Quantitative Chemistry Notes

14A Quantitative Chemistry

Defining Relative Molecular Mass (RMM) or Formula Mass

• The RMM of a molecule is found by adding the atomic masses (RAM) of all the atoms in the molecule.
• To simplify calculations, round RAM to a whole number using the periodic table (e.g., H = 1.0079 rounds to 1; O = 15.9994 rounds to 16).
• Example: Water molecule (H2O)
  • Each H2O molecule contains 2 hydrogen atoms (H) joined to 1 oxygen atom (O).
  • RMM_{H2O} = (2 \times H) + O = (2 \times 1) + 16 = 18
  • RMM has no units; it is also called formula mass.

The Mole: A Word-Number

• The 'mole' is a word that represents a specific number, similar to 'dozen', 'pair', or 'ream'.
• 1 mole = 6.02 \times 10^{23} items (Avogadro's number).
• The number of items in a dozen is always 12.
• 1 mole is always the same number of items.
• Analogy: A pumpkin is heavier than an egg, so a dozen pumpkins weighs more than a dozen eggs, even though the number of items is the same.

Molar Mass

• The mass of 1 mole varies according to the size/mass of the atoms or molecules.
• 1 mole of H atoms weighs 1 gram.
• 1 mole of C atoms weighs 12 grams because a C atom is 12 times as heavy as an H atom.

The Mole as a Unit of Amount

• The mole is the number of atoms you have when you weigh out the relative atomic mass of an element in grams.
• 6.02 \times 10^{23} C atoms in 12 g of 12C = 1 mole of C
• 6.02 \times 10^{23} H atoms in 1 g of 1H = 1 mole of H
• 6.02 \times 10^{23} Pb atoms in 207 g of 207Pb = 1 mole of Pb

Historical Context of the Mole

• In the 18th century, Avogadro first described the mole as the number of atoms or molecules of a substance when you take the relative mass in grams.
• In the early 20th century, Avogadro’s number was calculated to be about 6.02 \times 10^{23} particles.
• As technology improves, this number has been measured to an increasing degree of accuracy.
• However, 1 mole of any substance always contains the same number of particles.

Molar Mass Defined

• The molar mass of a substance is the mass of 1 mole of that substance in grams.
• This is equal to the RMM or formula mass in grams.
• Units: grams per mole (g/mol or gmol-1)
• Example 1: Water (H2O) has an RMM of 18.
  • 1 mole of water weighs 18 grams.
  • The molar mass of H2O is 18 grams per mole.
  • A glass holding 180 g of water contains 10 moles of water (since 18 \times 10 = 180).
• Molar mass is a measurable amount.
• Example 2: Glucose (C6H12O6) contains:
  • 6 x C atoms (RAM of C = 12)
  • 12 x H atoms (RAM of H = 1)
  • 6 x O atoms (RAM of O = 16)
  • Adding the masses: (6 \times 12) + (12 \times 1) + (6 \times 16) = 72 + 12 + 96 = 180
  • The formula mass of C6H12O6 is 180.
  • The molar mass of glucose (C6H12O6) is 180 grams per mole.
  • 180g of glucose is 1 mole of glucose.
  • 360g of glucose is 2 moles.
  • 90g of glucose is 0.5 moles.

Calculations Using Molar Mass

• Find the molar mass of calcium carbonate, CaCO3.
• What will be the mass of:
  • (a) 2 moles of CaCO3?
  • (b) 0.5 moles of CaCO3?
  • (c) 0.1 moles of CaCO3?