Chemistry: Class 11 — Chapter 5: Thermodynamics

• System: The specific part of the universe in which observations and measurements are made.
• Surroundings: Everything in the universe other than the system that can interact with it.
• Boundary: The real or imaginary wall that separates the system from its surroundings, allowing control over the movement of matter and energy.
• Relationship: $$\text{Universe} = \text{System} + \text{Surroundings}$$

Systems are classified based on the exchange of matter and energy with the surroundings:

• Open System: Can exchange both energy and matter with the surroundings (e.g., reactants in an open beaker).
• Closed System: Can exchange energy but not matter with the surroundings (e.g., reactants in a closed vessel made of conducting material like copper).
• Isolated System: Cannot exchange either energy or matter with the surroundings (e.g., reactants in a thermos flask).

• The state of a thermodynamic system is described by its macroscopic properties such as pressure ($p$), volume ($V$), temperature ($T$), and amount of substance ($n$).
• State Variables (or State Functions): Properties whose values depend only on the current state of the system and are independent of the path taken to reach that state (e.g., $U, H, S, G, p, V, T$).

The internal energy $U$ can change when:

• Heat passes into or out of the system ($q$).
• Work is done on or by the system ($w$).
• Matter enters or leaves the system.

An adiabatic process is one in which there is no transfer of heat between the system and surroundings ($q = 0$). The wall separating them is called an adiabatic wall.

• Work done on the system: $w > 0$ (positive)
• Work done by the system: $w < 0$ (negative)
• Heat absorbed by the system: $q > 0$ (positive)
• Heat released to the surroundings: $q < 0$ (negative)

The First Law states that energy can neither be created nor destroyed; the energy of an isolated system is constant.

Mathematical statement:

$$\Delta U = q + w$$

For a gas confined in a cylinder with a frictionless piston under constant external pressure ($p_{ex}$):

• Irreversible compression/expansion: $$w = -p_{ex} \Delta V = -p_{ex} (V_f - V_i)$$
• Reversible isothermal expansion of an ideal gas: $$w_{rev} = -2.303 nRT \log \frac{V_f}{V_i}$$
• Free Expansion: Expansion of a gas into a vacuum ($p_{ex} = 0$). Here, $w = 0$.

Enthalpy is a state function defined as the heat content of a system at constant pressure:

$$H = U + pV$$

For finite changes at constant pressure:

$$\Delta H = \Delta U + p\Delta V$$

Using the ideal gas law ($pV = nRT$), for reactions involving gases:

$$\Delta H = \Delta U + \Delta n_g RT$$

Where $\Delta n_g$ is the number of moles of gaseous products minus the number of moles of gaseous reactants.

• For exothermic reactions (heat evolved): $\Delta H < 0$
• For endothermic reactions (heat absorbed): $\Delta H > 0$

• Extensive Property: A property whose value depends on the quantity or size of matter present in the system (e.g., mass, volume, internal energy $U$, enthalpy $H$, heat capacity $C$).
• Intensive Property: A property whose value is independent of the quantity or size of matter present (e.g., temperature $T$, density, pressure $p$, molar properties like molar volume $V_m$).

The heat capacity of a system is the quantity of heat required to raise its temperature by one degree Celsius (or one Kelvin):

$$q = C \Delta T$$

• Molar Heat Capacity ($C_m$): Heat capacity for one mole of a substance ($C_m = C/n$).
• Specific Heat Capacity ($c$): Heat capacity per unit mass of a substance ($q = c \times m \times \Delta T$).

• At constant volume: $q_V = C_V \Delta T = \Delta U$
• At constant pressure: $q_p = C_p \Delta T = \Delta H$
• For one mole of an ideal gas: $$C_p - C_V = R$$

For chemical reactions at constant volume, heat changes are measured in a sealed steel vessel called a bomb calorimeter immersed in a water bath.

• Since volume is constant ($\Delta V = 0$), no work is done ($w = 0$).
• The heat evolved is equal to the change in internal energy: $q_V = \Delta U$.

