Thermochemistry: Energy, Enthalpy, and Standard Enthalpies of Reaction

Thermochemistry (Chapter 5)

Introduction to Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, that accompany chemical reactions and physical changes. It is essential for understanding how energy is transferred and transformed in chemical processes.

Energy and Its Forms

Potential Energy

Potential energy is the energy an object possesses due to its position or chemical composition. For example, a cyclist at the top of a hill has high potential energy, which decreases as they descend.

• Definition: Energy stored due to position or arrangement.

• Example: Chemical bonds in molecules store potential energy.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion.

• Definition: Energy of movement.

• Example: A moving bicycle or molecules in motion.

Units of Energy

Joule and Calorie

The SI unit of energy is the Joule (J). Another commonly used unit is the calorie (cal), especially in nutrition.

• Joule (J): $1~J = 1~N \cdot m = 1~kg~m^2~s^{-2}$

• Calorie: $1~cal = 4.184~J$

• Application: Nutrition labels often use calories to indicate energy content.

Work and Heat

Definitions

Energy can be transferred as work or heat:

• Work (w): Energy used to cause an object to move.

• Formula: $w~(J) = F~(N) \times d~(m)$

• Heat (q): Energy used to cause the temperature of an object to change.

• Direction: Heat always flows from warmer objects to cooler objects.

System and Surroundings

Definitions

In thermochemistry, the system is the part of the universe we study (e.g., reactants and products in a reaction), while the surroundings are everything else.

• System: The chemical species involved in the reaction.

• Surroundings: The environment outside the system.

First Law of Thermodynamics

Law of Conservation of Energy

The First Law of Thermodynamics states that energy can neither be created nor destroyed. The total energy of the universe is constant.

• Implication: Energy lost by the system is gained by the surroundings, and vice versa.

• Example: Hot water cooling releases energy to the environment, but the total energy remains unchanged.

Internal Energy

Definition and Change

Internal energy (E) is the sum of all kinetic and potential energies of the components of a system.

• Change in internal energy: $\Delta E = E_{final} - E_{initial}$

• Endergonic: $\Delta E > 0$ (system absorbs energy)

• Exergonic: $\Delta E < 0$ (system releases energy)

Exchange of Energy

Energy exchange between system and surroundings occurs as heat (q) or work (w):

• Formula: $\Delta E = q + w$

• Sign conventions:

  • q > 0: System gains heat

  • q < 0: System loses heat

  • w > 0: Work done on system

  • w < 0: Work done by system

Heat Exchange: Endothermic and Exothermic Processes

Definitions

• Endothermic: Heat is absorbed by the system from the surroundings ($q > 0$).

• Exothermic: Heat is released by the system to the surroundings ($q < 0$).

• Example: Combustion of hydrogen is exothermic.

Enthalpy (H)

Definition and Properties

Enthalpy (H) is a thermodynamic function that accounts for heat flow at constant pressure, when only pressure-volume work is performed.

• Formula: $\Delta H = \Delta E + P\Delta V$

• At constant pressure: $\Delta H = q_p$ (heat at constant pressure)

• Extensive property: Value depends on the amount of substance.

Enthalpies of Reaction

Calculating Enthalpy Change

The enthalpy change for a reaction ($\Delta H_{rxn}$) is the enthalpy of products minus the enthalpy of reactants.

• Formula: $\Delta H_{rxn} = H_{products} - H_{reactants}$

• Direction: $\Delta H$ for the reverse reaction is equal in magnitude but opposite in sign to the forward reaction.

• Physical state: $\Delta H$ depends on the physical states of reactants and products.

Hess's Law

Statement and Application

Hess's Law states that if a reaction is carried out in a series of steps, the overall enthalpy change is the sum of the enthalpy changes for the individual steps.

• Formula: $\Delta H_{overall} = \sum \Delta H_{steps}$

• Application: Useful for calculating $\Delta H$ for reactions that are difficult to measure directly.

• Example: Formation of water from hydrogen and oxygen can be broken into steps, and the total $\Delta H$ is the sum of the steps.

Standard Enthalpy of Formation ($\Delta H_f^\circ$)

Definition

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change for the formation of one mole of a compound from its elements in their most stable forms at 25°C and 1 atm.

• Formula: $\Delta H_f^\circ$ for an element in its most stable form is zero.

• Example: $\Delta H_f^\circ$(H2, g) = 0$;$\Delta H_f^\circ$(C, graphite) = 0$

• Application: Used to calculate enthalpy changes for reactions using tabulated values.

Calculation of Reaction Enthalpy Using Standard Enthalpies of Formation

Formula and Example

To calculate the standard enthalpy change for a reaction:

• Formula: $\Delta H_{rxn} = \sum n \Delta H_f^\circ (\text{products}) - \sum m \Delta H_f^\circ (\text{reactants})$

• n, m: Stoichiometric coefficients of products and reactants.

• Example: For the reaction $C_6H_{12} + 9O_2 \rightarrow 6CO_2 + 6H_2O$, use tabulated $\Delta H_f^\circ$ values to calculate $\Delta H_{rxn}$.

Summary Table: Key Concepts in Thermochemistry

Concept	Definition	Formula	Example/Application
Potential Energy	Energy due to position or composition	—	Chemical bonds
Kinetic Energy	Energy due to motion	—	Moving molecules
Work (w)	Energy to move an object	$w = F \times d$	Ball thrown by pitcher
Heat (q)	Energy to change temperature	—	Heating water
Internal Energy (E)	Total energy of system	$\Delta E = q + w$	Energy change in reaction
Enthalpy (H)	Heat at constant pressure	$\Delta H = \Delta E + P\Delta V$	Combustion reactions
Standard Enthalpy of Formation ($\Delta H_f^\circ$)	Enthalpy for forming 1 mol from elements	—	$\Delta H_f^\circ$(O2, g) = 0$

Additional info: The notes include visual examples (e.g., rocket launch, heating water) to illustrate energy transformations and the practical relevance of thermochemistry in real-world applications.