3.1 Formula Mass and the Mole Concept

Formula mass and the mole concept are key to understanding chemical calculations. They help us quantify substances and their interactions at the atomic level, bridging the gap between the microscopic world of atoms and the macroscopic world we can measure.

These concepts are essential for stoichiometry, which allows us to predict quantities in chemical reactions. By mastering formula mass and moles, you'll be able to solve complex chemistry problems and understand how substances interact in precise ratios.

Formula Mass and Mole Concept

Formula masses of chemical compounds

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• Formula mass represents sum of atomic masses for all atoms in a chemical formula expressed in atomic mass units (amu) or grams per mole (g/mol)
• Calculate formula mass by identifying elements and subscripts in the compound
  • Locate atomic mass of each element using periodic table
  • Multiply atomic mass by subscript for each element
  • Sum products to determine overall formula mass
• Example: Calculating formula mass of glucose ($C_6H_{12}O_6$)
  • Carbon (C): 6 × 12.01 amu = 72.06 amu
  • Hydrogen (H): 12 × 1.01 amu = 12.12 amu
  • Oxygen (O): 6 × 16.00 amu = 96.00 amu
  • Formula mass of glucose = 72.06 amu + 12.12 amu + 96.00 amu = 180.18 amu or g/mol
• Example: Determining formula mass of sodium chloride (NaCl)
  • Sodium (Na): 1 × 22.99 amu = 22.99 amu
  • Chlorine (Cl): 1 × 35.45 amu = 35.45 amu
  • Formula mass of NaCl = 22.99 amu + 35.45 amu = 58.44 amu or g/mol
• Formula mass is used to calculate percent composition of compounds

Mole concept and Avogadro's number

• Mole represents amount of substance containing same number of particles as atoms in 12 grams of carbon-12
  • Avogadro's number ($6.022 \times 10^{23}$) quantifies particles in one mole
• One mole of any substance comprises Avogadro's number of particles (atoms, molecules, ions, or formula units)
• Molar mass signifies mass of one mole of a substance numerically equal to formula mass with units of grams per mole (g/mol)
• Relationship between moles and Avogadro's number: 1 mole = $6.022 \times 10^{23}$ particles and 1 mole of a substance = molar mass in grams
• Example: One mole of water ($H_2O$) contains $6.022 \times 10^{23}$ water molecules and has a molar mass of 18.02 g/mol
• Example: One mole of sodium (Na) consists of $6.022 \times 10^{23}$ sodium atoms and has a molar mass of 22.99 g/mol

Conversions in chemical substances

• Conversion factors based on mole concept: 1 mole = molar mass in grams and 1 mole = $6.022 \times 10^{23}$ particles
• Convert between mass and moles:
  1. Mass to moles: divide mass by molar mass
  2. Moles to mass: multiply number of moles by molar mass
• Convert between moles and number of particles:
  1. Moles to particles: multiply number of moles by Avogadro's number
  2. Particles to moles: divide number of particles by Avogadro's number
• Convert between mass and number of particles:
  1. Mass to particles: convert mass to moles, then moles to particles
  2. Particles to mass: convert particles to moles, then moles to mass
• Dimensional analysis sets up conversion problems ensuring correct units in final answer
• Example: Converting 25.0 grams of water ($H_2O$) to moles
  • Molar mass of $H_2O$ = 18.02 g/mol
  • $25.0\,g\,H_2O \times \frac{1\,mol\,H_2O}{18.02\,g\,H_2O} = 1.39\,mol\,H_2O$
• Example: Determining number of oxygen atoms in 0.500 moles of $O_2$
  • $0.500\,mol\,O_2 \times \frac{6.022 \times 10^{23}\,atoms\,O_2}{1\,mol\,O_2} \times \frac{2\,atoms\,O}{1\,molecule\,O_2} = 6.02 \times 10^{23}\,atoms\,O$

Chemical formulas and stoichiometry

• Empirical formula represents simplest whole-number ratio of atoms in a compound
• Molecular formula shows the actual number of atoms of each element in a molecule
• Stoichiometry uses mole ratios from balanced chemical equations to calculate quantities of reactants and products
• Limiting reagent determines the maximum amount of product that can be formed in a chemical reaction