Mole Calculations (DP IB Physics: HL)

The Mole

• The mole is one of the seven SI base units
• It is used to measure the amount of substance 
• One mole is defined as follows:

The amount of substance that contains as many elementary entities as the number of atoms in 12 g of carbon-12

• This amount of substance is exactly 6.02214076 × 10²³ elementary entities (i.e. particles, atoms, molecules)
  • At IB level, this number can be rounded to 6.02 × 10²³
• One mole of gas contains a number of particles (atoms or molecules) equal to the Avogadro constant
• Therefore, to calculate the number of particles N in a gas, knowing the number of moles n, the following relationship must be used:

N = nN_A

• Where:
  • N = number of gas particles
  • n = number of moles of gas (mol)
  • N_A = 6.02 × 10²³ mol^–1 (Avogadro constant)

Molar Mass

• The molar mass M of a substance is defined as the mass m of the substance divided by the amount (in moles) of that substance
• The molar mass is calculated as follows:

• Where:
  • M = molar mass in g mol^–1
  • m = mass in grams (g)
  • n = number of moles (mol)

Step 1: Write down the relationship between the molar mass M and the mass m 

Step 2: Rearrange the equation to find the mass m of n = 1 mol of nitrogen

m = Mn

m = 28.02 g mol^–1 × 1 mol

m = 28.02 g

Step 3: Identify the number of nitrogen atoms in 1 mol of nitrogen

• • n = 1 mol of nitrogen contains a number of molecules equal to the Avogadro constant
  • From the data booklet, N_A = 6.02 × 10²³

N_molecules = nN_A

N_molecules = 6.02 × 10²³

• • Each nitrogen molecule contains 2 atoms of nitrogen
  • n = 1 mol of nitrogen contains a number of atoms equal to twice the number of molecules

N_atoms = 2 × N_molecules = 2 × (6.02 × 10²³)

N_atoms = 1.2 × 10²⁴

Step 4: Divide the mass of 1 mol of nitrogen m by the number of atoms in 1 mol of nitrogen N_atoms in order to find the mass of a nitrogen atom 

Mass of a nitrogen atom = 2.3 × 10^–23 g