Chapter 6 - Quantifying Atoms and Compounds

Relative Masses of Elements

• Masses of isotopes are relative to the mass of a carbon-12 atom, which is assigned a value of 12 exactly.

  • Hydrogen-1 has a relative mass of 1.

  • Carbon-13 has a relative mass of 13.

  • Carbon-14 has a relative mass of 14.

• Relative isotopic mass:

  • There are no units for relative masses.

  • Isotopic notation shows the mass number and symbol (e.g., ^{12}_6C or ^{12}C).

Relative Atomic Masses

• The periodic table contains values for relative atomic mass of elements.

• Most elements have two or more isotopes.

• Key Takeaway: Relative atomic mass is a weighted average of the sum of the (% abundance × relative isotopic mass).

• Formula: Ar = \frac{\Sigma (\% \text{ abundance } \times \text{ relative isotopic mass})}{100}

• Example: Chlorine has 2 isotopes:

  • 35-chlorine: 75% abundance

  • 37-chlorine: 25% abundance

  • Ar(Cl) = \frac{(75 \% \times 35) + (25 \% \times 37)}{100} = 35.5

Relative Molecular Masses

• Use the molecular formula to determine the relative molecular mass, M_r, of a molecule.

• Relative molecular masses do not have units.

• M_r is the weighted average of a molecule’s masses of the formula units on a scale where carbon-12's mass is exactly 12.

• Example: Carbon monoxide (CO)

  • M_r(CO) = Ar(C) + Ar(O) = 12.0 + 16.0 = 28.0

• Use subscripts in molecular formulas when determining the relative molecular mass of multiple atoms of the same element.

• Example: Water (H_2O)

  • Mr(H2O) = (2 \times Ar(H)) + (1 \times Ar(O)) = (2 \times 1.0) + (1 \times 16.0) = 18.0

Relative Formula Masses

• Use the chemical formula to determine relative formula mass, M_r, of an ionic compound.

• Relative masses do not have units.

• M_r is the weighted average of a substance’s masses of the formula units on a scale where carbon-12's mass is exactly 12.

• Example: Sodium chloride (NaCl)

  • M_r(NaCl) = Ar(Na) + Ar(Cl) = 23.0 + 35.5 = 58.5

• Use subscripts in chemical formulas when determining the relative formula mass of multiple ions.

• Example: Barium iodide (BaI_2)

  • Mr(BaI2) = Ar(Ba) + (2 \times Ar(I)) = 137.3 + (2 \times 126.9) = 391.1

Mass Spectrometry

• In mass spectrometry, a sample of an element is put into a mass spectrometer, and the output is a mass spectrum.

• Analytical technique.

• The x-axis shows mass-to-charge ratio (m/z).

• The number of peaks in a mass spectrum represents the number of isotopes of an element.

• The height of the peak represents the relative or percentage abundance of the particular isotope.

• Mass spectrometry: Analytical technique used to measure the mass of ions relative to their charge.

• Mass-to-charge ratio (m/z): The mass of an ion divided by its charge.

Avogadro's Constant and the Mole

• One mole of atoms = 6.02 \times 10^{23} atoms.

• Counting in moles is easier than working with extremely large numbers.

• 12 g exactly of C-12 = 1 mol C atoms.

• Entities are things that can be counted (e.g., atoms, molecules, ions, electrons).

• Mole: 6.02 \times 10^{23} entities.

• Entities: Atoms, molecules, compounds, ions, electrons.

• Avogadro’s constant, N_A: The number of atoms in exactly 12 g of ^{12}C, 6.02 \times 10^{23} \text{ mol}^{-1}.

• Relationship of mole to Avogadro's constant (formula): \text{n} = \frac{N}{N_A}

• Where:

  • n = amount of substance, in mole (mol)

  • N = number of particles (e.g. atoms, molecules, ions, electrons)

  • N_A = Avogadro’s constant, 6.02 \times 10^{23} \text{ mol}^{-1}

Molar Mass

• Molar Mass, M: The mass in g of one mol of substance, g mol-1.

  • Symbol: M

  • Units: g mol-1

• Relative Molecular Mass, Mr: Weighted average of a molecule’s masses of the formula units on a scale on which the mass of a carbon-12 atom is assigned a value of 12 exactly.

  • Symbol: Mr

  • Relative molecular mass does not have units.

• Relationship between mass and mole:

  • n = \frac{m}{M}

  • Where:

    • n = amount of substance, in mole (mol)

    • m = mass, in grams, g

    • M = Molar mass, g mol-1

Percentage Composition

• Percentage means parts of 100.

• Percentage composition: Percentage by mass of an element in a compound.

• Formula: The % by mass of an element in a compound = (\frac{\text{molar mass of element}}{\text{molar mass of compound}}) \times 100

Empirical Formula

• The empirical formula (EF) of a compound is the simplest ratio of elements in the compound.

Molecular Formula

• The molecular formula (n.) is the actual number of atoms of each element in a molecule.

• Steps to determine the molecular formula

  • Determine molar mass of EF.

  • Divide the molar mass of the molecule by the molar mass of EF.

  • Multiply the EF by the number obtained in step 2.