MP Board Class 11 Chemistry: Chemical Thermodynamics

Quick Revision Notes & Formula Sheet

1. Basic Terms & Definitions (मूल अवधारणाएं)

System (निकाय): The part of the universe under thermodynamic study.
Surroundings (परिवेश): Everything outside the system that can interact with it. $$\text{Universe} = \text{System} + \text{Surroundings}$$
Types of Systems:
1. Open System: Exchanges both matter and energy with surroundings (e.g., hot tea in an open beaker).
2. Closed System: Exchanges energy but NOT matter (e.g., hot tea in a closed metal vessel).
3. Isolated System: Exchanges NEITHER matter NOR energy (e.g., hot tea in a thermos flask).
State Functions: Properties that depend only on the current state of the system, not on the path taken (e.g., $P, V, T, U, H, S, G$).
Path Functions: Properties that depend on the path taken to achieve a state (e.g., Heat ($q$), Work ($w$)).
Extensive Properties: Depend on the amount of matter present (e.g., Mass, Volume, Internal Energy, Enthalpy, Entropy).
Intensive Properties: Independent of the amount of matter present (e.g., Temperature, Pressure, Density, Specific Heat, Molar Volume).

2. First Law of Thermodynamics (ऊष्मागतिकी का प्रथम नियम)

Energy can neither be created nor destroyed; it can only be converted from one form to another (Law of Conservation of Energy).

$$\Delta U = q + w$$

Where:

$\Delta U$ = Change in internal energy (आंतरिक ऊर्जा में परिवर्तन)
$q$ = Heat supplied to system
$w$ = Work done on system

IUPAC Sign Conventions:

$q > 0$ (+ve): Heat absorbed by the system.
$q < 0$ (-ve): Heat released by the system.
$w > 0$ (+ve): Work done on the system (Compression / संपीडन).
$w < 0$ (-ve): Work done by the system (Expansion / प्रसार).

3. Work Done Formulas (कार्य के सूत्र)

General Pressure-Volume Work:

$$w = - P_{\text{ext}} \cdot \Delta V = - P_{\text{ext}} (V_2 - V_1)$$

1. Reversible Isothermal Process ($T = \text{constant}$):

$$w_{\text{rev}} = - 2.303 \cdot n R T \cdot \log_{10}\left(\frac{V_2}{V_1}\right)$$ OR $$w_{\text{rev}} = - 2.303 \cdot n R T \cdot \log_{10}\left(\frac{P_1}{P_2}\right)$$

2. Irreversible Isothermal Process:

$$w_{\text{irrev}} = - P_{\text{ext}} (V_2 - V_1)$$

3. Free Expansion (Expansion in vacuum, $P_{\text{ext}} = 0$):

$$w = 0$$

4. Isochoric Process ($\Delta V = 0$):

$$w = 0 \implies \Delta U = q_v$$

5. Adiabatic Process ($q = 0$):

$$\Delta U = w_{\text{ad}}$$

4. Enthalpy ($H$) & Internal Energy ($U$)

Enthalpy Definition: $H = U + P V$
Enthalpy Change at Constant Pressure: $$\Delta H = \Delta U + P \Delta V$$ $$\Delta H = q_p$$
Relationship between $\Delta H$ and $\Delta U$ for Gaseous Reactions: $$\Delta H = \Delta U + \Delta n_g R T$$

Where:
- $\Delta n_g = (\text{Moles of gaseous products}) - (\text{Moles of gaseous reactants})$
- $R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$
Exothermic Reaction (ऊष्माक्षेपी): Heat released, $\Delta H < 0$ (-ve)
Endothermic Reaction (ऊष्माशोषी): Heat absorbed, $\Delta H > 0$ (+ve)

