Premed · Premed · General Chemistry 1
Lecture 5: Thermochemistry: Energy and Enthalpy
General Chemistry I
Learning Objectives
By the end of this lecture, students will be able to:
- Define energy, work, and heat, and distinguish between kinetic and potential energy
- State the first law of thermodynamics and apply it to chemical systems
- Define enthalpy and explain why it is useful for reactions at constant pressure
- Distinguish between exothermic and endothermic processes using enthalpy diagrams
- Calculate enthalpy changes using stoichiometry
- Define and use standard enthalpies of formation to calculate reaction enthalpies
Lecture Content
I. Energy: Fundamental Concepts
Energy is the capacity to do work or transfer heat. It takes two fundamental forms. Kinetic energy (KE) is the energy of motion, given by KE = 1/2 mv^2. Thermal energy, the energy associated with molecular motion, is a form of kinetic energy. Potential energy (PE) is stored energy that depends on position or composition. Chemical energy -- the energy stored in chemical bonds -- is a form of potential energy, as is gravitational potential energy (PE = mgh). The law of conservation of energy states that energy can be converted from one form to another but cannot be created or destroyed. The SI unit of energy is the joule (J), defined as kg*m^2/s^2. The calorie is an alternative unit: 1 cal = 4.184 J, and 1 kcal (equal to 1 food Calorie) = 4184 J.
II. System and Surroundings
In thermodynamics, the system is the part of the universe being studied, typically the reacting chemicals, while the surroundings encompass everything else. Together, they make up the universe. Systems are classified by what they can exchange with their surroundings: an open system exchanges both matter and energy, a closed system exchanges energy but not matter, and an isolated system exchanges neither. Energy transfer between a system and its surroundings occurs in two ways: as heat (q) or as work (w).
III. Heat and Work
Heat (q) is energy transferred because of a temperature difference between the system and its surroundings. When q is positive, heat flows into the system (an endothermic process from the system's perspective); when q is negative, heat flows out (an exothermic process). Work (w) is energy transferred by a force acting over a distance. In chemistry, the most relevant form of work is pressure-volume (PV) work: w = -P_ext * delta_V. When a system expands (delta_V > 0), it does work on the surroundings, so w is negative. When the surroundings compress the system (delta_V < 0), work is done on the system, making w positive.
IV. The First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy equals the sum of heat and work: delta_E = q + w. Internal energy (E) is a state function, meaning it depends only on the current state of the system and not on the path taken to reach that state. Heat and work individually, however, are not state functions -- they are path-dependent. Because energy is conserved, the change in the system's internal energy is equal in magnitude but opposite in sign to the change in the surroundings: delta_E_system = -delta_E_surroundings.
<image>An energy diagram illustrating the first law of thermodynamics for a chemical reaction in a piston-cylinder setup. The diagram shows a cylinder with a movable piston containing reacting gases. Arrows indicate: (1) heat flowing out of the system to surroundings (labeled q < 0), (2) the piston moving upward as gas expands (labeled w < 0, system does work on surroundings). Below, the equation delta_E = q + w is shown, with a bar chart comparing magnitudes of q and w contributing to delta_E. A sign convention table is included: "+q = heat absorbed, -q = heat released, +w = work done on system, -w = work done by system."</image>
V. Enthalpy (H)
Enthalpy is defined as H = E + PV and is itself a state function. At constant pressure, the enthalpy change equals the heat transferred: delta_H = q_p. Because most chemistry takes place at constant atmospheric pressure, enthalpy is the most practical energy quantity for describing reactions.
An exothermic reaction releases heat to the surroundings and has a negative enthalpy change (delta_H < 0). In such reactions, the products sit at a lower enthalpy than the reactants, and the reaction mixture feels warm. Combustion reactions and the neutralization of a strong acid with a strong base are classic examples. An endothermic reaction absorbs heat from the surroundings and has a positive enthalpy change (delta_H > 0). The products have higher enthalpy than the reactants, and the reaction mixture feels cold. Dissolving ammonium nitrate in water and photosynthesis are familiar endothermic processes.
