Internal Energy, Enthalpy, and Thermodynamics in Chemical Reactions

Internal Energy and Enthalpy

Energy and Chemical Reactions

Chemical reactions involve the transfer and transformation of energy at the molecular level. Understanding how energy is released, quantified, and related to chemical reactivity is essential in thermodynamics.

• Energy Release: The energy released during a chemical reaction originates from changes in the arrangement and movement of atoms and molecules.

• Quantification: Energy changes are measured using observable quantities such as heat and work.

• Chemical Reactivity: The energy change influences the spontaneity and extent of chemical reactions.

• Thermodynamics: The branch of science that deals with energy changes in chemical processes.

Thermodynamic Definitions

Thermodynamics uses specific terms to describe energy changes in chemical systems.

• System: The part of the universe under study (e.g., the reactants and products in a reaction vessel).

• Surroundings: Everything outside the system.

• Internal Energy (E): The sum of the kinetic and potential energies of all particles in the system.

• Direct measurement of internal energy is impractical due to the vast number of particles in chemical systems.

Heat and Work

Changes in internal energy are most easily tracked through heat and work.

• Heat (q): Energy transferred due to a temperature difference between system and surroundings.

• Work (w): Energy transferred when a force moves an object.

• Heat and work are interconvertible forms of energy.

Internal Energy Change

The change in internal energy ($riangle E$) is the sum of heat and work exchanged by the system.

• Equation: $riangle E = E_f - E_i = q + w$

• Sign Conventions:

  • Energy into the system: $riangle E > 0$

  • Energy out of the system: $riangle E < 0$

  • Heat into the system: $q > 0$

  • Heat out of the system: $q < 0$

  • Work done on the system: $w > 0$

  • Work done by the system: $w < 0$

• Example: If a system evolves 100 kJ of heat ($q = -100$ kJ) and has 50 kJ of work done on it ($w = +50$ kJ), then $riangle E = -100 + 50 = -50$ kJ.

First Law of Thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or transformed.

• Energy Conservation: $riangle E_{sys} = - riangle E_{surr}$ $riangle E_{sys} + riangle E_{surr} = 0$

• The total energy of the universe remains constant.

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

State Functions

State functions depend only on the initial and final states of a system, not on the path taken.

• Examples of State Functions:

  • Internal energy ($E$)

  • Volume ($V$)

  • Pressure ($P$)

  • Height above sea level

• Non-State Functions:

  • Heat ($q$)

  • Work ($w$)

• Different combinations of heat and work can result in the same change in internal energy.

Constant Pressure Conditions

Most chemical reactions are performed under constant pressure, simplifying the measurement of energy changes.

• Equation: $riangle E = q + w$

• Open containers ensure constant atmospheric pressure.

Enthalpy

Enthalpy ($H$) is a thermodynamic quantity that simplifies energy calculations under constant pressure.

• Definition: $H = E + PV$

• Change in Enthalpy: $riangle H = riangle E + riangle (PV) = riangle E + P riangle V$

• At constant pressure ($riangle P = 0$): $riangle H = riangle E + P riangle V$

• Expansion Work: $w = -P riangle V$

• At constant pressure, the enthalpy change equals the heat exchanged: $riangle H = q$

Comparing Enthalpy & Internal Energy

Enthalpy changes are generally easier to measure than internal energy changes, especially under constant pressure.

• For many chemical reactions, especially those with little or no expansion work, $riangle H hickapprox riangle E$.

• Enthalpy provides sufficient information for most practical purposes in chemistry.

Reactions That Don’t Involve Gases

For reactions involving only liquids and solids, volume changes are negligible.

• Equation: $riangle H = riangle E + P riangle V$

• If $riangle V hickapprox 0$, then $P riangle V hickapprox 0$ and $riangle H hickapprox riangle E$.

• Example: $ext{H}_2 ext{SO}_4(aq) + 2 ext{KOH}(aq) ightarrow ext{K}_2 ext{SO}_4(aq) + 2 ext{H}_2 ext{O}(l)$

Reactions That Do Involve Gases

Reactions involving gases can have significant volume changes, but the $P riangle V$ term is often much smaller than $riangle H$.

• Equation: $riangle H = riangle E + P riangle V$

• Example: $2 ext{H}_2(g) + ext{O}_2(g) ightarrow 2 ext{H}_2 ext{O}(g)$ $riangle H = -483.5$ kJ $P riangle V = 2.5$ kJ $riangle H hickapprox riangle E$ since $riangle H ext{ is much greater than } P riangle V$.

Expansion Work

Expansion work occurs when a system changes volume against an external pressure, such as a gas pushing a piston.

• Equation: $w = -P riangle V$

• Example Calculation: If volume expands from 120.0 mL to 455.8 mL against 3.20 atm: $riangle V = 455.8 - 120.0 = 335.8$ mL $= 0.3358$ L $w = -3.20 imes 0.3358 = -1.0746$ L·atm $1$ L·atm $= 101$ J $w = -1.0746 imes 101 = -108.5$ J $= -0.109$ kJ

Summary Table: Key Thermodynamic Quantities

Quantity	Definition	State Function?
Internal Energy ($E$)	Sum of kinetic and potential energies	Yes
Enthalpy ($H$)	$E + PV$	Yes
Heat ($q$)	Energy transferred due to temperature difference	No
Work ($w$)	Energy transferred by force	No

Key Equations

• $riangle E = q + w$

• $H = E + PV$

• $riangle H = riangle E + P riangle V$

• $w = -P riangle V$

• At constant pressure: $riangle H = q$

Additional info:

• These notes cover core concepts from General Chemistry Chapter 9: Thermochemistry, including the first law of thermodynamics, state functions, and the relationship between internal energy and enthalpy.

• Expansion work is a key concept in understanding energy changes in reactions involving gases.