5. Heat Capacities (ऊष्मा धारिता)

Heat Capacity ($C$): Amount of heat required to raise the temperature of a system by $1^\circ\text{C}$ or $1\text{ K}$. $$C = \frac{q}{\Delta T}$$
Specific Heat Capacity ($c$): Heat required per unit mass ($1\text{ g}$). $$c = \frac{q}{m \cdot \Delta T}$$
Molar Heat Capacity ($C_m$): Heat required per mole ($1\text{ mol}$). $$C_m = \frac{q}{n \cdot \Delta T}$$
Heat Capacity at Constant Volume ($C_v$): $$C_v = \left(\frac{\Delta U}{\Delta T}\right)_v$$
Heat Capacity at Constant Pressure ($C_p$): $$C_p = \left(\frac{\Delta H}{\Delta T}\right)_p$$
Mayer's Relation (for ideal gas): $$C_p - C_v = R$$
Poisson's Ratio ($\gamma$): $$\gamma = \frac{C_p}{C_v}$$ (Monoatomic = 1.66, Diatomic = 1.40, Triatomic = 1.33)

6. Thermochemistry (ऊष्मा रसायन)

Hess's Law of Constant Heat Summation:

The total enthalpy change in a chemical reaction is the same regardless of whether the reaction takes place in one step or in several steps.

$$\Delta H = \Delta H_1 + \Delta H_2 + \Delta H_3 + \dots$$

Important Enthalpies of Reaction:

Standard Enthalpy of Formation ($\Delta_f H^\circ$): Enthalpy change when 1 mole of a substance is formed from its elements in their standard state.
- Note: $\Delta_f H^\circ$ of pure elements in standard state = $0$ (e.g., $O_{2(g)}, C_{\text{graphite}}, Fe_{(s)}$).
Enthalpy of Reaction from Enthalpy of Formation: $$\Delta_r H^\circ = \sum \Delta_f H^\circ (\text{Products}) - \sum \Delta_f H^\circ (\text{Reactants})$$
Enthalpy of Reaction from Bond Enthalpies: $$\Delta_r H^\circ = \sum \text{Bond Enthalpy (Reactants)} - \sum \text{Bond Enthalpy (Products)}$$

7. Second Law of Thermodynamics & Entropy ($S$)

Entropy ($S$): Measure of randomness or degree of disorder in a system.
- State function, Extensive property.
- Units: $\text{J K}^{-1} \text{mol}^{-1}$
Entropy Change Formula: $$\Delta S = \frac{q_{\text{rev}}}{T}$$
Total Entropy Change ($\Delta S_{\text{total}}$): $$\Delta S_{\text{total}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}}$$
Second Law Statement:
- For a spontaneous (natural) process, total entropy of universe always increases: $$\Delta S_{\text{total}} > 0 \quad (\text{Spontaneous})$$ $$\Delta S_{\text{total}} = 0 \quad (\text{Equilibrium})$$ $$\Delta S_{\text{total}} < 0 \quad (\text{Non-spontaneous})$$
Order of Entropy: $\text{Gas} > \text{Liquid} > \text{Solid}$

8. Gibbs Free Energy ($G$) & Spontaneity

Gibbs Energy Definition: $G = H - T S$
Gibbs-Helmholtz Equation: $$\Delta G = \Delta H - T \Delta S$$

Criteria for Spontaneity (at Constant $T$ and $P$):

$\Delta G$ Value	Nature of Process
$\Delta G < 0$ (-ve)	Spontaneous (स्वतः प्रवर्तित)
$\Delta G = 0$	Equilibrium (साम्यावस्था)
$\Delta G > 0$ (+ve)	Non-spontaneous (स्वतः अप्रवर्तित)

Temperature Dependence on Spontaneity:

$\Delta H$	$\Delta S$	$\Delta G = \Delta H - T\Delta S$	Spontaneity Condition
-	+	Always -	Spontaneous at all temperatures
+	-	Always +	Non-spontaneous at all temperatures
-	-	- (at low $T$)	Spontaneous at low temperatures
+	+	- (at high $T$)	Spontaneous at high temperatures

9. Gibbs Energy & Equilibrium Constant

Relationship between Standard Gibbs Free Energy Change ($\Delta G^\circ$) and Equilibrium Constant ($K$):

$$\Delta G^\circ = - R T \ln K$$ $$\Delta G^\circ = - 2.303 \cdot R T \cdot \log_{10} K$$