Problem 69 - General Chemistry: Principles and Modern Applications

Question

The standard enthalpy of reaction for the decomposition of calcium carbonate is \(\Delta H^{\circ}=813.5 \mathrm{kJmol}^{-1}\) As temperature increases, does the concentration of calcium carbonate increase, decrease, or remain the same? Explain.

Step-by-Step Solution

Answer

As the temperature increases, the concentration of calcium carbonate will decrease due to the endothermic nature of the reaction. This happens in accordance with Le Chatelier's principle, as the reaction shifts to the right (favoring the products), thus lowering the concentration of the reactant (calcium carbonate).

Step 1: Identify the Type of Reaction

The enthalpy of reaction, \(\Delta H^{\circ}\), is positive (813.5 kJ/mol). Thus, the reaction is endothermic, meaning it absorbs heat from its environment. For the decomposition of calcium carbonate, the reaction can be written as follows: \(CaCO_{3}(s) \rightarrow CaO(s) + CO_{2}(g)\), \(\Delta H^{\circ}=813.5 \mathrm{kJ mol}^{-1}\)

Step 2: Apply Le Chatelier's Principle

According to Le Chatelier's principle, a system at equilibrium will adjust to counteract a change in conditions. In this case, since the reaction is endothermic, an increase in temperature will be interpreted as an increase in reactants for the system, and thus the reaction will shift to the right to absorb this excess heat, favoring the formation of products.

Step 3: Determine the Effect on Calcium Carbonate Concentration

Since the reaction shifts to the right in response to a temperature increase, the concentration of the reactant, calcium carbonate, will decrease. The system uses the excess heat to decompose more calcium carbonate and thus decreases its concentration to make up for the increased temperature.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a foundational concept in chemistry that describes how a chemical system at equilibrium adjusts to changes in its environment. When an external condition, such as temperature, pressure, or concentration of reactants or products, is altered, the equilibrium will shift in a direction that helps to counteract the change.

For instance, if the temperature of a system is increased, as in the case of an endothermic reaction, the system will respond by shifting the equilibrium to the right — favoring the production of more products — to absorb the excess heat. Conversely, if the temperature is decreased, an exothermic reaction will shift to produce more reactants and release heat, helping to maintain a stable temperature. Le Chatelier's Principle is an essential tool for predicting the behavior of chemical reactions under different conditions and is fundamental to understanding reaction kinetics and industrial applications where maintaining a constant state is crucial.

Endothermic Reaction

An endothermic reaction is characterized by the absorption of heat from its surroundings, which results in a net intake of energy. In such reactions, the standard enthalpy change \( \Delta H^{\text{\circ}} \) is positive, indicating that energy is required to drive the process forward.

These reactions can be recognized by their need for heat — they feel cold to the touch as they occur because they draw thermal energy from their environment. Examples include the melting of ice or the decomposition of calcium carbonate as described in the exercise. Understanding endothermic reactions is important in many fields including thermodynamics, environmental science, and engineering, as they relate to energy transfer and the physical changes of materials under varying temperatures.

Calcium Carbonate Decomposition

The decomposition of calcium carbonate \( CaCO_{3} \) is a classic example of an endothermic reaction. When calcium carbonate is heated, it breaks down to form calcium oxide \( CaO \) and carbon dioxide gas \( CO_{2} \) with the absorption of heat.

This process, which is described by the chemical equation \( CaCO_{3}(s) \rightarrow CaO(s) + CO_{2}(g) \) with a standard enthalpy change \( \Delta H^{\text{\circ}} = 813.5 \text{ kJ/mol} \) is crucial in various industries, such as the production of lime for cement and as a part of the cycle in carbon sequestration and release in nature. By understanding the conditions under which calcium carbonate decomposes, scientists and engineers can better control industrial processes and predict environmental impacts.

Chemical Equilibrium

Chemical equilibrium is the state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of the reactants and products. It does not mean that the reactions have stopped, but that they are occurring at the same rate and the system is stabilized.

However, a chemical equilibrium can be disrupted by changes in temperature, pressure, or concentrations, which can cause the system to reallocate substances to re-establish equilibrium according to Le Chatelier's Principle. Understanding equilibrium is particularly important in synthetic chemistry, pharmaceuticals, and biological systems, as many reactions are reversible and equilibria can be manipulated to favor the production of desired compounds.