R2.1.1 Chemical equations and stoichiometry

Chemical Equations and Their Role in Representing Reactions

Imagine you are baking a cake.
The recipe specifies exact amounts of flour, sugar, eggs, and butter to create the perfect dessert.
If you use too much or too little of any ingredient, the result might not turn out as expected.

In chemistry, a chemical equation serves as this "recipe" for a chemical reaction. It tells you the precise ratios of reactants (ingredients) and products (results) involved.

Representing Chemical Reactions with Equations

Definition

Chemical equation

A chemical equation is a symbolic representation of a chemical reaction. It shows the reactants (starting substances) on the left side, the products (substances formed) on the right, and an arrow indicating the direction of the reaction.

Example

$C_{2} H_{6} + O_{2} \to C O_{2} + H_{2} O$

This equation represents the combustion of ethane ( $C_{2} H_{6}$ ) in oxygen ( $O_{2}$ ) to produce carbon dioxide ( $C O_{2}$ ) and water ( $H_{2} O$ ).

However, this equation is not yet complete—it must be balanced to adhere to the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

Analogy

Think of balancing a chemical equation like balancing a seesaw. Both sides must have equal weight—in this case, the number of atoms—so the reaction remains stable and accurate.

Balancing Chemical Equations: Why and How?

When balancing a chemical equation, the goal is to ensure the number of atoms of each element is the same on both sides of the equation.
This reflects the fact that atoms are simply rearranged during a reaction, not created or destroyed.

Steps to Balance a Chemical Equation:

Write the unbalanced equation: Start by listing the reactants and products. For example, $C_{2} H_{6} + O_{2} \to C O_{2} + H_{2} O$
Count the atoms of each element on both sides of the equation.
- Reactants: 2 carbons, 6 hydrogens, 2 oxygens.
- Products: 1 carbon, 2 hydrogens, 3 oxygens.
Add coefficients to balance the atoms, starting with the element that appears in the fewest compounds.
- Balance carbon: $C_{2} H_{6} + O_{2} \to 2 C O_{2} + H_{2} O$ .
- Balance hydrogen: $C_{2} H_{6} + O_{2} \to 2 C O_{2} + 3 H_{2} O$ .
- Balance oxygen: $C_{2} H_{6} + 3.5 O_{2} \to 2 C O_{2} + 3 H_{2} O$ .
Adjust coefficients to whole numbers, if necessary:
- Multiply all coefficients by 2: $2 C_{2} H_{6} + 7 O_{2} \to 4 C O_{2} + 6 H_{2} O$ .
Verify the balance: Ensure the number of each type of atom is the same on both sides.

Common Mistake

One common mistake is forgetting to adjust all coefficients when converting to whole numbers. Always double-check that the equation remains balanced after this step.

State Symbols in Equations

To provide additional information, state symbols indicate the physical state of each substance:

$(s)$ : Solid
$(l)$ : Liquid
$(g)$ : Gas
$(a q)$ : Aqueous (dissolved in water)

Example

The balanced equation for the combustion of ethane with state symbols is:

$2 C_{2} H_{6} (g) + 7 O_{2} (g) \to 4 C O_{2} (g) + 6 H_{2} O (l)$

Tip

Always include state symbols in your chemical equations when known, as they provide important context about the reaction conditions.

Deducing Chemical Equations from Reactants and Products

Sometimes, you are given the reactants and products and need to deduce the balanced equation. Let’s practice this with an example.

Example question

Anaerobic Fermentation of Glucose

Write the balanced equation for the anaerobic fermentation of glucose ( $C_{6} H_{12} O_{6}$ ) to form ethanol ( $C_{2} H_{5} O H$ ) and carbon dioxide ( $C O_{2}$ ).

Solution

Write the unbalanced equation:
$C_{6} H_{12} O_{6} \to C_{2} H_{5} O H + C O_{2}$
Count atoms for each element:
- Reactants: 6 carbons, 12 hydrogens, 6 oxygens.
- Products: 2 carbons (ethanol) + 1 carbon (carbon dioxide) = 3 carbons; 6 hydrogens (ethanol); 3 oxygens.
Add coefficients to balance the equation:
- Balance carbon: $C_{6} H_{12} O_{6} \to 2 C_{2} H_{5} O H + 2 C O_{2}$ .
- Balance hydrogen: Already balanced with 12 hydrogens on each side.
- Balance oxygen: Reactants have 6 oxygens; products have 4 (ethanol) + 2 (carbon dioxide) = 6 oxygens.
Verify the balance:
- Reactants: 6C, 12H, 6O.
- Products: 6C, 12H, 6O.

The balanced equation is:

$C_{6} H_{12} O_{6} (a q) \to 2 C_{2} H_{5} O H (a q) + 2 C O_{2} (g)$

Example

In this reaction, glucose is broken down into ethanol and carbon dioxide, a process commonly used in brewing and biofuel production.

Redox Reactions and Half-Equations

For reactions involving electron transfer, such as in batteries or corrosion, it’s useful to write half-equations.
These equations separately show the oxidation (loss of electrons) and reduction (gain of electrons) processes.

Writing Half-Equations

Identify the species being oxidized and reduced.
Write the oxidation and reduction half-equations, balancing atoms and charges.
Combine the half-equations, ensuring the number of electrons lost equals the number gained.

Example

Reaction Between Zinc and Copper(II) Sulfate

When zinc metal reacts with copper(II) sulfate ( $C u S O_{4}$ ), zinc displaces copper:

$Z n (s) + C u^{2 +} (a q) \to Z n^{2 +} (a q) + C u (s)$

Step 1: Write the half-equations.

Oxidation (zinc loses electrons): $Z n (s) \to Z n^{2 +} (a q) + 2 e^{-}$ .
Reduction (copper gains electrons): $C u^{2 +} (a q) + 2 e^{-} \to C u (s)$ .

Step 2: Combine the half-equations:
$Z n (s) + C u^{2 +} (a q) \to Z n^{2 +} (a q) + C u (s)$

Common Mistake

Ensure the number of electrons lost in oxidation equals the number gained in reduction. Forgetting this step leads to an unbalanced overall equation.

Reflection and Practice

Self review

Write the balanced equation for the combustion of propane ( $C_{3} H_{8}$ ) in oxygen.
Deduce the half-equations for the reaction between magnesium and hydrochloric acid, where hydrogen gas is produced.
How would you explain the importance of balanced equations to someone unfamiliar with chemistry?

Theory of Knowledge

To what extent does the universal language of chemical equations contribute to global scientific collaboration?
How might differing interpretations of these symbols lead to misunderstandings?

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R2.1.1 Chemical equations and stoichiometry

Chemical Equations and Their Role in Representing Reactions

Representing Chemical Reactions with Equations

Balancing Chemical Equations: Why and How?

Steps to Balance a Chemical Equation:

State Symbols in Equations

Deducing Chemical Equations from Reactants and Products

Anaerobic Fermentation of Glucose

Redox Reactions and Half-Equations

Writing Half-Equations

Reaction Between Zinc and Copper(II) Sulfate

Reflection and Practice

You've read 2/2 free chapters this week.

Chemical Equations: The Language of Chemistry

Example