The Avogadro Constant (OCR Gateway GCSE Chemistry: Combined Science)

The Mole & the Avogadro Constant

• Chemical amounts are measured in moles
  
• The mole, symbol mol, is the SI unit of amount of substance
  
• One mole of a substance contains the same number of the stated particles, atoms, molecules, or ions as one mole of
• any other substance
  
• Previously the mole was defined as the number of atoms present in exactly 12.00 g of carbon-12
• However, this definition was based on mass and so was not an SI unit
• In 2018, the International union of Pure & Applied Chemistry decided to change the definition to

One mole contains exactly 6.022 140 76 × 10²³ elementary entities

• This number is known as the Avogadro number and when used with units of mol^-1 is called the Avogadro Constant
• For practical purposes a rounded version of the constant can be used in exams: 6.02 x 10²³ mol^-1
• The reason we have mol^-1 as the unit is because this is the number of entities per mole of substance
  • For example:
    
    • One mole of sodium (Na) contains  6.02 x 10²³  atoms of sodium
      
    • One mole of hydrogen (H₂) contains  6.02 x 10²³  molecules of hydrogen
      
    • One mole of sodium chloride (NaCl) contains  6.02 x 10²³ formula units of sodium chloride
• The mass of 1 mole of a substance is known as the molar mass
• For an element, it is the same as the relative atomic mass written in grams
• For a compound it is the same as the relative formula mass or relative molecular mass in grams

Calculating the Mass of One Atom or One Molecule

• To calculate the mass of one atom of an element we divide the molar mass of that element by the Avogadro constant:

 

• To calculate the mass of one molecule of a compound we divide the molar mass of that compound by the Avogadro constant

Answer 1

From the Periodic Table, we can find the relative atomic mass of the elements

The A_r of C = 12.0, Al = 27.0 and H = 1.0

Mass of 1 atom of Al  

Answer 2

The molar mass of ethane is: (12.0 x 2) + (1.0 x 6) = 30.0 g mol^-1

Mass of 1 molecule of C₂H₆

Linking Moles & Masses

• One mole of any element is equal to the relative atomic mass of that element in grams
• This is called the molar mass
• If you had 6.02 x 10²³ atoms of carbon in your hand, that number of carbon atoms would have a mass of 12.0 g (because the A_r of carbon is 12.0)
• So one mole of helium atoms would have a mass of 4.0 g (A_r of He is 4.0), one mole of lithium would have a mass of 7.0 g (A_r of Li is 7.0) and so on
• To find the mass of one mole of a compound, we add up the relative atomic masses
  • So one mole of water would have a mass of (2 x 1.0) + 16.0 = 18.0 g
  • So one carbon atom has the same mass as 12 hydrogen atoms

Calculating Moles & Masses

• Although elements and chemicals react with each other in molar ratios, in the laboratory we use digital balances and grams to measure quantities of chemicals as it is impractical to try and measure out moles
• Therefore we have to be able to convert between moles and grams
• We can use the following formula to convert between moles, mass in grams and the molar mass:

Formula triangle for moles, mass and molar mass

Answer:

• • From the Periodic Table, the relative atomic mass of Zn is 65.4
  • So, the molar mass is 65.4 g mol^-1
  • The mass is calculated by moles x molar mass
  • This comes to 0.250 mol x 65.4 g mol^-1 = 16.3 g

Answer:

• • The molar mass of sucrose is 342.3 g mol^-1
  • The number of moles is found by mass ÷ molar mass
  • This comes to  2.64 g ÷ 342.3 g mol^-1 = 7.71 x 10^-3 mol