AQA A-Level Physical Chemistry 3.1.2 Amount of Substance Balanced Equations and Stoichiometry
3.1.2

Balanced Equations and Stoichiometry

Master writing balanced chemical equations with state symbols, Reacting Mass calculations, Percentage Yield, and Atom Economy.

A balanced chemical equation shows the relative number of moles of each reactant and product involved in a chemical reaction. Stoichiometry is the study of these quantitative relationships in chemical reactions.

State Symbols

Every balanced chemical equation in A-Level Chemistry should include state symbols to specify the physical state of each species:

Reacting Mass Calculation Pathway

To calculate the mass of a product or reactant from a known mass of another species, use this standard three-step pathway:

Stoichiometry Pathway Mass of A (g) Known Mass divide by Mr Moles of A (mol) n = m / Mr Equation Ratio Mass / Moles of B multiply by Mr
✏️ Worked Example 1: Reacting Mass Calculation
Calculate the mass of iron produced when 16.0 g of iron(III) oxide, \( \text{Fe}_2\text{O}_3 \), is reacted completely with excess carbon monoxide. \[ \text{Fe}_2\text{O}_3\text{(s)} + 3\text{CO(g)} \to 2\text{Fe(s)} + 3\text{CO}_2\text{(g)} \]

Step 1: Find the moles of the reactant with known mass, \( \text{Fe}_2\text{O}_3 \).

\( M_r(\text{Fe}_2\text{O}_3) = (2 \times 55.8) + (3 \times 16.0) = 159.6 \text{ g mol}^{-1} \)

\[ n(\text{Fe}_2\text{O}_3) = \frac{16.0}{159.6} = 0.100 \text{ mol} \]

Step 2: Use the stoichiometric ratio from the balanced equation to find moles of \( \text{Fe} \).

The equation shows 1 mole of \( \text{Fe}_2\text{O}_3 \) produces 2 moles of \( \text{Fe} \). Therefore, the ratio is \( 1 : 2 \).

\[ n(\text{Fe}) = 0.100 \times 2 = 0.200 \text{ mol} \]

Step 3: Convert moles of \( \text{Fe} \) to mass.

\( A_r(\text{Fe}) = 55.8 \text{ g mol}^{-1} \)

\[ m(\text{Fe}) = 0.200 \times 55.8 = 11.2 \text{ g} \]

Percentage Yield

In practice, the actual mass of product obtained in a reaction is almost always less than the theoretical maximum mass calculated. The percentage yield tells us how efficient the process is:

\[ \text{Percentage Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \]

Reasons for a yield of less than 100% include:

✏️ Worked Example 2: Calculating Percentage Yield
In Worked Example 1, the theoretical yield of iron was calculated as 11.2 g. If the experiment is performed and only 9.0 g of iron is collected, what is the percentage yield?

Plug the values into the yield equation:

\[ \text{Percentage Yield} = \frac{9.0}{11.2} \times 100 = 80.4\% \]

Atom Economy

Atom economy is a measure of the proportion of starting materials that end up in the desired product rather than as waste products.

\[ \text{Atom Economy} = \frac{\text{Molecular Mass of Desired Product}}{\text{Sum of Molecular Masses of all Reactants}} \times 100 \]
📝 AQA Examiner Tip

When calculating atom economy, you must multiply the relative formula mass of each species by its balancing coefficient from the balanced equation. For example, if a reactant is \( 3\text{H}_2 \), you must use \( 3 \times 2.0 = 6.0 \) in the total mass calculation.

✏️ Worked Example 3: Calculating Atom Economy
Calculate the percentage atom economy for the production of hydrogen (the desired product) in the reaction: \[ \text{CH}_4\text{(g)} + \text{H}_2\text{O(g)} \to \text{CO(g)} + 3\text{H}_2\text{(g)} \]

Step 1: Find the total formula mass of the desired product.

Desired product = \( 3\text{H}_2 \). Mass = \( 3 \times (2 \times 1.0) = 6.0 \text{ g mol}^{-1} \)

Step 2: Find the sum of the formula masses of all reactants.

Reactants = \( \text{CH}_4 + \text{H}_2\text{O} \)

Sum = \( [12.0 + (4 \times 1.0)] + [(2 \times 1.0) + 16.0] = 16.0 + 18.0 = 34.0 \text{ g mol}^{-1} \)

Step 3: Calculate atom economy.

\[ \text{Atom Economy} = \frac{6.0}{34.0} \times 100 = 17.6\% \]

Economic and Environmental Benefits

Developing reactions with high atom economies and yields is a central goal of industrial green chemistry:

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