Basic Thermodynamics in General Chemistry: Laws, State Functions, and Equilibrium

Basic Thermodynamics

Introduction to Thermodynamics

Thermodynamics is the branch of physical science that deals with the relationships between heat, work, temperature, and energy. It describes processes involving changes in temperature, transformation of energy, and the relationship between heat and work.

• Thermodynamic System: The part of the universe under study, defined by specific boundaries. Everything outside the system is called the surroundings.

• System Boundary: Separates the system from its surroundings.

• Types of Systems:

  • Open System: Can exchange both matter and energy with surroundings.

  • Closed System: Can exchange energy but not matter with surroundings.

  • Isolated System: Cannot exchange either matter or energy with surroundings.

State Functions and Path Functions

Thermodynamic properties are classified as either state functions or path functions:

• State Function: A property that depends only on the current state of the system, not on how it got there (e.g., temperature, pressure, volume, internal energy, enthalpy, entropy).

• Path Function: A property that depends on the specific process or path taken between two states (e.g., heat q, work w, activation energy).

Temperature is a measure of the average kinetic energy of the atoms or molecules in a system and is a state function.

Heat (q): The thermal energy transferred between systems due to a temperature difference.

Work (w): The energy required to move something against a force. For gases, expansion or compression work is given by:

$w = -P \Delta V$

Activation Energy: The energy required to form a transition state to initiate a reaction. It is a path variable because it depends on the reaction pathway.

Internal Energy and the First Law of Thermodynamics

Internal Energy (U): The total energy (kinetic and potential) associated with the structure and motion of molecules within the system. It is a state function.

The change in internal energy is given by:

$\Delta U_{system} = U_{final} - U_{initial}$

Law of Conservation of Energy: Energy can neither be created nor destroyed; it can only change form. For the universe:

$\Delta U_{univ} = 0$

The energy lost by the system must equal the energy gained by the surroundings and vice versa.

First Law of Thermodynamics: The change in internal energy of a closed system equals the sum of heat and work exchanged with the surroundings:

$\Delta U_{system} = q + w$

Although q and w are not state functions, their sum (ΔU) is a state function.

Enthalpy and Thermochemistry

Enthalpy (H): A state function used to describe heat changes at constant pressure. The change in enthalpy is:

$\Delta H_{system} = H_{final} - H_{initial}$

Standard Enthalpy of Reaction (ΔH0r): The enthalpy change for a reaction under standard conditions (usually 298 K and 1 bar).

Standard Enthalpy of Formation (ΔH0f): The enthalpy change when one mole of a compound is formed from its elements in their most stable forms.

The standard enthalpy of formation of any element in its standard state is zero by definition.

The standard enthalpy of reaction is calculated as:

$\Delta H^0_r = \sum_j \, \nu_j \Delta H^0_f (\text{products}) - \sum_i \, \nu_i \Delta H^0_f (\text{reactants})$

where $\nu$ are stoichiometric coefficients.

Exothermic and Endothermic Reactions

• Exothermic Reaction: Releases heat to the surroundings ($\Delta H < 0$).

• Endothermic Reaction: Absorbs heat from the surroundings ($\Delta H > 0$).

The Second Law of Thermodynamics and Entropy

The second law of thermodynamics states that the total entropy of a system and its surroundings always increases for a spontaneous process:

$\Delta S_{surroundings} + \Delta S_{system} \geq 0$

Entropy (S): A measure of energy dispersal or microscopic disorder in a system. It is a state function, with units J·K-1.

The change in entropy is:

$\Delta S_{system} = S_{final} - S_{initial}$

The standard entropy change for a reaction is:

$\Delta S^0_r = \sum_j \, \nu_j S^0 (\text{products}) - \sum_i \, \nu_i S^0 (\text{reactants})$

Gibbs Free Energy and Spontaneity

Gibbs Free Energy (G): A thermodynamic potential that predicts the spontaneity of a process at constant temperature and pressure. It is a state function.

$G = H - T \times S$

The standard Gibbs energy change for a reaction is:

$\Delta G^0_r = \Delta H^0_r - T \times \Delta S^0_r$

• If $\Delta G^0_r < 0$, the reaction is spontaneous in the forward direction.

• If $\Delta G^0_r > 0$, the reaction is non-spontaneous in the forward direction.

• If $\Delta G^0_r = 0$, the reaction is at equilibrium.

Chemical Equilibrium and Equilibrium Constants

At equilibrium, the rates of the forward and reverse reactions are equal. The equilibrium constant (K) expresses the ratio of product and reactant concentrations (or partial pressures) at equilibrium.

• Kc: Based on concentrations (mol/L).

• Kp: Based on partial pressures (bar or atm).

For a general reaction: $aA + bB \rightleftharpoons cC + dD$

$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

For reactions involving gases:

$K_p = K_c (RT)^{-\Delta n}$

where $\Delta n =$ (moles of gaseous products) $-$ (moles of gaseous reactants).

For heterogeneous equilibria, pure solids and liquids are omitted from the equilibrium expression.

Gibbs Energy and the Equilibrium Constant

The relationship between standard Gibbs energy change and the equilibrium constant is:

$\Delta G^0_r = -RT \ln K$

where $R$ is the gas constant and $T$ is the temperature in Kelvin.

• If $K \gg 1$, products predominate at equilibrium.

• If $K \ll 1$, reactants predominate at equilibrium.

Binding Equilibrium and Dissociation Constant

In biochemical systems, the binding of a drug (D) to a receptor (R) forms a complex (RD):

$R + D \rightleftharpoons RD$

The dissociation constant ($K_d$) is given by:

$K_d = \frac{[R][D]}{[RD]}$

A small $K_d$ indicates a stable complex. The association constant ($K_a$) is the inverse of $K_d$.

Essential Operational Skills

• Calculate standard enthalpies, entropies, and Gibbs energies of reactions.

• Calculate equilibrium constants ($K_{eq}$) and binding dissociation constants ($K_d$).

Relevant Images