Problem 89 - Chemistry Matter and Change

Question

For a given compound, what does the standard enthalpy of formation describe?

Step-by-Step Solution

Answer

The standard enthalpy of formation (ΔHf°) describes the change in enthalpy when one mole of a compound is formed from its constituent elements in their most stable forms under standard conditions (1 atm pressure and 298.15 K temperature). It is represented by the general equation \( \Delta H^\circ_{rxn} = \sum n \Delta H^\circ_{f(products)} - \sum m \Delta H^\circ_{f(reactants)} \), where \( \Delta H^\circ_{rxn} \) is the standard enthalpy change for the reaction, and \( n \) and \( m \) are the stoichiometric coefficients for products and reactants. For example, when forming water (H₂O) from hydrogen (H₂) and oxygen (O₂), the standard enthalpy of formation for water is -285.8 kJ/mol, meaning 285.8 kJ of heat is released when one mole of water is formed under standard conditions.

Step 1: Definition

The standard enthalpy of formation, denoted as ΔHf°, is the change in enthalpy that occurs when one mole of a compound is formed from its constituent elements in their most stable forms under standard conditions (1 atm pressure and 298.15 K temperature).

Step 2: General Equation

The general equation for the enthalpy of formation of a compound can be represented as: \( \Delta H^\circ_{rxn} = \sum n \Delta H^\circ_{f(products)} - \sum m \Delta H^\circ_{f(reactants)} \) where \( \Delta H^\circ_{rxn} \) is the standard enthalpy change for the reaction, \( n \) and \( m \) are the stoichiometric coefficients for products and reactants, and \( \Delta H^\circ_{f} \) represents the standard enthalpy of formation for each compound involved in the reaction.

Step 3: Example

For example, let's consider the formation of water (H₂O) from its elements, hydrogen (H₂) and oxygen (O₂). The balanced chemical equation for this reaction is: \( H₂ (g) + \frac{1}{2} O₂ (g) \rightarrow H₂O (l) \) The standard enthalpy of formation for water can be obtained from tables and is found to be -285.8 kJ/mol. This means that 285.8 kJ of heat is released when one mole of water is formed from its elements under standard conditions.

Key Concepts

Chemical Thermodynamics

Chemical thermodynamics is all about the study of energy changes in chemical processes. Essentially, it explores how energy is absorbed or released in reactions. When we talk about enthalpy, it refers to the heat content of a system at constant pressure. Standard enthalpy of formation fits right into this because it is a specific type of enthalpy change. It's particularly useful for predicting the energy changes during the formation of compounds from their elements.

• Thermodynamics helps us understand if a reaction can occur spontaneously.
• It provides insights into the equilibrium position of a chemical process.
• We learn about how much energy we need to input or how much energy we expect to gain from a reaction.

With the concept of enthalpy in mind, thermodynamics becomes a powerful tool for both scientific research and practical applications, like in engineering and environmental sciences. It helps us to predict product formation and energy requirement for processes.

Enthalpy Change

The enthalpy change of a reaction, often denoted as ΔH, is a measure of the total energy absorbed or released during the transformation of reactants into products. Enthalpy change is crucial because it tells us whether a chemical reaction is exothermic or endothermic.
An exothermic reaction releases energy into the surroundings, usually in the form of heat, and has a negative ΔH. Conversely, an endothermic reaction absorbs energy from the surroundings and has a positive ΔH.
Consider this equation for enthalpy change:\[\Delta H = \sum n \Delta H^\circ_{f(products)} - \sum m \Delta H^\circ_{f(reactants)}\]Here is how the equation works:

• \( n \) and \( m \) are the coefficients of the products and reactants from the balanced chemical equation.
• \( \Delta H^\circ_{f} \) is the standard enthalpy of formation for each compound.

This formula provides us with the enthalpy change for the overall chemical reaction, helping us determine heat flow and energy exchange.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to form new substances. During a reaction, bonds between atoms in the reactants are broken, and new bonds form to create the products. Understanding the energy associated with these reactions is central to chemical thermodynamics.
For any given chemical reaction, three main steps are involved:

• Breaking of bonds in reactants, which requires energy input.
• Formation of new bonds to create products, which releases energy.
• The net energy change is represented by the enthalpy change (ΔH).

Using the example of water formation:- The reaction \( H_2 (g) + \frac{1}{2} O_2 (g) \rightarrow H_2O (l) \) shows us that bonds in hydrogen and oxygen molecules are broken and bonds in water molecules are formed.- The standard enthalpy of formation for water, -285.8 kJ/mol, indicates the overall energy change when water is synthesized from its elements.
By calculating these changes and comparing energy inputs and outputs, we better understand the "cost" and "gain" of reactions in terms of energy. This understanding is crucial for tasks like optimizing reaction conditions or designing energy-efficient processes.