n \times N_A$

• N = number of particles (atoms, molecules, ions)
• Used to convert between moles and number of particles

Mass spectrometer measures mass-to-charge ratio (m/z)

• x-axis: m/z ratio (for +1 ions, this equals atomic mass)
• y-axis: relative abundance
• Peaks: represent different isotopes

Percentage of each isotope naturally occurring

• Determined from peak heights in mass spectrum
• Used to calculate weighted average atomic mass

Isotopes: Atoms of same element with different numbers of neutrons

• Same atomic number (Z), different mass number (A)
• Average atomic mass = Sigma(isotope mass × relative abundance)

Example: Chlorine has two naturally occurring isotopes:

• $^{35}$Cl (75.77% abundance, 34.969 amu)
• $^{37}$Cl (24.23% abundance, 36.966 amu)
• Average = $(0.7577 \times 34.969) + (0.2423 \times 36.966) = 35.45$ amu

1. Assume 100g sample (percent -> grams)
2. Convert grams -> moles for each element
3. Divide by smallest mole value
4. Multiply if needed to get whole numbers

Empirical formula: Simplest whole-number ratio of atoms Molecular formula: Actual number of atoms in molecule

Example: Glucose

• Molecular formula: $C_6H_{12}O_6$
• Empirical formula: $CH_2O$ (divide all subscripts by 6)

Calculating from percent composition or combustion data

1. Assume 100g sample (percent -> grams)
2. Convert grams -> moles for each element
3. Divide by smallest mole value
4. Multiply if needed to get whole numbers

Percent composition: $\% \text{element} = \frac{\text{mass of element in compound}}{\text{total mass}} \times 100\%$

Purity: Percentage of desired substance in mixture

For compound $C_xH_yO_z$: $\%C = \frac{x \times M_C}{M_{compound}} \times 100\%$

$F = k_e \frac{q_1 q_2}{r^2}$

Explains:

• Electrons closer to nucleus are more tightly held (higher binding energy)
• Increased nuclear charge -> stronger attraction for electrons
• Shielding by inner electrons reduces effective nuclear charge

Valence electrons: Outermost shell electrons; involved in chemical bonding

• Group number (for main group elements) = valence electrons

Core electrons: Inner shell electrons; not involved in bonding

• All electrons except those in outermost shell

Aufbau Principle: Fill orbitals from lowest to highest energy Pauli Exclusion Principle: Maximum 2 electrons per orbital with opposite spins Hund's Rule: One electron per orbital of equal energy before pairing

Order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p

Photoelectron spectroscopy measures binding energy of electrons

• x-axis: binding energy (higher BE = closer to nucleus)
• y-axis: signal intensity (number of electrons)
• Peaks: represent different subshells (s, p, d, f)
• Peak height: proportional to number of electrons in subshell

• Higher binding energy = electrons held more tightly
• s electrons have higher BE than p electrons in same shell
• BE increases across a period (greater Z_eff)
• BE decreases down a group (greater distance from nucleus)

Ionization Energy (IE): Energy required to remove electron from gaseous atom

• Left to right: Increases (greater Z_eff)
• Top to bottom: Decreases (greater distance, shielding)
• Large jump between removing valence vs. core electrons

Electronegativity (EN): Ability to attract electrons in covalent bond

• Left to right: Increases
• Top to bottom: Decreases
• Fluorine is most electronegative (4.0)

Atomic radius trends:

• Left to right: Decreases (increased effective nuclear charge)
• Top to bottom: Increases (additional electron shells)

Ionic radius:

• Cations are smaller than parent atoms (lose shell)
• Anions are larger than parent atoms (electron-electron repulsion)
• Isoelectronic series: more protons -> smaller ion

Energy change when electron is added to gaseous atom

• Generally increases left to right (more negative values)
• Generally decreases top to bottom
• Exceptions: Group 2 and Group 18 (full subshells)

Ionic bond forms between metal and nonmetal through electron transfer

• Metal loses electron(s) -> becomes cation (+)
• Nonmetal gains electron(s) -> becomes anion (-)
• Electrostatic attraction holds ions together

Octet rule: Atoms tend to gain/lose/share electrons to achieve noble gas configuration