For reactions carried out at constant atmospheric pressure, a simple coffee-cup calorimeter can be used.

• The heat absorbed or evolved is equal to the enthalpy change: $q_p = \Delta H$.

The enthalpy change accompanying a chemical reaction is the difference between the sum of enthalpies of products and reactants:

$$\Delta_r H = \sum a_i H_{\text{products}} - \sum b_i H_{\text{reactants}}$$

Where $a_i$ and $b_i$ are the stoichiometric coefficients.

The enthalpy change when all participating substances are in their standard states (pure form at $1\text{ bar}$ and a specified temperature, usually $298\text{ K}$).

• Standard Enthalpy of Fusion ($\Delta_{fus} H^\ominus$): Enthalpy change accompanying the melting of one mole of a solid substance in its standard state.
• Standard Enthalpy of Vaporisation ($\Delta_{vap} H^\ominus$): Enthalpy change required to vaporize one mole of a liquid at constant temperature and standard pressure.
• Standard Enthalpy of Sublimation ($\Delta_{sub} H^\ominus$): Enthalpy change when one mole of a solid substance directly sublimes into gas at constant temperature and standard pressure.

The enthalpy change for the formation of one mole of a compound from its constituent elements in their most stable reference states of aggregation.

• By convention, the standard enthalpy of formation of any element in its most stable reference state is taken as zero (e.g., $\Delta_f H^\ominus [\text{O}_2(g)] = 0$, $\Delta_f H^\ominus [\text{C}(\text{graphite})] = 0$).

If a reaction takes place in several steps, its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.

Enthalpy is a state function, meaning $\Delta_r H$ is independent of the path taken.

The enthalpy change per mole of a substance when it undergoes complete combustion with oxygen under standard conditions.

The enthalpy change on breaking one mole of bonds completely to obtain atoms in the gas phase (e.g., $\text{H}_2(g) \rightarrow 2\text{H}(g)$).

• Bond Dissociation Enthalpy: Energy required to break one mole of a specific covalent bond in a gaseous diatomic molecule.
• Mean Bond Enthalpy: The average energy required to break a specific bond in polyatomic molecules (e.g., C-H bond in methane).
• Reaction enthalpy calculation using bond enthalpies: $$\Delta_r H^\ominus = \sum \text{Bond enthalpies}_{\text{reactants}} - \sum \text{Bond enthalpies}_{\text{products}}$$

The enthalpy change when one mole of an ionic compound dissociates into its gaseous ions. It is determined indirectly using the Born-Haber Cycle.

• Enthalpy of Solution: Enthalpy change when one mole of a substance dissolves in a specified amount of solvent. At infinite dilution, ionic interactions become negligible.
• $$\Delta_{sol} H^\ominus = \Delta_{lattice} H^\ominus + \Delta_{hyd} H^\ominus$$
• Enthalpy of Dilution: The heat change associated with adding more solvent to a solution.

A spontaneous process is an irreversible process that has a natural tendency to occur without the assistance of an external agency.

Entropy is a measure of the degree of randomness or disorder in a system.

• Mathematical definition for a reversible process: $$\Delta S = \frac{q_{rev}}{T}$$
• Second Law of Thermodynamics: For any spontaneous process in an isolated system, there is a natural tendency for entropy to increase ($\Delta S_{total} = \Delta S_{sys} + \Delta S_{surr} > 0$).

Gibbs energy is a state function defined to predict spontaneity for closed systems at constant temperature and pressure:

$$G = H - TS$$

The Gibbs Equation:

$$\Delta G = \Delta H - T\Delta S$$

Criteria for spontaneity at constant $T$ and $p$:

• $\Delta G < 0$ (negative): The process is spontaneous.
• $\Delta G > 0$ (positive): The process is non-spontaneous.
• $\Delta G = 0$: The system is at equilibrium.

The entropy of any pure crystalline substance approaches zero as the temperature approaches absolute zero ($0\text{ K}$).