Problem 38 - Chemistry The Science in Context

Question

Gypsum is the common name of calcium sulfate dihydrate \(\left(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right) .\) When gypsum is heated to \(150^{\circ} \mathrm{C},\) it loses most of the water in its formula and forms plaster of Paris \(\left(\mathrm{CaSO}_{4} \cdot 0.5 \mathrm{H}_{2} \mathrm{O}\right):\) \(2\left(\mathrm{CaSO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)(s) \rightarrow 2\left(\mathrm{CaSO}_{4} \cdot 0.5 \mathrm{H}_{2} \mathrm{O}\right)(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\) What is the sign of \(\Delta H\) for making plaster of Paris from gypsum?

Step-by-Step Solution

Answer

Answer: The sign of ΔH for this reaction is negative, as it is an exothermic reaction involving heat loss.

Step 1: Recall the definitions of exothermic and endothermic reactions

An exothermic reaction is a chemical reaction in which heat is released to the surroundings, resulting in a decrease in the energy of the system. In this case, ΔH is negative. On the other hand, an endothermic reaction is a chemical reaction in which heat is absorbed from the surroundings, resulting in an increase in the energy of the system. In this case, ΔH is positive.

Step 2: Examine the given reaction

We have the following reaction: \(2\left(\mathrm{CaSO}_{4} \cdot 2\mathrm{H}_{2} \mathrm{O}\right)(s) \rightarrow 2\left(\mathrm{CaSO}_{4} \cdot 0.5 \mathrm{H}_{2} \mathrm{O}\right)(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\) The water molecules in gypsum are being removed by heating to form plaster of Paris and water as steam. The steam escapes, so the energy stored in the bonds of gypsum is lost during the process.

Step 3: Determine the sign of ΔH for the reaction

Since the reaction involves heat loss (steam escape), it is an exothermic reaction. Therefore, the sign of ΔH for this reaction is negative. ΔH < 0

Key Concepts

Endothermic Reactions

Endothermic reactions are an essential type of chemical reaction that absorb heat from their surroundings. As you might imagine, this means that the system gaining energy results in a positive change in enthalpy, denoted as \( \Delta H > 0 \).

To better understand this concept, imagine ice melting into water. The ice absorbs heat from its environment to change phase. This absorption is endothermic because energy, in the form of heat, is required to break the bonds and transition the ice into a liquid state. In the case of our original exercise above, if forming plaster of Paris required additional energy from the surroundings, it would be an endothermic reaction. However, as stated in the problem, heating leads to a loss of water as steam, pointing towards an exothermic path.

This example shows that in endothermic reactions:

• Energy is absorbed from the surroundings.
• The temperature of the surroundings decreases.
• \( \Delta H \) is positive.

Exothermic Reactions

Exothermic reactions happen when heat is released into the surroundings during a chemical change. This release of energy causes \( \Delta H \) to be negative. During these reactions, the system loses energy, usually in the form of heat, which is then released to the environment.

In the example from the original exercise, heating gypsum results in the loss of water as steam, which is an indication of exothermic behavior since the water is actually steam (a gas) that's leaving the system. The bonds within the water molecules absorb energy from the environment to break free and escape, leading to a net release of energy from the solidifying material.

Key features of exothermic reactions include:

• Energy is released to the surroundings.
• The temperature of the surroundings increases.
• \( \Delta H \) is negative.

This is often visible in various everyday processes, such as freezing, condensation, or combustion reactions, all of which release energy.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the relationships between chemical reactions and energy changes involving heat.

When analyzing reactions like the formation of plaster of Paris, thermochemistry helps us understand how and why certain chemical processes consume or release energy. In the context of the exercise, thermochemistry allows us to predict that the heating of gypsum produces steam, indicating that energy is released during this transformation, characterizing it as an exothermic reaction.

To grasp thermochemistry more thoroughly, consider these points:

• It quantifies energy changes in both physical and chemical changes.
• It uses concepts such as enthalpy (\( \Delta H \)), where a negative value represents energy release (exothermic) and a positive value represents energy absorption (endothermic).
• Provides insights into reaction feasibility and conditions, such as temperature and pressure required for a reaction to occur.

Thermochemistry is pivotal in fields like environmental science, materials science, and engineering, where controlling energy flow is often critical.