Problem 12 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Calcite and aragonite are two forms of calcium carbonate. Calculate the enthalpy change for the transition from calcite to aragonite. (AH(calcite) \(=-1206.9 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(\Delta \mathrm{H}\) (aragonite) \(=\) \(-1207.1 \mathrm{kJ} \mathrm{mol}^{-1}\), j (Section 13.3)

Step-by-Step Solution

Answer

The enthalpy change for the transition from calcite to aragonite is \(-0.2\, \text{kJ} \cdot \text{mol}^{-1}\).

Step 1: Understand the Concept

We need to calculate the enthalpy change for the transition from one form of calcium carbonate, calcite, to another form, aragonite. This is done by calculating the difference in their respective enthalpy values.

Step 2: Identify Known Values

Given: \( \Delta H(\text{calcite}) = -1206.9\, \text{kJ} \cdot \text{mol}^{-1} \) and \( \Delta H(\text{aragonite}) = -1207.1\, \text{kJ} \cdot \text{mol}^{-1} \). These values represent the enthalpy of formation for each form of calcium carbonate.

Step 3: Set Up the Expression for Enthalpy Change

The enthalpy change \( \Delta H_{\text{transition}} \) for the transition from calcite to aragonite can be expressed as: \( \Delta H_{\text{transition}} = \Delta H(\text{aragonite}) - \Delta H(\text{calcite}) \).

Step 4: Substitute and Calculate

Substitute the given values into the expression: \[ \Delta H_{\text{transition}} = (-1207.1) - (-1206.9) \] Calculate the result: \[ \Delta H_{\text{transition}} = -1207.1 + 1206.9 \] \[ \Delta H_{\text{transition}} = -0.2\, \text{kJ} \cdot \text{mol}^{-1} \]

Key Concepts

Calcium Carbonate

Calcium carbonate is a common chemical compound with the formula \( \text{CaCO}_3 \). It is widely found in nature in the form of the minerals calcite, aragonite, and vaterite. Each of these forms, known as polymorphs, has unique physical characteristics. Calcium carbonate is mainly used in the production of lime, as a dietary calcium supplement, and as an ingredient in various industrial processes.

The most common polymorphs of calcium carbonate are calcite and aragonite. While they have the same chemical composition, they differ in crystal structure.

• **Calcite** is the more stable and abundant form, often found in sedimentary rocks such as limestone.
• **Aragonite**, although less stable at room temperature, forms in marine and freshwater environments and is found in mollusk shells and coral.

This variation in structure affects the physical properties, such as hardness and color, of the mineral forms. Understanding these differences helps in various fields such as geology, material science, and even biochemistry.

Calcite to Aragonite Transition

The transition from calcite to aragonite involves a change in structure at a molecular level. Although both are forms of calcium carbonate, they stabilize under different conditions of pressure and temperature. This transition is crucial in understanding geological processes and material science.

The enthalpy change, or \( \Delta H \), for the transition indicates the energy difference between the two forms.

• **Negative enthalpy change**, as in the given exercise (-0.2 kJ/mol), suggests the transition from calcite to aragonite releases energy slightly, albeit almost negligible.

Analyzing this transition aids in areas such as mineral extraction and synthesis, where understanding stability and environmental conditions is critical.

In the lab, this transition can be induced through specific pressure and temperature alterations, providing insights into engineering and earth sciences.

Inorganic Chemistry

Inorganic chemistry involves the study of inorganic compounds, excluding organic compounds based on carbon-hydrogen bonds. It encompasses a wide range of substances, including metals, minerals, and organometallic compounds.

Calcium carbonate and its polymorphs are prime subjects of study in inorganic chemistry. The investigation of their properties, reactions, and synthesis falls under this discipline.

• **Reactivity and transformation**: Studying the transition from one form of calcium carbonate to another involves understanding bond strengths, reactivity, and the conditions that promote such changes.
• **Applications**: Inorganic chemistry principles are applied in fields like materials science to develop new materials with specific properties.

Understanding entities like calcium carbonate helps chemists design applications in areas such as construction, pharmaceuticals, and environmental science.

Thermodynamics

Thermodynamics is a branch of physical science concerned with heat and temperature and their relation to energy and work. The principles of thermodynamics are essential for understanding changes in enthalpy and other energy exchanges.

In our context, the transition from calcite to aragonite is a thermodynamic process. It involves calculations of enthalpy change, representing the heat content difference due to a transition or reaction.

• **First Law of Thermodynamics**: This law states that energy cannot be created or destroyed, only transformed. This principle underlies the calculation that the energy difference during the calcite to aragonite transition involves a transfer of energy rather than an absolute gain or loss.
• **Enthalpy change**: It is a crucial indicator of energy absorption or release during chemical processes, helping predict the feasibility and spontaneity of a reaction under given conditions.

By analyzing such processes, thermodynamics allows scientists to design and optimize industrial processes, improving efficiency and innovation.