Question

The decomposition of \(\mathrm{Ca}(\mathrm{OH})_{2}(s)\) into \(\mathrm{CaO}(s)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\) at constant pressure requires the addition of \(109 \mathrm{~kJ}\) of heat per mole of \(\mathrm{Ca}(\overline{\mathrm{OH}})_{2}\). (a) Write a balanced thermochemical equation for the reaction. (b) Draw an enthalpy diagram for the reaction.

Short answer

(a) The balanced thermochemical equation for the given reaction is: Ca(OH)2 (s) + 109 kJ → CaO (s) + H2O (g) (b) The enthalpy diagram for this reaction shows an initial enthalpy level for reactants, an increase of 109 kJ, and a final enthalpy level for products. A horizontal arrow connects the reactants and products, representing the overall energy change (ΔH) of +109 kJ, indicating that the reaction is endothermic.

Step-by-step solution

(a) Write a balanced thermochemical equation

Since the reaction involves the decomposition of calcium hydroxide (Ca(OH)2) into calcium oxide (CaO) and water (H2O), we write the following balanced equation: Ca(OH)2 (s) → CaO (s) + H2O (g) Now, to include the heat required for the reaction, which is 109 kJ per mole of Ca(OH)2, we write the thermochemical equation as: Ca(OH)2 (s) + 109 kJ → CaO (s) + H2O (g)

(b) Draw an enthalpy diagram for the reaction

To draw the enthalpy diagram for the reaction, follow these steps: 1. On a piece of paper or using a graphics program, draw two horizontal lines representing the initial enthalpy and final enthalpy levels. Label these lines "Reactants" and "Products," respectively, since they represent the enthalpies of the reactants and products in the reaction. 2. Next, draw a vertical arrow pointing upwards from the "Reactants" line, indicating the addition of 109 kJ of heat to the system. Label this arrow "+109 kJ." 3. Now, draw a downward arrow from the upper part of the vertical arrow pointing to the "Products" line, indicating the conversion of calcium hydroxide to calcium oxide and water when heat is supplied. Label this arrow "Ca(OH)2 (s) → CaO (s) + H2O (g)." 4. Finally, draw a horizontal arrow connecting the "Reactants" line and "Products" line, representing the overall energy change (ΔH) during the reaction. Label this arrow "ΔH = +109 kJ." The enthalpy diagram should show that the reaction requires an external energy input of 109 kJ to convert the reactants (calcium hydroxide) into the products (calcium oxide and water). The positive value of ΔH indicates that the reaction is endothermic.

Key concepts

Enthalpy Diagram

The enthalpy diagram is a visual tool used in thermochemistry to illustrate the energy changes during a chemical reaction. Imagine you are watching the energy levels of a reaction as if you were observing the elevation levels on a hiking trail. On this trail, the reactants start at one elevation (or energy level), and the products end up at another.

The ‘hiking path’ that connects these points represents the process of the reaction itself. When you plot this on a graph, the vertical axis represents enthalpy (H), which is a measure of the total energy of a system. The horizontal axis represents the progression of the reaction from reactants to products.

If the reaction requires energy input, such as the decomposition of calcium hydroxide, the path leads uphill, indicating an increase in enthalpy and characterizing the process as endothermic. Conversely, for exothermic reactions, the path would lead downhill, showcasing a release of energy. In your studies, enthalpy diagrams can provide an intuitive grasp of such energetic changes.

Endothermic Reactions

Endothermic reactions, like our friend inviting the warmth of the sun to start the day, absorb energy from their surroundings. This energy absorption is often in the form of heat, leading to an increase in the enthalpy (ΔH > 0) of the system. Because the system ‘soaks up’ energy, the temperature of the surroundings decreases. It's like when you mix baking soda and vinegar for a school volcano project and touch the mixture to find it colder.

Endothermic reactions are essential for various natural and industrial processes — from photosynthesis in plants, where they use sunlight to make food, to the production of certain materials like ammonium nitrate for fertilizers. Remember that these reactions require a continuous input of energy to proceed, like sustaining a campfire with more wood to keep burning.

Chemical Decomposition

Chemical decomposition, like a skilled magician separating a deck of cards into individual suits, involves breaking down a compound into simpler substances or elements. It’s a critical process both in nature and industry, playing a role in everything from the rotting of organic matter to the recycling of metal from ores.

In your exercise, calcium hydroxide undergoes decomposition to form calcium oxide and water vapor when energy is added. This breakdown often requires an initial energy investment to overcome the forces holding the compound together, akin to needing a firm grip to tear a piece of tough fabric. Understanding the decomposition process allows chemists to predict and control reactions for applications such as waste management, material production, and even the design of medication.