avogadros number

Avogadro's Number and the Mole

Introduction

• Laboratory samples contain vast numbers of atoms, ions, or molecules.

• Example: A teaspoon of water has approximately 2 x 10^23 water molecules.

• Chemists utilize a counting unit, the mole, to handle these large quantities.

Understanding the Mole

• Definition: The mole (abbreviated as mol) is the counting unit in chemistry, analogous to everyday terms like dozen.

• One mole contains as many particles as there are atoms in 12 grams of isotopically pure carbon-12 (12C).

• Avogadro's Number: Approximately 6.022 x 10^23, denoting the number of particles in one mole of any substance.

• This number is also referred to as Na, in honor of Amedeo Avogadro.

• Avogadro's number is often written with units as molecules per mole (6.02 x 10^23 mol^-1).

Examples of Avogadro's Number

• One mole of 12C = 6.02 x 10^23 carbon atoms.

• One mole of water (H2O) = 6.02 x 10^23 H2O molecules.

• One mole of nitrate ions (NO3^-) = 6.02 x 10^23 NO3^- ions.

• The scale of Avogadro’s number is difficult to grasp; it could cover the Earth with a three-mile thick layer of marbles if evenly distributed.

Molar Mass

• Molar mass relates to the mass of one mole of a substance, expressed in grams per mole (g/mol).

• Each element has an atomic weight which corresponds to its molar mass in grams.

• Example: Carbon (C) has an atomic weight of 12 amu, so one mole of C weighs 12 g.

• For different elements, their mass per mole varies according to their atomic weights.

• Example Mass Comparisons:

  • 1 mole of 12C = 12 g

  • 1 mole of magnesium (24Mg) = 24 g

Relationship of Molar Mass and Atomic Mass

• The atomic weight of an element in atomic mass units (amu) numerically equals the mass in grams of one mole of that element.

• For example:

  • Chlorine (Cl) has an atomic weight of 35.5 amu, hence one mole of Cl atoms weighs 35.5 g.

  • Gold (Au) with an atomic weight of 197 amu, means one mole of Au weighs 197 g.

• Similar logic applies to compounds:

  • Water (H2O) has a molecular weight of 18 amu, so its molar mass is 18 g/mol.

  • Sodium chloride (NaCl) has a formula weight of 58.5 amu; consequently, its molar mass is 58.5 g/mol.

Importance of Chemical Form in Moles

• When discussing moles, the chemical form must be clear to avoid ambiguity.

• Example: "One mole of nitrogen" may refer to either nitrogen atoms (N) or nitrogen molecules (N2).

• For nitrogen (N2), the molar mass is different (28.0 g for N2 compared to 14.0 g for N).

• Always clarify whether referring to N or N2 in calculations and discussions.

Converting Between Mass, Moles, and Particles

• Chemical equations relate amounts of reactants and products using mole conversions.

• Dimensional Analysis helps in converting between grams, moles, and the number of particles:

  • Example Calculation:

    • Assume a copper penny weighs approximately 3 g (pure copper).

    • Molar mass of copper (Cu) = 63.5 g/mol.

    • To find copper atoms in the penny:

      • 3 g Cu × (1 mol Cu / 63.5 g Cu) × (6.02 x 10^23 Cu atoms / 1 mol Cu) = 3 x 10^22 Cu atoms.

• Large numbers are expected when calculating atoms in samples, while the number of moles may be small.