Glossary

3.2 Internal energy and enthalpy

5 min read•july 30, 2024

The is all about energy conservation. It's like keeping track of your bank account, but with energy instead of money. This law helps us understand how energy moves and changes in different processes.

and are key players in this energy game. They help us figure out how much heat is gained or lost during chemical reactions and physical changes. Understanding these concepts is crucial for solving real-world problems in chemistry and engineering.

Internal Energy vs Enthalpy

Defining Internal Energy and Enthalpy

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  • Internal energy is the total kinetic and potential energy of all particles within a system
    • Extensive property depends on the quantity of matter present (1 mole of water vs 2 moles of water)
  • Enthalpy is a thermodynamic property defined as the sum of a system's internal energy and the product of its pressure and volume H=U+PVH = U + PV
    • Measure of the total heat content of a system at
    • Commonly used in chemistry to describe heat changes in reactions and phase transitions

Comparing Internal Energy and Enthalpy

  • Changes in internal energy are related to heat and work exchanged between the system and its surroundings [ΔU = q - w](https://www.fiveableKeyTerm:δu_=_q_-_w)
    • Heat (q) is the transfer of thermal energy between the system and surroundings
    • Work (w) is the energy transfer due to a force acting over a distance (e.g., expansion or compression of a gas)
  • Changes in enthalpy are associated with heat exchange at constant pressure ΔH=qpΔH = q_p
    • At constant pressure, the change in enthalpy equals the heat exchanged with the surroundings
  • Both internal energy and enthalpy are state functions
    • Their values depend only on the current state of the system, not on the path taken to reach that state
    • Allows for the application of Hess's law and the construction of thermochemical cycles

First Law of Thermodynamics Applications

Calculating Changes in Internal Energy

  • The first law of thermodynamics states that the change in internal energy of a system (ΔU) is equal to the heat added to the system (q) minus the work done by the system (w): ΔU=q−wΔU = q - w
    • Sign conventions: heat absorbed by the system (q > 0), heat released by the system (q < 0), work done by the system (w < 0), work done on the system (w > 0)
  • For processes involving only pressure-volume work w=−PΔVw = -PΔV
    • Pressure-volume work occurs when a system expands or contracts against an external pressure
    • Example: expansion of a gas in a piston-cylinder assembly

Calculating Changes in Enthalpy

  • For processes occurring at constant pressure, the change in enthalpy (ΔH) is equal to the heat exchanged with the surroundings: ΔH=qpΔH = q_p
    • qpq_p is the heat exchanged at constant pressure
  • The change in enthalpy can also be calculated using the equation: ΔH=ΔU+PΔVΔH = ΔU + PΔV
    • Relates the change in enthalpy to the change in internal energy and the pressure-volume work done
  • Example: calculating the enthalpy change for the combustion of methane at constant pressure
    • CH4(g)+2O2(g)→CO2(g)+2H2O(l)CH_4 (g) + 2O_2 (g) → CO_2 (g) + 2H_2O (l)

Heat, Work, and Energy Changes

Adiabatic and Isothermal Processes

  • In an (q = 0), the change in internal energy is equal to the negative of the work done: ΔU=−wΔU = -w
    • For an adiabatic process at constant pressure, ΔH=−wΔH = -w
    • Example: rapid compression or expansion of a gas in an insulated container
  • In an (ΔT = 0), the change in internal energy is zero ΔU=0ΔU = 0, and the heat exchanged is equal to the work done: q=wq = w
    • For an isothermal process at constant pressure, ΔH=qp=wΔH = q_p = w
    • Example: slow expansion or compression of a gas in a heat reservoir

Isobaric and Isochoric Processes

  • In an isobaric process (ΔP = 0), the change in enthalpy is equal to the heat exchanged: ΔH=qpΔH = q_p
    • The change in internal energy is given by ΔU=qp−PΔVΔU = q_p - PΔV
    • Example: heating a liquid at constant pressure
  • In an isochoric process (ΔV = 0), no pressure-volume work is done (w = 0), and the change in internal energy is equal to the heat exchanged: ΔU=qvΔU = q_v
    • The change in enthalpy is equal to the change in internal energy: ΔH=ΔUΔH = ΔU
    • Example: heating a gas in a rigid container at constant volume

