Mole & Molar Mass

Mole

Mole is the amount of substance that contains as many particles as there are atoms in exactly 12 grams of pure carbon-12.

• The number of particles in ONE mole of anything is $6.0 \times 10^{23}$. It is called the Avogadro’s number ($\text{N}_{A}$)
• Mole is a SI unit. It is commonly written as mol.
• What is mole used for? As a way to “count” the number of particles in a reaction.

Useful Equation:

$$\text{No. of particles} = \text{No. of moles} \times (6.0 \times 10^{23})$$

Examples:

If a small cylinder of hydrogen gas is deemed to contain $3.0 \times 10^{20}$ hydrogen molecules. Calculate the number of moles of hydrogen in the cylinder.

• $$\text{No. of moles} = \frac{\text{No. of particles}}{6.0 \times 10^{23}}$$
• We end up with $5.0 \times 10^{-4}$ mol

Consider 0.8 mole of $\text{C}_{6}\text{H}_{14}$, calculate the number of moles of C atoms and H atoms.

• From the chemical formulae, 1 mole of $\text{C}_{6}\text{H}_{14}$ will contain 6 moles of C atoms and 14 moles of H atoms.
• Hence, number of moles of C atoms will be $6 \times 0.8 = 4.8$ mol
• Number of moles of H atoms will be $14 \times 0.8 = 11.2$ mol

Molar Mass

Molar mass is the mass of a given substance (chemical element or chemical compound) divided by its amount of substance.

• In simpler words: molar mass is the mass in grams of 1 mole of substance
• Molar mass is used to calculate the mass of X moles of substance
• The mass of 1 mole of carbon-12 atoms is 12 grams.
• Trick: Since the mass of 1 mole of carbon-12 atoms is 12 grams, if the relative atomic/molecular mass of a substance is 50 units, the molar mass of the substance will be 50 grams. (Convert units to grams)

$$\text{Mass of sub.} = \text{No. of moles of sub.} \times \text{Molar mass}$$

Example:

Calculate the mass of 2.5 moles of ammonia molecules

• The relative molecular mass of ammonia ($\text{NH}_{3}$) is $14 + 3(1) = 17$ units
• Hence, mass of 1 mole of ammonia is 17 grams
• This will give $17 \times 2.5 = 42.5$ grams for 2.5 moles of ammonia

Calculate the number of moles of molecules in 9.0 g of oxygen

• Oxygen is $\text{O}_{2}$. Relative molecular mass of oxygen molecules is $16 + 16 = 32$ units
• This will give a molar mass of 32 grams.
• $\text{Number of moles} = \frac{9}{32} = 0.281 \, \text{mol}$