Molar Mass (VCE SSCE Chemistry): Revision Notes

Molar Mass

Introduction to molar mass

In chemistry, we often need to know how many particles of a substance we're working with, but counting individual atoms or molecules is impossible in a laboratory. Instead, chemists use balances to weigh substances. The concept of molar mass provides the crucial link between the mass of a substance we can measure and the number of moles (and therefore particles) it contains.

Different elements and compounds have particles with different masses. This means that one mole of different substances will have different masses, just as a dozen oranges weighs more than a dozen mandarins because each orange is heavier than each mandarin. Understanding molar mass allows you to convert easily between the mass of a substance and the amount in moles.

Molar masses of elements

The molar mass of an element is the mass, in grams, of one mole of that element. It uses the symbol $M$ and has the unit $\text{g} \cdot \text{mol}^{-1}$.

Finding the molar mass of an element is straightforward: simply take the relative atomic mass ($A_r$) from the periodic table and add the unit $\text{g} \cdot \text{mol}^{-1}$. For example, oxygen has a relative atomic mass of $16.0$, so its molar mass is $16.0 \text{ g} \cdot \text{mol}^{-1}$.

This convenient relationship works because Avogadro's constant was specifically chosen so that $12 \text{ g}$ of carbon-12 contains exactly $6.02 \times 10^{23}$ atoms. The table below shows how relative atomic mass relates to molar mass for several elements:

Molar masses of molecules and ionic compounds

Molecules and ionic compounds contain two or more atoms bonded together. To find the molar mass of a molecule or ionic compound, you need to add up the relative atomic masses of all the atoms in its chemical formula.

Let's look at how this works for some common substances:

For example, water ($\text{H}_2\text{O}$) contains 2 hydrogen atoms and 1 oxygen atom. Using the periodic table:

• Hydrogen: $A_r = 1.0$
• Oxygen: $A_r = 16.0$

Therefore: $M(\text{H}_2\text{O}) = (2 \times 1.0) + 16.0 = 18.0 \text{ g} \cdot \text{mol}^{-1}$

The image below shows one mole samples of different substances - notice how each has a different mass and volume:

Calculations using moles and molar mass

A fundamental formula in chemistry links the amount of substance (in moles), its mass (in grams), and its molar mass:

$n = \frac{m}{M}$

where:

• $n$ = amount in mol
• $m$ = mass in g
• $M$ = molar mass in $\text{g} \cdot \text{mol}^{-1}$

This formula can be rearranged to find mass if you know the number of moles:

$m = n \times M$

Calculations using moles, mass and Avogadro's constant

Sometimes you need to find the actual number of particles (atoms, molecules, or ions) in a sample. This requires combining the formula for molar mass with the formula involving Avogadro's constant:

$n = \frac{m}{M} \text{ and } n = \frac{N}{N_A}$

where:

• $N$ = number of particles
• $N_A$ = Avogadro's constant = $6.02 \times 10^{23} \text{ mol}^{-1}$

Case study: The sting of a bee

Pentyl ethanoate ($\text{C}_7\text{H}_{14}\text{O}_2$) is a compound that gives bananas their characteristic smell. Interestingly, it's also a pheromone that bees release when they sting.

When a bee stings, it releases a tiny amount of pentyl ethanoate - only $1.0 \times 10^{-6} \text{ g}$ (one millionth of a gram). This chemical acts as an alarm signal, attracting other bees to the area and triggering defensive behaviour. Beekeepers use smoke to mask this pheromone, which calms the bees and allows safe handling of hives.

Using our knowledge of molar mass, we can calculate exactly how many molecules of pentyl ethanoate are released in a single sting:

Remember!