1.2: Know that the mole (mol) is the unit for amount of substance and be able to perform calculations using the Avogadro constant L (6.02 x 10^23 mol^-1)

Definitions:

• Mole: 1 mole is the amount of substance that contains as many particles as there are in exactly 12 grams of carbon-12.
• Avogadro's Constant (L): This has a value of 6.02 x 10²³. It is the number of particles in 1 mole.

Examples:

        1. Calculate the number of molecules in 2 moles of H₂O.

• When you are asked for the number of moles, it is pretty straightforward, you simply have to multiply the number of moles by Avogadro's constant (L,  6.02 x 10²³).
• In this case: 2 x  6.02 x 10²³ = 12.04 x 10²³ (molecules), or 1.204 x 10²⁴ (molecules).

        2. Calculate the number of molecules in 24 grams of CaCO₃.

• You must be careful, as you are given the mass in grams of CaCO₃, NOT THE NUMBER OF MOLES, so you must convert it to moles using the equation nº of moles, n = mass, m / molar mass, M_r. 
• M_r of CaCO₃ = 100
• Therefore n = 24/100 = 0.24 moles.
• Finally, you multiply it by Avogadro's constant (L,  6.02 x 10²³), so 0.24 x 6.02 x 10²³ = 1.4448 x 10²³molecules.

        3. a) Calculate the number of chloride ions (Cl^-) in 2 moles of NaCl.

• Notice you are asked to find the number of chloride ions but don't worry, it's the same procedure as before with a little extra step, you just have to look at the compound and see how many Cl^-s there are. There is only 1 Cl^- ion in NaCl.
• Now, simply multiply the nº of moles by the nº of ions (Cl^-) and by Avogadro's constant (L,  6.02 x 10²³): (1 x 1 x 6.02 x 10²³ = 6.02 x 10²³).

            b) Calculate the number of sulphate ions (SO₄^-2) in 1.5 moles of Al₂(SO₄)₃.

• Follow the same principle, nº of moles x nº of ions (SO₄) x Avogadro's constant (L,  6.02 x 10²³): (1.5 x 3 x 6.02 x 10²³ = 2.709 x 10²⁴).

        4. How many moles are there in 1.505 x 10²⁴ water molecules.

• Here we just have to apply the same concept but inversely, knowing that  6.02 x 10₂₃ molecules make up 1 mole, we can use this same ratio to find that 1.505 x 10²⁴/6.02 x 10₂₃ is equal to the number of moles (2.5 moles).

Practice Question:

A solution contains 58.5 g of water (H₂O) and 35.7 g of ammonia (NH₃), find the total number of hydrogen atoms in the solution.

Answer:

First convert the mass to moles: moles of water = 58.5/18 = 3.25 moles, moles of ammonia = 35.7/17 = 2.1 moles. Then use nº of moles x nº of atoms (H) x Avogadro's constant (L,  6.02 x 10²³), so for water: 3.25 x 2 x 6.02 x 10²³ = 3.913 x 10²⁴; and for ammonia: 2.1 x 3 x 6.02 x 10²³ = 3.7926 x 10²⁴. Finally add the two together (3.913 x 10²⁴ + 3.7926 x 10²⁴. = 7.7056 x 10²⁴ molecules) and you have the total number of hydrogen atoms in the solution.