The mole concept
•Carbon-12 isotope has a relative mass of 12. To calculate the number of carbon-12 atoms that are present in 12g of carbon-12 we need to know the mass of 1 carbon-12 atom.
•1 atom of carbon-12 = 2.004 x 10-23 g
•X atoms of carbon-12 = 12 g
•X = 12 / 2.004 x 10-23
= 6 x 1023 atoms of carbon-12
•The word mole (symbol, mol) represents a number.
•A mole is defined as the amount of substance that contains as many elementary particles (atoms, molecules or ions) as there are atoms in 12 g of carbon-12 isotope.
•The number of atoms or ions in 1 mole of an element or compound is 6.02 x 10^23 and is called Avogadro’s number (NA).
•The molar mass (M) of an element is defined as the mass of 1 mol of the element expressed in grams per mole (gmol-1).
•Molar mass is calculated by adding the relative atomic masses (Ar) of each atom of each element present in the formula.
Carbon: M (C ) = 12 gmol-1
Hydrogen: M (H2) = 2 x 1 = 2 gmol-1
Water: M (H2O) = 2 x 1 + 16 = 18 gmol-1
Copper Sulfate: M (CuSO4) = 63.5 + 32 + 4 x 16 = 159.5 gmol-1
Changing moles to particles:
Example: A sample of chlorine gas (Cl2) has 4.0 mol of substance.
Calculate the number of chlorine molecules.
Number of chlorine molecules
= n x 6.02 x 10^23
= 4.0 x 6.02 x 10^23
= 2.4 x 10^24
Calculate the number of chlorine atoms.
1 molecule of chlorine (Cl2) contains 2 atoms of chlorine (Cl).
Number of chlorine atoms
= 2 x number of chlorine molecules
= 2 x 2.4 x 10^24
= 4.8 x 10^24
Changing moles to mass
Calculate the amount of substance, moles, of 36 g of water, H20.
n = m / M
= 36 / (2 x 1 + 16)
= 36 / 18
= 2 mol
Calculate the mass of 5.0 moles of carbon dioxide, CO2
m = n x M
= 5.0 x (12 + 2 x 16)
= 5.0 x 44
= 220 g
Changing mass to particles
•To calculate mass from number of particles requires 2 calculations.
•Step 1: Calculate amount of substance (n) from number of particles using the rule.
n = number of particles / 6.02 x 10^23
•Step 2: Calculate mass from amount of substance using the rule.
m = n x M
What is the mass of 3.01 x 10^23 molecules of hydrochloric acid, HCl
= 3.01 x 1023 / 6.02 x 10^23
= 0.5 mol
= n x M = 0.5 x (1 + 35.5)
= 0.5 x 36.5 = 18.25 g