Definitions of a mole

Key Concepts

• Mole is abbreviated to mol and given the symbol n

• 1 mole contains the same number of particles as there are in 12g of carbon-12 atoms by definition.
  This number is called Avogadro's number or Avogadro's constant (N_A) and is equal to 6.022 x 10²³ particles.

• 1 mole of a pure substance has a mass in grams equal to its molecular mass (MM) [also known as molecular weight (MW) or formula mass (FM) or formula weight (FW)].
  This is often referred to as the molar mass.

• 1 mole of an ideal gas has a volume of:

      22.4 litres (22.4L) at S.T.P.
      [Standard Temperature and Pressure, 0^oC (273K) and 101.3kPa (1 atm)]

      24.47 litres (24.47L) at S.L.C
      [Standard Laboratory Conditions, 25^oC (298K) and 101.3kPa (1atm)]

Examples

Avogadro's Number (N_A)

• 1 mole of atoms or molecules contains 6.022 x 10²³ atoms or molecules
      eg, 1 mole of helium atoms (He) contains 6.022 x 10²³ helium atoms (He)

• To find the number of atoms in a known number of moles,
      multiply the moles by 6.022 x 10²³
      eg, 2 moles of helium atoms (He) contains 2 x 6.022 x 10²³
      = 1.2044 x 10²⁴ helium atoms. (He)

• To find the moles of atoms,
      divide the number of atoms by 6.022 x 10²³
      eg, If we have 4.2154 x 10²³ neon atoms, how many moles of neon atoms are there?
      Moles of neon atoms = (4.2154 x 10²³) ÷ (6.022 x 10²³)
      = 0.7 mol

• 1 mole of molecules contains 6.022 x 10²³ molecules.
      eg, 1 mole of oxygen molecules (O₂) contains 6.022 x 10²³ oxygen molecules (O₂).

• To find the moles of molecules,
      multiply the number of molecules by 6.022 x 10²³
      eg, ½ mole of oxygen molecules (O₂) contains ½ x 6.022 x 10²³
      = 3.011 x 10²³ oxygen molecules (O₂).

• To find the number of molecules,
      divide the moles of molecules by 6.022 x 10²³
      eg, If we have 6.022 x 10²¹ chlorine molecules (Cl₂), how many moles of chlorine molecules are there?
      Moles of chlorine molecules = (6.022 x 10²¹) ÷ (6.022 x 10²³)
      = 0.01 mol

• 1 mole of molecules does not necessarily contain 1 mole of atoms of each element in the formula
      eg, 1 mole of HCl WILL contain 1 mole of hydrogen atoms (H) and 1 mole of chlorine atoms (Cl)
      eg, 1 mole of HCl contains 6.022 x 10²³ hydrogen atoms and 6.022 x 10²³ chlorine atoms
      eg, 5 moles of oxygen molecules (O₂) contains 5 x 2 = 10 moles of oxygen atoms (O)
      eg, 5 moles of oxygen molecules contains 10 x 6.022 x 10²³ = 6.022 x 10²⁴ oxygen atoms.
      eg, 1 mole of ammonia molecules (NH₃) will contain 1 mole of nitrogen atoms (N) and 3 moles of hydrogen atoms (H)
      1 mole of ammonia molecules contains 6.022 x 10²³ nitrogen atoms and 3 x 6.022 x 10²³ = 1.8066 x 10²⁴ hydrogen atoms

Molar Mass

• 1 mole of a pure substance has a mass in grams equal to its molecular mass (MM).
      eg, 1 mole of Helium (a monatomic gas with the formula He) has a mass equal to its relative atomic mass, 4.003g
      eg, 1 mole of hydrogen gas (a diatomic gas with the formula H₂) has a mass equal to 2 x 1.008 = 2.016g
      eg, 1 mole of ammonia gas (NH₃) has a mass equal to 14.01 + (3 x 1.008) = 17.034g
      eg, 1 mole of water (H₂O) has a mass equal to (2 x 1.008) + 16.00 = 18.016g

Ideal Gas Volumes

• at S.T.P [0^oC (273K), 101.3kPa (1 atm)], an ideal gas has a volume of 22.4L

• To find the volume of a certain number of moles of gas, multiply the moles by 22.4L
      eg, What is the volume of 2.5 moles of chlorine gas at S.T.P?
      Volume of chlorine gas = 2.5 x 22.4 = 56.0L

• To find the moles of a certain volume of gas, divide the volume by 22.4L
      eg, How many moles of argon are in 3.36L of argon gas at S.T.P?
      moles of argon gas = 3.36 ÷ 22.4 = 0.15 mol

• at S.L.C [25^oC (298K), 101.3kPa (1 atm)], an ideal gas has a volume of 24.47L
      eg, To find the volume of a certain number of moles of gas, multiply the moles by 24.47L
      What is the volume of 0.2 moles of hydrogen sulfide gas at S.L.C?
      Volume of hydrogen sulfide gas = 0.2 x 24.47 = 4.894L

• To find the moles of a certain volume of gas, divide the volume by 24.47L
      eg, How many moles of carbon monoxide are in 70.5L of carbon monoxide gas at S.L.C?
      moles of argon gas = 70.5 ÷ 24.47 = 2.881 mol

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