3.4 - Reacting Mass Calculations

Reacting masses through the mole

• The numbers in front of the formulae in a balanced equation show amounts in moles. In:
  • Mg + 2HCl → MgCl₂ + H₂
• One mole of magnesium reacts with two moles of hydrochloric acid to give one mole of magnesium chloride and one mole of hydrogen.

Why you go via moles

• Two masses can't be compared directly, because a gram of one substance contains a different number of particles from a gram of another.
• The route runs: mass → amount in moles → across the equation → mass.

The method

1. Write out the balanced equation.
2. Work out the relative formula mass ($M_{\text{r}}$) of the known substance and the wanted substance.
3. Turn the known mass into an amount in moles - $\text{Moles}=\frac{\text{mass}}{M_{\text{r}}}$.
4. Use the balancing numbers in the equation to find the moles of the wanted substance.
5. Turn that amount back into a mass - $\text{Mass}=\text{moles}\times M_{\text{r}}$.

A relative formula mass is always for one unit of the formula, so the number in front plays no part in step 2 - it only applies at step 4 when comparing moles.

Worked example - Product mass through the mole

Lithium burns in air to form lithium oxide:

4Li + O₂ → 2Li₂O

Calculate the mass of lithium oxide formed when 105 g of lithium is burned in air. Relative atomic masses: O = 16, Li = 7.

Balancing numbers from reacting masses

• If you know the reacting masses and the formula of each substance, you can find the balancing numbers from the measurements alone.
• Balancing numbers are a ratio of amounts in moles.

The method

1. Write the equation with no balancing numbers - Reactants on the left, products on the right.
2. Work out the relative formula mass of each substance.
3. Divide each measured mass (in grams) by its relative formula mass to get the amount in moles.
4. Divide every amount by the smallest amount.
5. If any number isn't whole, multiply them all by the same integer until they're all whole numbers.
6. Write these numbers in front of the formulae in the equation (a 1 is not written).

Missing masses

If one mass isn't measured, find it using the conservation of mass: the total mass of products equals the total mass of reactants, so the missing mass is the difference.

Worked example - Balancing from four masses

16.0 g of methanol, CH₃OH, reacted completely with 24.0 g of oxygen, O₂, to form 22.0 g of carbon dioxide, CO₂, and 18.0 g of water, H₂O. Write the balanced symbol equation. Relative atomic masses: H = 1, C = 12, O = 16.