Enthalpy as a State Function

Path Independence and Hess's Law

  • Enthalpy, like internal energy, is a state function
    • Its value depends only on the current state of the system, not on the path taken to reach that state
  • The change in enthalpy between two states is independent of the path taken
    • Simplifies thermodynamic calculations and allows for the application of Hess's law
  • Hess's law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps or processes that make up the overall reaction, regardless of the pathway
    • Example: calculating the enthalpy of formation of a compound using a series of reactions

Thermochemical Cycles

  • The state function property of enthalpy enables the construction of thermochemical cycles
    • Used to calculate enthalpy changes for reactions that are difficult to measure directly
  • Thermochemical cycles involve a series of reactions or processes that start and end with the same state
    • The sum of the enthalpy changes for each step in the cycle equals zero ΣΔH=0ΣΔH = 0
  • Example: using a Born-Haber cycle to calculate the lattice energy of an ionic compound

Enthalpy Changes in Reactions and Transitions

Standard Enthalpies of Formation and Reaction

  • The standard enthalpy of formation ΔH°fΔH°_f is the enthalpy change 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 298 K)
    • Example: the standard enthalpy of formation of water H2O(l)H_2O (l) is -285.8 kJ/mol
  • The standard enthalpy of reaction ΔH°rxnΔH°_{rxn} can be calculated using the standard enthalpies of formation of the reactants and products:
    • ΔH°rxn=Σ(n×ΔH°f(products))−Σ(n×ΔH°f(reactants))ΔH°_{rxn} = Σ(n × ΔH°_f(products)) - Σ(n × ΔH°_f(reactants))
    • n is the stoichiometric coefficient
    • Example: calculating the enthalpy of combustion of methane using standard enthalpies of formation

Phase Transitions and Heat Capacities

  • The enthalpy change for a , such as melting or vaporization, is called the enthalpy of fusion ΔHfusΔH_{fus} or enthalpy of vaporization ΔHvapΔH_{vap}, respectively
    • These values are specific to each substance and can be used to calculate the heat required or released during a phase change
    • Example: calculating the energy needed to melt a given mass of ice
  • The (C) of a substance is the amount of heat required to raise its temperature by one degree Celsius or Kelvin
    • (c) is the heat capacity per unit mass
    • CmC_m is the heat capacity per mole of the substance
  • The enthalpy change for a temperature change can be calculated using the equation: ΔH=C×ΔTΔH = C × ΔT
    • C is the heat capacity and ΔT is the change in temperature
    • Example: calculating the heat required to raise the temperature of a sample of water by 20°C

Key Terms to Review (17)

