Question

Propane (C \(3 \mathrm{H}_{8}\) ) reacts with elemental oxygen gas to produce carbon dioxide and liquid water with an accompanying enthalpy change of \(-2,220 \mathrm{~kJ}\). Write a properly balanced thermochemical equation for this process.

Short answer

The balanced thermochemical equation is: \( \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \quad \Delta H = -2,220 \text{ kJ} \).

Step-by-step solution

Write the Unbalanced Chemical Equation

First, identify the reactants and products. The reactants are propane (\( \text{C}_3\text{H}_8 \)) and oxygen gas (\( \text{O}_2 \)). The products are carbon dioxide (\( \text{CO}_2 \)) and liquid water (\( \text{H}_2\text{O} \)). The unbalanced equation is: \[ \text{C}_3\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]

Balance the Carbon Atoms

Balance the number of carbon atoms present in propane with the carbon atoms in carbon dioxide. Since there are three carbon atoms in propane, you would need three molecules of carbon dioxide to balance it: \[ \text{C}_3\text{H}_8 + \text{O}_2 \rightarrow 3\text{CO}_2 + \text{H}_2\text{O} \]

Balance the Hydrogen Atoms

Balance the hydrogen atoms by adjusting water molecules. Propane has eight hydrogen atoms, so use four water molecules to balance the hydrogen: \[ \text{C}_3\text{H}_8 + \text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \]

Balance the Oxygen Atoms

Now balance the oxygen atoms. The right side has a total of ten oxygen atoms (six from carbon dioxide and four from water). Use five molecules of oxygen on the reactant side to balance: \[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \]

Add Enthalpy Change to the Balanced Equation

Write the enthalpy change next to the balanced equation, as this indicates it is a thermochemical equation. Since enthalpy is released, the reaction is exothermic: \[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \quad \Delta H = -2,220 \text{ kJ} \]

Key concepts

Chemical Reaction Balancing

Balancing a chemical reaction involves ensuring the same number of each type of atom appears on both sides of the equation. This principle adheres to the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

Start by identifying the reactants and products. For the combustion of propane, the reactants are propane (\(\text{C}_3\text{H}_8\)) and oxygen (\(\text{O}_2\)). The products are carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)).

Here’s a quick guide to balancing:

• Begin with elements that appear in only one reactant and one product, such as carbon in propane becoming carbon dioxide.
• Balance compounds involving hydrogen next, adjusting the water molecules to balance the eight hydrogen atoms in propane.
• Finally, balance oxygen atoms while keeping an eye on the total number needed from both carbon dioxide and water combined.

These steps ensure the balanced equation represents exactly what happens chemically, molecular by molecular.

Enthalpy Change

Enthalpy change represents the heat energy change occurring during a reaction under constant pressure. It is critical for understanding energy flow. In our example, the combustion of propane releases heat and is classified as an exothermic reaction because the enthalpy change (\(\Delta H\)) is negative. Specifically, it is \(-2220\) kJ, meaning this amount of energy is released per mole of propane combusted.

To interpret the enthalpy change:

• Know that a negative \(\Delta H\) indicates energy is given off, increasing the surroundings' temperature.
• For exothermic reactions like this, bonds in the products are more stable than those in the reactants, releasing energy to form stronger bonds.

The symbol \(\Delta H\) tagged onto the chemical equation transforms it into a thermochemical equation, marrying the chemical and thermal changes for a complete depiction of the reaction.

Combustion Reaction

A combustion reaction is a chemical process where a substance reacts rapidly with oxygen to release energy in the form of light and heat. Combustion of hydrocarbons, like propane, is a common type of this reaction, yielding carbon dioxide and water as products.

The typical indicators of a combustion reaction include:

• Presence of \(\text{O}_2\) as a reactant and \(\text{CO}_2\) and \(\text{H}_2\text{O}\) as products.
• Release of energy, observable as flames or increased heat.
• Process occurs with both small and large molecular compounds, provided oxygen is available.

These reactions, especially in the context of energy production and engines, are crucial for understanding environmental impacts and efficiency improvements.