Enthalpy Changes
Enthalpy Changes
Enthalpy, symbolized as $H$, is a thermodynamic quantity that is a measure of the total heat content of a system. It is defined as the sum of the internal energy $U$ of the system and the product of its pressure $P$ and volume $V$:
$$ H = U + PV $$
Enthalpy changes, $\Delta H$, represent the heat absorbed or released by a system at constant pressure during a chemical or physical process. It is an important concept in thermodynamics and chemistry, particularly in the study of chemical reactions and phase changes.
Types of Enthalpy Changes
There are several types of enthalpy changes that are important to understand:
- Enthalpy of Reaction ($\Delta H_{\text{rxn}}$): The enthalpy change that occurs during a chemical reaction at constant pressure.
- Enthalpy of Formation ($\Delta H_{\text{f}}$): The change in enthalpy when one mole of a compound is formed from its elements in their standard states.
- Enthalpy of Combustion ($\Delta H_{\text{c}}$): The enthalpy change when one mole of a substance is completely burned in oxygen.
- Enthalpy of Fusion ($\Delta H_{\text{fus}}$): The change in enthalpy when one mole of a solid turns into a liquid at its melting point.
- Enthalpy of Vaporization ($\Delta H_{\text{vap}}$): The change in enthalpy when one mole of a liquid turns into a gas at its boiling point.
Table of Differences
| Property | Enthalpy of Reaction | Enthalpy of Formation | Enthalpy of Combustion |
|---|---|---|---|
| Definition | Change during a reaction | Change forming 1 mole from elements | Change when 1 mole is burned |
| Standard Conditions | 298 K, 1 atm | 298 K, 1 atm, elements in standard states | 298 K, 1 atm |
| Sign Convention | Exothermic (-), Endothermic (+) | Negative for exothermic, Positive for endothermic | Usually negative (exothermic) |
| Calculation | Sum of products - Sum of reactants | Sum of products - Sum of elements | Heat released during combustion |
Formulas
The enthalpy change for a reaction can be calculated using the enthalpies of formation of the reactants and products:
$$ \Delta H_{\text{rxn}} = \sum (\Delta H_{\text{f,products}}) - \sum (\Delta H_{\text{f,reactants}}) $$
For a combustion reaction, the enthalpy change is the heat released during the process:
$$ \Delta H_{\text{c}} = -q $$
where $q$ is the heat released.
Examples
Example 1: Enthalpy of Reaction
Consider the reaction of hydrogen gas with oxygen to form water:
$$ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) $$
The enthalpy of formation for $H_2O(l)$ is $-285.8 \text{ kJ/mol}$. Since the elements are in their standard states, their enthalpy of formation is zero. Thus, the enthalpy of reaction is:
$$ \Delta H_{\text{rxn}} = [2 \times (-285.8 \text{ kJ/mol})] - [2 \times 0 + 1 \times 0] = -571.6 \text{ kJ} $$
Example 2: Enthalpy of Combustion
For the combustion of methane:
$$ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) $$
The enthalpy of combustion for methane can be calculated if the enthalpies of formation for $CO_2$ and $H_2O$ are known, and the heat released is measured. Suppose the enthalpies of formation are $-393.5 \text{ kJ/mol}$ for $CO_2$ and $-285.8 \text{ kJ/mol}$ for $H_2O$, and the enthalpy of formation for $CH_4$ is $-74.8 \text{ kJ/mol}$. The enthalpy of combustion is:
$$ \Delta H_{\text{c}} = [1 \times (-393.5 \text{ kJ/mol}) + 2 \times (-285.8 \text{ kJ/mol})] - [1 \times (-74.8 \text{ kJ/mol})] $$ $$ \Delta H_{\text{c}} = -890.3 \text{ kJ/mol} $$
Example 3: Enthalpy of Fusion
The enthalpy of fusion for water is $6.01 \text{ kJ/mol}$. This is the amount of energy required to melt one mole of ice at 0°C and 1 atm.
Example 4: Enthalpy of Vaporization
The enthalpy of vaporization for water is $40.7 \text{ kJ/mol}$. This is the amount of energy required to vaporize one mole of water at 100°C and 1 atm.
Understanding enthalpy changes is crucial for predicting the heat exchange in chemical reactions, designing chemical processes, and understanding the energy requirements for phase changes. It also plays a vital role in the study of reaction spontaneity and equilibrium.