Adiabatic Process: An adiabatic process is a thermodynamic change in which no heat is exchanged with the surroundings. During this process, any change in the system's internal energy is solely due to work done on or by the system, which makes it a critical concept in understanding how energy is conserved and transformed in various thermodynamic systems.
Bond Enthalpy: Bond enthalpy is the amount of energy required to break one mole of a specific type of bond in a molecule, measured under standard conditions. It reflects the strength of a bond, where stronger bonds have higher bond enthalpies. Understanding bond enthalpy helps in predicting how much energy will be absorbed or released during chemical reactions, linking closely to concepts like internal energy and the overall enthalpy change in reactions.
Chemical Reaction Enthalpy: Chemical reaction enthalpy refers to the heat change associated with a chemical reaction at constant pressure. This value is crucial because it helps in understanding the energy changes that occur when reactants are transformed into products, allowing chemists to predict whether a reaction will release or absorb heat, and hence, whether it is exothermic or endothermic.
Constant pressure: Constant pressure refers to a thermodynamic condition where the pressure of a system remains unchanged during a process. This concept is crucial when examining how energy changes occur in systems, especially when discussing heat transfer, work done by or on the system, and changes in enthalpy, which connects energy to pressure and volume. Understanding constant pressure helps clarify how processes unfold in real-world applications like chemical reactions and phase changes.
Enthalpy: The equation $$h = u + pv$$ defines enthalpy (h) as the sum of the internal energy (u) of a system and the product of its pressure (p) and volume (v). This relationship highlights the importance of enthalpy in understanding heat transfer processes, particularly in constant pressure conditions, where it becomes a key term for evaluating energy changes during chemical reactions and phase transitions.
First Law of Thermodynamics: The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This principle emphasizes the conservation of energy in all physical and chemical processes, influencing various fundamental concepts including heat, work, and the behavior of systems at the molecular level.
Heat Capacity: Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). This concept is vital in understanding how substances interact with thermal energy and connects to ideas like thermal equilibrium and temperature measurements, as well as internal energy and enthalpy changes in chemical reactions.
Internal Energy: Internal energy is the total energy contained within a system, resulting from the kinetic and potential energies of the molecules. It encompasses all forms of energy present at the molecular level, such as vibrational, rotational, and translational motions. Understanding internal energy is essential as it connects to key principles like thermodynamic processes, heat exchange, and work done on or by the system.
Isothermal Process: An isothermal process is a thermodynamic process in which the temperature of a system remains constant while heat is exchanged with its surroundings. This constancy of temperature has profound implications for how energy, heat, and work interact within a system, linking it closely to concepts like internal energy and enthalpy changes.
Latent Heat: Latent heat is the amount of energy absorbed or released by a substance during a phase change without changing its temperature. This concept is crucial for understanding how internal energy and enthalpy are affected during processes like melting, boiling, and condensation. It highlights the relationship between heat transfer and changes in state, playing a key role in determining the enthalpy of reactions and the applications of Hess's Law.
Molar heat capacity: Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius at constant pressure or volume. This concept is crucial as it connects energy transfer through heat with the internal energy and enthalpy changes in a system. Understanding molar heat capacity helps in comprehending how substances absorb and store thermal energy, influencing their behavior during chemical reactions and phase changes.
Phase transition: A phase transition is the process where a substance changes from one state of matter to another, such as from solid to liquid or liquid to gas. This process is marked by energy changes and shifts in molecular arrangement, which can significantly affect the physical properties of the substance involved. Phase transitions are crucial in understanding behaviors of real gases, how energy states relate to enthalpy and internal energy, and how equilibrium conditions change with varying temperature and pressure.
Reaction enthalpy: Reaction enthalpy is the heat change that occurs during a chemical reaction at constant pressure, measured in joules or kilojoules. It reflects the difference in enthalpy between the products and reactants, which provides insight into the energy dynamics of a reaction. Understanding reaction enthalpy is crucial for predicting whether a reaction is exothermic (releases heat) or endothermic (absorbs heat) and for applying this knowledge to various chemical processes and thermodynamic calculations.
Second Law of Thermodynamics: The Second Law of Thermodynamics states that in any energy transfer or transformation, the total entropy of an isolated system can never decrease over time, and is often expressed in terms of the irreversibility of natural processes. This law highlights the tendency of systems to evolve towards a state of maximum entropy, which has important implications for energy, heat, work, and spontaneity in various processes.
Specific Heat Capacity: Specific heat capacity is the amount of heat energy required to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). This concept is crucial when examining how energy, heat, and work interact, as it directly influences how substances absorb and transfer heat. Additionally, specific heat capacity connects to the internal energy and enthalpy of a system by affecting how energy is stored within substances, which is essential for understanding thermodynamic processes.
Standard State: The standard state refers to the reference conditions used to define the properties of substances, specifically at a pressure of 1 bar and a specified temperature, typically 25°C (298 K). This concept is crucial for comparing thermodynamic values like internal energy, enthalpy, free energy, and chemical potential across different reactions and processes, ensuring consistency and accuracy in calculations.
δu = q - w: The equation $$\delta u = q - w$$ expresses the change in internal energy ($$\delta u$$) of a system in relation to heat added to the system ($$q$$) and work done by the system ($$w$$). This relationship highlights the first law of thermodynamics, which states that energy cannot be created or destroyed but can only change forms. By understanding this equation, you can analyze how energy is transferred and transformed within a system, affecting both internal energy and enthalpy, as well as various applications of the first law in real-world scenarios.
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