The Mole

Counting With Moles

    What are Moles?

  • A mole is a specific quantity, like one dozen (12), used to count large amounts of entities (atoms, molecules, etc.)
  • One mole of something contains exactly the number of entities given by Avogadro's number
  • Avogadro's Number: 6.02 * 1023 (rounded to 3 significant digits)

    Molar Mass (M):

  • The mass of one mole of a substance, expressed in units of g/mol (grams per mole)
  • The molar mass of an element has the same value as the element's relative atomic mass
    • Example: carbon has a relative atomic mass of 12.01, hence its molar mass is 12.01 g/mol
  • The following equation can be used for molar conversions: M = m/n or n = m/M, where n is the number of moles, m is the mass in grams, and M is the molar mass

Using Moles With Chemical Formulas

    The Law of Definite Proportions:

  • For any given compound, the ratio of constituent elements is fixed
  • Example: every water molecule (H2O) is composed of exactly two hydrogen atoms, and one oxygen atom
  • This is useful, because we know that the ratio of atoms is the same in any sample of a given compound

    Percentage Composition:

  • The relative amount for each element in a compound, which is based on the mass of the individual elements and the total mass of the compound
  • Example (H2O):
    • First calculate the molar mass of the whole compound (2 * 1.01 + 16.00 = 18.02 g/mol)
    • Then find the molar mass of each element multiplied by its relative amount in a compound
      • Hydrogen has a molar mass of 1.01, and there are two hydrogens → 2.02 g/mol
      • Oxygen has a molar mass of 16.00, and there is one oxygen → 16.00 g/mol
    • Finally, divide the molar mass of each element by the total molar mass of the compound to get the percent composition (Hydrogen: 11%, Oxygen: 89%)

    Empirical Formula:

  • Represents the simplest whole-number ratio of atoms of each element in a chemical compound
  • This can be determined for a substance given its percent composition, by essentially working backwards where you find the relative molar amount of each element using its percent and molar mass
  • Example: the empirical formula of ethane (C2H6) is CH3

    Molecular Formula:

  • Represents the actual number of atoms of each element in a chemical compound
  • This can be determined for a substance given its empirical formula and total molar mass, where dividing the actual molar mass by the molar mass of the empirical formula gives the number that you have to multiply each element by in the formula
  • Example: the molecular formula of glucose is C6H12O6

Moles and Concentrations

    Concentration of a Solution (C):

  • The quantity of the solute dissolved in the solution as a ratio
  • This is often expressed as the number of moles or mass of the solute in a given volume

    Calculating Concentration From Mass

  • The concentration of a solution can be expressed in grams per cubic decimeter, and found by dividing the mass of the solute by the volume of the solution
  • C = m/V
    • C is the solution's concentration (g dm–3)
    • m is the solute's mass (g)
    • V is the total volume of the solution (dm3)

    Calculating Concentration From Moles

  • The concentration of a solution can be expressed in moles per cubic decimeter, and found by dividing the number of moles of the solute by the volume of the solution
  • C = n/V
    • C is the solution's concentration (mol dm–3)
    • n is the number of moles of the solute (mol)
    • V is the total volume of the solution (dm3)