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 balanced thermochemical equation for the combustion of ethanol is: \[C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g) + 1235 \, kJ\] To draw an enthalpy diagram: 1. Label vertical axis as "Enthalpy" or "Energy." 2. Draw a horizontal line for reactants: "Reactants: C_2H_5OH(l) + 3O_2(g)". 3. Draw a horizontal line below for products: "Products: 2CO_2(g) + 3H_2O(g)". 4. Draw an arrow downward from reactants to products, labeled "-1235 kJ".

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

The combustion of ethanol involves the reaction of ethanol with oxygen gas to form carbon dioxide and water. To balance this chemical equation, we need to ensure that there are equal numbers of each element on both sides of the equation. The balanced chemical equation for the combustion of ethanol is: \[C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g)\]

Step 2: Include the heat released in the balanced thermochemical equation

Given that the heat released per mole of ethanol is 1235 kJ, we can include this in the balanced chemical equation to make it a balanced thermochemical equation: \[C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(g) + 1235 \, kJ\]

Step 3: Draw an enthalpy diagram for the reaction

An enthalpy diagram shows the energy levels before and after a chemical reaction, and it will display the change in enthalpy during the reaction. Since the combustion of ethanol releases heat, it is an exothermic reaction, which means that the energy level of the reactants will be higher than that of the products. To draw an enthalpy diagram for this reaction: 1. Label the vertical axis as "Enthalpy" or "Energy." 2. Draw a horizontal line to represent the energy level of the reactants. Label this line "Reactants: C_2H_5OH(l) + 3O_2(g)". 3. Draw a horizontal line below the reactants line to represent the energy level of the products. Label this line "Products: 2CO_2(g) + 3H_2O(g)". 4. Draw an arrow pointing downwards from the reactants line to the products line, and label this arrow "-1235 kJ" to indicate the heat released during the reaction. The enthalpy diagram should now clearly show the energy change during the combustion of ethanol, with the reactants having a higher energy level than the products and the release of 1235 kJ of heat per mole of ethanol.

Key Concepts

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to produce heat and usually light. These reactions are predominantly exothermic, meaning they release energy. When we talk about ethanol combustion, it involves ethanol (\(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\)) burning in the presence of oxygen (\(\mathrm{O}_{2}(g)\)). This reaction produces carbon dioxide (\(\mathrm{CO}_{2}(g)\)) and water (\(\mathrm{H}_{2} \mathrm{O}(g)\)), releasing a substantial amount of heat.

The key components of a combustion reaction include:

• Fuel: The substance that is being burned—here, ethanol.
• Oxidizer: Typically oxygen, which reacts with the fuel.
• Products: The substances produced by the reaction, such as carbon dioxide and water.
• Energy: Often released as heat and light.

Ethanol's combustion is an example of a practical application in energy generation, making understanding these reactions valuable in real-world contexts like powering engines or heating systems.

Enthalpy Diagram

An enthalpy diagram is a visual representation used to understand the heat changes during a chemical reaction. It shows the difference in energy between reactants and products, highlighting whether a reaction is exothermic (releasing energy) or endothermic (absorbing energy).

In the case of ethanol's combustion:

• The vertical axis of the diagram represents the enthalpy, or energy.
• On the diagram, reactants such as ethanol and oxygen are shown at a higher energy level than the products.
• The products, carbon dioxide and water, are at a lower energy level, indicating energy release.
• This energy difference is labeled on the diagram, here as \(-1235 \, \mathrm{kJ}\) per mole of ethanol, representing the exothermic nature of the reaction.

This diagram helps visualize why energy is released in the chemical process and how much energy is involved, reinforcing the concept that energy conservation is maintained throughout chemical changes.

Balanced Chemical Equations

Balanced chemical equations are crucial in chemistry because they ensure that the number of each element remains constant throughout a reaction. This ties into the law of conservation of mass, where matter cannot be created or destroyed in an isolated system.

When writing a balanced equation for ethanol's combustion:

• The initial step is to count the atoms of each element involved — carbon, hydrogen, and oxygen in ethanol and oxygen gas.
• For the combustion of ethanol, the equation begins with \(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}(l) + 3\mathrm{O}_2(g) \rightarrow 2\mathrm{CO}_2(g) + 3\mathrm{H}_2\mathrm{O}(g)\).
• Balanced equations are achieved by adjusting coefficients so that each type of atom has the same number on both sides of the equation.

Adding in energy terms, like \(1235 \, \mathrm{kJ}\), results in a thermochemical equation. These equations provide a full picture of the chemical process, including energy changes, giving us a deeper understanding of the reaction's overall impact.