Problem 40 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

(a) The balanced thermochemical equation for the decomposition of slaked lime is: \( \mathrm{Ca(OH)_2\longrightarrow CaO + H_2O; \, ΔH = 109\,kJ/mol} \) (b) To draw the enthalpy diagram: 1. Label y-axis as enthalpy level (in kJ/mol) and x-axis as progress of the reaction. 2. Mark the initial energy level of the reactants (Ca(OH)₂) as point A. 3. Add ∆H (109 kJ/mol) to the initial energy level, mark as point B, representing the energy level of products (CaO and H₂O). 4. Draw an arrow from point A to point B, indicating heat addition. 5. Label arrow with enthalpy change (109 kJ/mol).

Step 1: Balanced chemical equation

To write a balanced chemical equation, we first need to identify the reactant and the products. In this case, the reactant is calcium hydroxide (Ca(OH)₂) and the products are calcium oxide (CaO) and water vapor (H₂O). Now, we can balance the number of atoms for each element on both sides of the equation, and include the heat added during the reaction. \( \mathrm{Ca(OH)_2\longrightarrow CaO + H_2O + 109\,kJ} \)

Step 2: Thermochemical equation

In the thermochemical equation, we will also mention the enthalpy change, \(ΔH\), which is given to be added heat per mole of reactant, 109 kJ. \( \mathrm{Ca(OH)_2\longrightarrow CaO + H_2O; \, ΔH = 109\,kJ/mol} \) (b) Draw an enthalpy diagram for the reaction.

Step 3: Enthalpy diagram

In an enthalpy diagram, the energy of the reaction is plotted against the progress of the reaction, showing the energy levels of the reactants and products. In this decomposition reaction, heat is added to the reactants, which raises their energy level to the combined energy level of the products. 1. The y-axis represents the enthalpy level (in kJ/mol), and the x-axis shows the progress of the reaction. 2. Mark the initial energy level of the reactants (Ca(OH)₂) on the y-axis. Label this point A. 3. Add the ∆H (109 kJ/mol) to the initial energy level of the reactants. Mark this point B on the y-axis, which represents the energy level of the products (CaO and H₂O). 4. Draw an arrow from point A to point B, indicating the addition of heat during the reaction. 5. Label the arrow with the given enthalpy change (109 kJ/mol).

Key Concepts

Thermochemical Equation

Understanding a thermochemical equation is pivotal as it provides crucial information about a chemical reaction, including the enthalpy change. A thermochemical equation is like a regular chemical equation with the addition of energy change information. It’s meticulously balanced not only regarding the atoms but also the energy involved. Our example from the slaked lime decomposition illustrates this concept.

In our case, the thermochemical equation is: \( \text{Ca(OH)_2 (s) } \rightarrow \text{ CaO (s) + H_2O (g) + 109 kJ} \). This equation tells us that when one mole of calcium hydroxide decomposes, it forms one mole of calcium oxide and one mole of water vapor, with an absorption of 109 kJ of heat. This heat amount is described as the enthalpy change (more on that in the next section), signifying the energy needed to drive the reaction at constant pressure.

When dealing with thermochemical equations, remember the following points:

• The phases of each compound must be indicated as (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions.
• Energy changes are usually noted in kJ (kilojoules), and the sign indicates whether the reaction absorbs (+) or releases (-) energy.
• Stoichiometric coefficients in the equation indicate the molar ratios of reactants and products and correlate to the ratio of energy change, as seen with the 109 kJ per mole of calcium hydroxide.

Enthalpy Change

Enthalpy change (ΔH) is the term scientists use to describe the heat energy exchange during a chemical reaction under constant pressure. It is a central concept in thermodynamics and an integral part of understanding energy flow within chemical systems. The enthalpy change can be endothermic (absorbing heat) or exothermic (releasing heat).

For the slaked lime decomposition described above, the reaction is endothermic since it requires the absorption of heat. The enthalpy change is positive, marked by a ΔH value of +109 kJ/mol. This signifies that energy is absorbed from the surroundings to break the bonds in calcium hydroxide while forming new bonds in calcium oxide and water vapor.

Understanding the enthalpy change gives insights into:

• The energy required to initiate a reaction, or the heat produced as a reaction by-product.
• Predicting whether a reaction will be spontaneous or needs external energy to proceed.
• Designing energy-efficient industrial processes and calculating the heat exchange in chemical reactions for various applications like heating and cooling systems.

Note that the enthalpy change correlates directly to the stoichiometry of the reaction. That’s why it’s crucial to associate the enthalpy change to the correct amount of reactants, just as the stoichiometric coefficients in the thermochemical equation illustrate.

Decomposition Reaction

A decomposition reaction occurs when a single compound breaks down into two or more simpler substances. These reactions are the reverse of synthesis reactions and play an essential role in both natural processes, like digestion, and industrial applications, such as the production of lime from limestone.

The decomposition of slaked lime (Ca(OH)_2) into calcium oxide (CaO) and water vapor (H_2O) is an exemplary decomposition reaction. It requires the addition of energy to overcome the chemical bonds in the compound. Here is what typically happens in a decomposition reaction:

• Complex molecules break down into simpler ones, typically requiring an input of energy.
• Decomposition may occur via various mechanisms, such as thermal decomposition, electrolysis, or photolysis, depending on the nature of the substance and conditions of the reaction.

The knowledge of the specific decompositions helps chemists and engineers to harness or mitigate these reactions. For example, understanding the decomposition of calcium hydroxide is crucial in industries such as construction (for the production of cement) and environmental engineering (for waste treatment processes).