Problem 39 - Chemistry The Central Science

Question

The complete combustion of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l),\) to form \(\mathrm{H}_{2} \mathrm{O}(g)\) and \(\mathrm{CO}_{2}(g)\) at constant pressure releases 1235 \(\mathrm{kJ}\) of heat per mole of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.

Step-by-Step Solution

Answer

The short answer for the problem is as follows: (a) The balanced thermochemical equation for the complete combustion of ethanol is: \( C_2H_5OH (l) + 3 O_2 (g) \rightarrow 3 H_2O (g) + 2 CO_2 (g) \quad \Delta H = -1,235 \, \text{kJ/mol}\) (b) The enthalpy diagram for this reaction shows that the reactants have higher energy levels than the products, with an arrow pointing downwards representing the heat released (\( \Delta H = -1,235 \, \text{kJ/mol} \)). The vertical axis is labeled as "Enthalpy (H)", and the diagram is titled "Enthalpy Diagram for the Combustion of Ethanol".

Step 1: Write the balanced equation for the combustion of ethanol

To begin, we need to identify the products of the combustion reaction. Combustion reactions involve reacting with oxygen (O2) to produce water (H2O) and carbon dioxide (CO2). The general equation for the complete combustion of ethanol, C2H5OH, can be written as: C2H5OH (l) + O2 (g) → H2O (g) + CO2 (g) Now, we balance the equation. The balanced equation is: C2H5OH (l) + 3 O2 (g) → 3 H2O (g) + 2 CO2 (g)

Step 2: Write the balanced thermochemical equation

We are given the heat released per mole of ethanol during this reaction as -1,235 kJ/mol. We use the balanced equation from Step 1 and add the heat to write the thermochemical equation: C2H5OH (l) + 3 O2 (g) → 3 H2O (g) + 2 CO2 (g) ΔH = -1,235 kJ/mol

Step 3: Draw an enthalpy diagram for the reaction

An enthalpy diagram is used to represent the change in heat during a reaction. The reactants are on the left, the products are on the right, and the difference in height represents the change in heat. Since heat is being released in this reaction (-1,235 kJ/mol), the products are at a lower energy level compared to the reactants. The enthalpy diagram for this reaction will look as follows: 1. Start by drawing two horizontal lines: one for the reactants and one for the products. Label the reactants line as "C2H5OH (l) + 3 O2 (g)" and the products line as "3 H2O (g) + 2 CO2 (g)". 2. Draw an arrow pointing downwards from the reactants line to the products line to represent the decrease in energy during the reaction. 3. Label the arrow with the heat value: ΔH = -1,235 kJ/mol. 4. Label the vertical axis as "Enthalpy (H)" 5. Label the diagram as "Enthalpy Diagram for the Combustion of Ethanol" The enthalpy diagram represents the exothermic nature of the combustion reaction, as heat is being released and the products have a lower enthalpy than the reactants.

Key Concepts

Thermochemical Equation

In chemistry, a thermochemical equation is a balanced chemical equation that includes the change in enthalpy (ΔH), which is the heat content of a system. It shows not only the quantity of substances involved in the reaction but also the heat exchange with surroundings. For the combustion of ethanol, the thermochemical equation is expressed as:

C₂H₅OH (l) + 3 O₂ (g) → 3 H₂O (g) + 2 CO₂ (g) ΔH = -1235 kJ/mol
This equation indicates that when 1 mole of ethanol completely combusts in excess oxygen, 1235 kJ of heat are released. The negative sign shows that this is an exothermic reaction, where energy is given out to the surrounding environment. Understanding thermochemical equations is crucial for students as it lays the foundation for exploring energy changes in chemical reactions.

Enthalpy Diagram

An enthalpy diagram visually represents the energy change during a chemical reaction. Energy is plotted on the vertical axis, while the reaction progress is along the horizontal axis. For the combustion of ethanol, the diagram highlights the energy levels of the reactants and products. Because the reaction is exothermic, the products rest at a lower energy level compared to the reactants.

Here's a simplified guide to interpreting such a diagram:

• At the start, reactants have a higher stored energy.
• An arrow pointing downwards shows the release of energy.
• The length of the arrow correlates to the magnitude of energy change, here labeled as ΔH = -1235 kJ/mol.
• The finished diagram helps visualize the energy flow from reactants to products, reinforcing the concept that heat is being released.

Utilizing enthalpy diagrams enhances a student's comprehension by providing a clear and concrete representation of abstract energy concepts in chemical processes.

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy through light or heat. The combustion of ethanol is a classic example, as it gives off heat when chemical bonds are formed in the products (water and carbon dioxide) that are more stable than the bonds in the reactants (ethanol and oxygen). This process can be remembered by the simple mantra: 'Exo' means 'exit,' thus energy exits the system.

Recognizing an exothermic reaction in a thermochemical equation or an enthalpy diagram can be straightforward:

• Thermochemical equations will have a negative ΔH value.
• Enthalpy diagrams show a downward arrow as heat is emitted.

For students, understanding exothermic reactions is fundamental as it relates to topics in thermodynamics and has practical applications in everyday life such as heating and combustion engines.

Balanced Chemical Equation

A balanced chemical equation is pivotal in stoichiometry as it ensures that the Law of Conservation of Mass is satisfied, meaning that atoms are neither created nor destroyed in a chemical reaction. To balance the equation for the combustion of ethanol, consider all atoms involved:

• Count all the atoms of each element in the reactants and products.
• Adjust coefficients before each formula to achieve the same number of atoms on both sides.
• Verify that the total mass of the reactants equals the total mass of the products.

After balancing, the resulting equation for the ethanol combustion is:C₂H₅OH (l) + 3 O₂ (g) → 3 H₂O (g) + 2 CO₂ (g)
Here we have the perfect stoichiometric ratio indicating that for every one mole of ethanol, three moles of diatomic oxygen are required to form three moles of water and two moles of carbon dioxide. This balanced equation serves as a blueprint, offering insights into the quantities of reactants needed and products formed – a critical skill for students aiming to predict the outcome of chemical reactions.