VI. Enthalpy Diagrams
Enthalpy diagrams plot enthalpy on the vertical axis, with reactants and products placed at their relative enthalpy levels. A downward arrow indicates an exothermic reaction (delta_H < 0), while an upward arrow signals an endothermic reaction (delta_H > 0). The length of the arrow represents the magnitude of the enthalpy change.
<image>Two side-by-side enthalpy diagrams. Left panel (Exothermic): y-axis labeled "Enthalpy (H)," reactants shown at a higher level, products at a lower level, with a downward red arrow labeled "delta_H < 0" between them. The released heat is shown as wavy arrows going from system to surroundings. The specific reaction shown is CH4(g) + 2O2(g) -> CO2(g) + 2H2O(l), delta_H = -890.4 kJ. Right panel (Endothermic): reactants at a lower level, products at a higher level, with an upward blue arrow labeled "delta_H > 0." Wavy arrows show heat flowing from surroundings into system. The specific reaction is N2(g) + O2(g) -> 2NO(g), delta_H = +180.5 kJ.</image>
VII. Thermochemical Equations
A thermochemical equation is a balanced chemical equation that includes the enthalpy change (delta_H). The delta_H value applies to the specific molar amounts indicated by the coefficients. Several key rules govern these equations. If a reaction is reversed, the sign of delta_H changes. If the coefficients are multiplied by a factor n, delta_H is also multiplied by n. And delta_H depends on the states of matter, so phases must always be specified. For example, 2 H2(g) + O2(g) -> 2 H2O(l) has delta_H = -571.6 kJ. Writing the equation for just one mole of water -- H2(g) + 1/2 O2(g) -> H2O(l) -- gives delta_H = -285.8 kJ. Reversing the original equation to show the decomposition of water yields delta_H = +571.6 kJ.
VIII. Stoichiometry of Enthalpy Changes
The enthalpy change can be treated as a stoichiometric quantity, just like moles of a reactant or product. Consider the reaction 2 H2(g) + O2(g) -> 2 H2O(l) with delta_H = -571.6 kJ. To determine how much heat is released when 10.0 g of H2 burns, convert to moles (10.0 g / 2.016 g/mol = 4.96 mol H2), then use the stoichiometric relationship: 4.96 mol H2 x (-571.6 kJ / 2 mol H2) = -1418 kJ. The negative sign confirms that this much energy is released.
IX. Standard Enthalpy of Formation (delta_H_f^0)
The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states at 1 atm and 25 C (298 K). The standard state of an element is its most stable form under these conditions: O2(g), N2(g), C(graphite), Fe(s), Hg(l), and Br2(l). By definition, the standard enthalpy of formation of any element in its standard state is zero.
Standard enthalpies of formation provide a powerful shortcut for calculating reaction enthalpies: delta_H_rxn^0 = sum[n delta_H_f^0(products)] - sum[n delta_H_f^0(reactants)], where n is the stoichiometric coefficient. This approach is essentially an application of Hess's law, which is covered in detail in the next lecture.
X. Bond Energies and Enthalpy (Preview)
Breaking bonds requires energy input (endothermic), while forming bonds releases energy (exothermic). The reaction enthalpy can therefore be approximated as: delta_H_rxn is roughly equal to the sum of bond energies of bonds broken minus the sum of bond energies of bonds formed. This method works best for gas-phase reactions and provides only an approximation. The key insight is that if more energy is released in forming new bonds than is required to break old bonds, the overall reaction is exothermic.
<image>A bond energy diagram for the reaction H2(g) + Cl2(g) -> 2 HCl(g). The diagram shows an energy profile: starting at the reactant level, an upward arrow labeled "Energy input: break H-H bond (436 kJ/mol) + break Cl-Cl bond (242 kJ/mol) = +678 kJ" leads to the separated atoms level. A downward arrow labeled "Energy released: form 2 H-Cl bonds (2 x 431 kJ/mol) = -862 kJ" leads to the product level. The net difference (delta_H = 678 - 862 = -184 kJ) is shown as the overall enthalpy change, with the product level lower than the reactant level, confirming the reaction is exothermic.</image>
