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.

Short answer

The final answers for the given question are: (a) The balanced thermochemical equation for the complete combustion of ethanol is: \[\text{C}_{2}\text{H}_{5}\text{OH} + 3\text{O}_{2} \rightarrow 3\text{H}_{2}\text{O} + 2\text{CO}_{2} \qquad \Delta H = -1235 \ \text{kJ/mol}\] (b) In the enthalpy diagram, the reactants (C₂H₅OH and O₂) are on the left side and the products (H₂O and CO₂) are on the right side. The energy level of the products is lower than the reactants since the reaction is exothermic. The change in enthalpy, indicated by a downward sloping line or arrow, is labeled as ΔH = -1235 kJ/mol.

Step-by-step solution

(a) Write a balanced thermochemical equation for the complete combustion of ethanol

To write a balanced thermochemical equation for the complete combustion of ethanol, we need to include all reactants and products involved in the reaction, as well as the heat released per mole of ethanol. The given information states that ethanol (C₂H₅OH) is combusted to form water (H₂O) and carbon dioxide (CO₂). Additionally, we know that complete combustion involves oxygen (O₂) as a reactant. Finally, we are given the heat released per mole of ethanol, which is -1235 kJ. Now, let's write the balanced thermochemical equation. First, we write the unbalanced equation: \[\text{C}_{2}\text{H}_{5}\text{OH} + \text{O}_{2} \rightarrow \text{H}_{2}\text{O} + \text{CO}_{2}\] Next, we balance the equation: \[\text{C}_{2}\text{H}_{5}\text{OH} + 3\text{O}_{2} \rightarrow 3\text{H}_{2}\text{O} + 2\text{CO}_{2}\] Finally, we add the heat released per mole of ethanol (-1235 kJ) to the equation: \[\text{C}_{2}\text{H}_{5}\text{OH} + 3\text{O}_{2} \rightarrow 3\text{H}_{2}\text{O} + 2\text{CO}_{2} \qquad \Delta H = -1235 \ \text{kJ/mol}\]

(b) Draw an enthalpy diagram for the complete combustion of ethanol

To draw an enthalpy diagram for the reaction, we would use the following steps: 1. Mark the reactants (C₂H₅OH and O₂) on the left side of the diagram, and the products (H₂O and CO₂) on the right side. Make sure to label each substance. 2. Draw a horizontal line, representing the energy level of the reactants, starting from the left side of the diagram. 3. Draw another horizontal line, representing the energy level of the products, starting from the right side of the diagram. Since the reaction is exothermic (heat is released), ensure that the product's energy level is lower than the reactants. 4. Connect the two horizontal lines with a downward sloping line or arrow, representing the change in enthalpy, and label this line with the given value of ΔH (-1235 kJ/mol). The enthalpy diagram should visually represent the energy changes during the reaction, emphasizing that the energy of the products is lower than the reactants, and the heat is released during the combustion process.

Key concepts

Thermochemical Equation

Understanding the concept of a thermochemical equation can significantly enhance comprehension of chemical reactions, especially those involving energy changes, such as combustion. A thermochemical equation is an expression that shows the starting substances (reactants) and the substances formed (products), along with the amount of heat absorbed or released during the reaction.

Let's consider the given exercise, where ethanol undergoes complete combustion. To craft a thermochemical equation first, we identify all reactants and products. For ethanol combustion, the reactants are ethanol \( \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} \) and oxygen \( \mathrm{O}_{2} \), while the products are water \( \mathrm{H}_{2}\mathrm{O} \) and carbon dioxide \( \mathrm{CO}_{2} \). Then, balancing the equation ensures the law of conservation of mass is upheld, meaning the number of atoms on each side must be equal.

The crucial part is including the energy aspect—here, the heat released, which is \( -1235 \mathrm{~kJ} \) per mole of ethanol. This is represented with a negative sign showing that it is an exothermic reaction in which energy is released to the surroundings. The complete balanced thermochemical equation thus integrates both matter and energy changes during the reaction.

Enthalpy Diagram

An enthalpy diagram is a graphic representation of the enthalpy change, also known as heat content, during a chemical reaction. These diagrams provide a visual way to analyze energy changes and are particularly helpful in comparing the enthalpy of reactants and products.

To build an enthalpy diagram based on the combustion of ethanol, begin with the reactants on the left and the products on the right. A horizontal line represents the energy level of each. Since the reaction releases heat, making it exothermic, the products will have a lower energy level than the reactants. Thus, we draw a downward arrow connecting these two levels, which correlates to heat release. This arrow is labeled with \( \Delta H = -1235 \mathrm{~kJ/mol} \), where \( \Delta H \) reflects the change in enthalpy.

These diagrams are important learning tools, reinforcing the idea that exothermic reactions result in a net energy release as they proceed from higher to lower energy states, a cornerstone concept for many areas of chemistry and thermodynamics.

Exothermic Reaction

An exothermic reaction is any chemical reaction that releases energy in the form of heat to its surroundings, resulting in a rise in temperature. This is characterized by a negative change in enthalpy (\( \Delta H < 0 \)). The combustion of ethanol is a classic example of an exothermic reaction as it liberates a significant amount of heat, making it a valuable source of energy.

Students may sometimes confuse the heat released with the energy required to initiate the reaction, known as activation energy. Despite exothermic reactions needing some energy to start, they ultimately release more energy than they consume. This excess energy is a by-product of the new bonds formed in the products being stronger, and thus lower in energy, than the bonds broken in the reactants. Understanding exothermic reactions is crucial in various applications, from everyday ones like burning fuel for heating to advanced ones such as chemical engineering and material sciences.