7.2 Enthalpy

Enthalpy is a key concept in thermochemistry, measuring the heat content of a system at constant pressure. It helps us understand energy changes in chemical reactions, distinguishing between exothermic (heat-releasing) and endothermic (heat-absorbing) processes.

Calculating enthalpy changes is crucial for predicting reaction spontaneity and energy flow. We use tools like Hess's law, standard enthalpies of formation, and calorimetry to determine these values, connecting energy changes to real-world chemical processes.

Enthalpy and its significance in chemical reactions

Definition and properties of enthalpy

• Enthalpy represents the total heat content of a system at constant pressure
• Enthalpy is a state function, its value depends only on the current state of the system, not the path taken to reach that state
• Enthalpy is an extensive property, its value depends on the amount of substance present in the system
• The standard enthalpy of formation (ΔH°f) is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states at 1 atm pressure and a specified temperature (usually 25°C)

Enthalpy changes in chemical reactions

• Enthalpy changes (ΔH) indicate the amount of heat absorbed or released by a system during a chemical reaction or physical process
• Exothermic reactions have a negative ΔH, releasing heat to the surroundings (combustion reactions)
• Endothermic reactions have a positive ΔH, absorbing heat from the surroundings (photosynthesis)
• The sign and magnitude of ΔH provide information about the thermal nature and heat exchange of a reaction

Calculating enthalpy changes using Hess's law and standard enthalpies of formation

Hess's law

• Hess's law states that the total enthalpy change for a reaction is independent of the pathway and is equal to the sum of the enthalpy changes for the individual steps
• Hess's law allows for the calculation of enthalpy changes for reactions that cannot be directly measured by adding together the enthalpy changes of other reactions that sum to the desired reaction
• Enthalpy changes for phase transitions (melting, vaporization, and sublimation) can be incorporated into Hess's law calculations

Calculating standard enthalpy of reaction

• The standard enthalpy of reaction (ΔH°rxn) can be calculated using the standard enthalpies of formation (ΔH°f) of the reactants and products:

$ΔH°rxn = ∑(n × ΔH°f (products)) - ∑(n × ΔH°f (reactants))$

where n is the stoichiometric coefficient

• Standard enthalpies of formation are tabulated for many compounds, allowing for the calculation of ΔH°rxn without directly measuring the heat of the reaction

Determining enthalpy change using calorimetry

Calorimetry basics

• Calorimetry is an experimental technique used to measure the heat exchanged during a chemical reaction or physical process
• In a constant-pressure calorimeter, the measured heat (q) is equal to the enthalpy change (ΔH) for the system
• The heat capacity (C) of a calorimeter is the amount of heat required to raise its temperature by one degree Celsius or Kelvin
• The specific heat capacity (c) is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin

Calculating enthalpy change from calorimetry data

• The enthalpy change for a reaction can be calculated using the equation:

$q = m × c × ΔT$ where m is the mass of the solution, c is the specific heat capacity, and ΔT is the temperature change

• The specific heat capacity of water (4.184 J/g·°C) is often used in aqueous calorimetry experiments
• The enthalpy change calculated from calorimetry data can be used to determine the thermal nature of the reaction (exothermic or endothermic)

Predicting reaction spontaneity based on enthalpy and entropy changes

Entropy and the second law of thermodynamics

• Entropy (S) is a measure of the disorder or randomness of a system
• A positive ΔS indicates an increase in disorder, while a negative ΔS indicates a decrease in disorder
• The second law of thermodynamics states that the entropy of the universe always increases for a spontaneous process
• Examples of entropy-increasing processes include gas expansion, mixing of substances, and melting of solids

Gibbs free energy and spontaneity

• The Gibbs free energy change (ΔG) combines the effects of enthalpy and entropy changes to determine the spontaneity of a reaction at constant temperature and pressure:

$ΔG = ΔH - TΔS$

where T is the absolute temperature in Kelvin

• A reaction is spontaneous when ΔG is negative, non-spontaneous when ΔG is positive, and at equilibrium when ΔG is zero
• The temperature of a system can affect the spontaneity of a reaction by influencing the relative magnitudes of the enthalpy and entropy terms in the Gibbs free energy equation
• Examples of spontaneous reactions include the rusting of iron and the decomposition of hydrogen peroxide