Avogadro & the Mole (Edexcel IAL Chemistry)

The Mole & Avogadro Calculations

Spec point — 1.2

• The Avogadro constant(N_A or L) is the number of particles equivalent to the relative atomic mass or molecular mass of a substance

  • The Avogadro constant applies to atoms, molecules, ions and electrons

• The value of N_A is 6.02 x 10²³mol^-1

• The mass of a substance with this number of particles is called a mole (mol)

  • This can be called the molar mass
  • This is the mass of substance that contains the same number of fundamental units as exactly 12.00g of carbon-12

• The amount / number of moles of a substance, n, the mass of the substance, m, and the molar mass, M, are linked by the equation:

n = $\frac{mass,m}{Molar mass,M}$

• One mole of any element is equal to the relative atomic mass of that element in grams

  • If you had one mole of carbon in your hand, that is 6.02 x 10²³ atoms of carbon, you would have a mass of 12.00 g
  • One mole of water would have a mass of (2 x 1 + 16) = 18 g

Worked Example

1. What is the molar mass of water?
2. How many moles are there in 100 g of water?
3. How many water molecules are there in 100g of water?

Answers

1. Molar mass of water, H₂O = (2 x 1.0) + 16.0 = 18.0 g mol^-1
2. Moles $=\frac{mass}{molar mass}=\frac{100}{18.0}=$5.56 moles (to 3 s.f.)
3. Number of molecules = number of moles x Avogadro's constant = 5.56 x (6.02 x 10²³) = 3.35 x 10²⁴ molecules

Worked Example What is the mass of the following:

1. Five hundred million atoms of platinum
2. (1.31 x 10²²) molecules of ethanol

Answer 1:

Number of moles $=\frac{\mathrm{number} \mathrm{of} \mathrm{particles}}{\mathrm{Avogadro}'s\mathrm{constant},N_{A}}=\frac{500\times10^{6}}{6.02\times10^{23}}=$8.31 x 10^-16 moles

Mass = moles x molar mass = (8.31 x 10^-16) x 195.1 = 1.62 x 10^-13 g (lots of atoms, a tiny mass)

Answer 2:

Molar mass of ethanol, C₂H₅OH = (2 x 12.0) + (5 x 1.0) + 16.0 + 1.0 = 46.0 g mol^-1

Number of moles $=\frac{\mathrm{number} \mathrm{of} \mathrm{particles}}{\mathrm{Avogadro}'s\mathrm{constant},N_{A}}=\frac{1.31\times10^{22}}{6.02\times10^{23}}=$0.0218 moles

Mass = moles x molar mass = 0.0218 x 46.0 = 1.00 g (an exceptionally large number of molecules in just 1 g)

Exam Hint

• When you are completing calculations using Avogadro's constant, you may end up with answers that seem very large or very small - don't automatically assume that they must be wrong

• Remember, Avogadro's constant is a VERY large number:

  • 6.02 x 10²³ or 602 000 000 000 000 000 000 000

• So when you multiply or divide by Avogadro's constant, your answers will, naturally, become very large or very small