Chemistry Thermodynamics (Class 11)

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1. Basic Concepts System: Part of the universe under investigation. Open System: Exchanges both matter and energy. Closed System: Exchanges energy but not matter. Isolated System: No exchange of matter or energy. Surroundings: Everything else in the universe. Boundary: Separates system from surroundings. State Functions: Properties depending only on the initial and final states of the system, not on the path taken (e.g., $P, V, T, U, H, S, G$). Path Functions: Properties depending on the path taken (e.g., $q$ - heat, $w$ - work). Extensive Properties: Depend on the amount of matter (e.g., $V, n, U, H, S, G$). Intensive Properties: Independent of the amount of matter (e.g., $P, T, \rho$, molarity). 2. Internal Energy ($U$) and First Law of Thermodynamics Internal Energy ($U$): Sum of all forms of energy of the particles in the system (kinetic, potential). First Law of Thermodynamics (Conservation of Energy): Energy can neither be created nor destroyed. $\Delta U = q + w$ $\Delta U$: Change in internal energy $q$: Heat absorbed by the system (positive) or released by the system (negative) $w$: Work done on the system (positive) or by the system (negative) Work ($w$): Pressure-Volume Work: $w = -P_{ext} \Delta V$ (for irreversible process) Reversible Work: $w = -nRT \ln \frac{V_2}{V_1}$ (for isothermal expansion of ideal gas) Work done by the system is negative. Work done on the system is positive. Heat ($q$): Heat absorbed by the system is positive. Heat released is negative. Specific heat capacity ($c$): $q = mc\Delta T$ Molar heat capacity ($C$): $q = nC\Delta T$ 3. Enthalpy ($H$) Definition: $H = U + PV$ Change in Enthalpy: $\Delta H = \Delta U + P\Delta V$ (at constant pressure) For reactions involving gases: $\Delta H = \Delta U + \Delta n_g RT$ Exothermic Reaction: Heat released by system, $\Delta H Endothermic Reaction: Heat absorbed by system, $\Delta H > 0$. Relationship between $\Delta H$ and $\Delta U$: At constant volume: $\Delta H = \Delta U + V\Delta P$ (approx. $\Delta H \approx \Delta U$ if no gas change) At constant pressure: $\Delta H = \Delta U + P\Delta V$ 4. Types of Enthalpy Changes Standard Enthalpy of Formation ($\Delta H_f^\circ$): Enthalpy change when 1 mole of a compound is formed from its elements in their standard states (298 K, 1 atm). $\Delta H_f^\circ$ of an element in its most stable state is zero. Standard Enthalpy of Reaction ($\Delta H_r^\circ$): $\Delta H_r^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$ Standard Enthalpy of Combustion ($\Delta H_c^\circ$): Heat change when 1 mole of a substance is completely burnt in oxygen. Standard Enthalpy of Neutralization ($\Delta H_{neut}^\circ$): Heat change when 1 mole of $H^+$ ions are neutralized by 1 mole of $OH^-$ ions in dilute solution. (approx. $-57.1 \text{ kJ/mol}$ for strong acid/base). Standard Enthalpy of Solution ($\Delta H_{sol}^\circ$): Heat change when 1 mole of a substance dissolves in a specified amount of solvent. Standard Enthalpy of Fusion ($\Delta H_{fus}^\circ$): Heat required to melt 1 mole of solid at its melting point. Standard Enthalpy of Vaporization ($\Delta H_{vap}^\circ$): Heat required to vaporize 1 mole of liquid at its boiling point. 5. Hess's Law of Constant Heat Summation The total enthalpy change for a reaction is the same, whether the reaction takes place in one step or in several steps. Allows calculation of $\Delta H$ for reactions that cannot be measured directly. If a reaction is reversed, the sign of $\Delta H$ changes. If an equation is multiplied by a factor, $\Delta H$ is also multiplied by that factor. 6. Second Law of Thermodynamics and Entropy ($S$) Entropy ($S$): A measure of the disorder or randomness of a system. Second Law: The entropy of an isolated system tends to increase over time. For a spontaneous process, the total entropy of the universe increases ($\Delta S_{total} > 0$). $\Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings}$ For reversible process: $\Delta S = \frac{q_{rev}}{T}$ For phase transitions: $\Delta S_{fus} = \frac{\Delta H_{fus}}{T_f}$, $\Delta S_{vap} = \frac{\Delta H_{vap}}{T_b}$ Factors increasing entropy: Increase in volume or number of particles. Phase change from solid to liquid to gas. Increase in temperature. Mixing of substances. 7. Third Law of Thermodynamics The entropy of a perfectly crystalline substance at absolute zero (0 K) is zero. This provides a reference point for calculating absolute entropies. 8. Gibbs Free Energy ($G$) and Spontaneity Definition: $G = H - TS$ Change in Gibbs Free Energy (at constant $T, P$): $\Delta G = \Delta H - T\Delta S$ Criteria for Spontaneity: $\Delta G $\Delta G = 0$: Process is at equilibrium. $\Delta G > 0$: Process is non-spontaneous (spontaneous in reverse direction). Effect of $\Delta H$ and $\Delta S$ on spontaneity: $\Delta H$ $\Delta S$ $\Delta G = \Delta H - T\Delta S$ Spontaneity $-$ $+$ $-$ Spontaneous at all temperatures $+$ $-$ $+$ Non-spontaneous at all temperatures $-$ $-$ $-$ at low $T$, $+$ at high $T$ Spontaneous at low temperatures $+$ $+$ $+$ at low $T$, $-$ at high $T$ Spontaneous at high temperatures 9. Heat Capacity Heat Capacity ($C$): Amount of heat required to raise the temperature of a substance by $1^\circ C$ or $1 K$. $C = \frac{q}{\Delta T}$ Specific Heat Capacity ($c$): Heat capacity per unit mass. $c = \frac{q}{m\Delta T}$ (Units: J/g·K) Molar Heat Capacity ($C_m$): Heat capacity per mole. $C_m = \frac{q}{n\Delta T}$ (Units: J/mol·K) Heat Capacity at Constant Volume ($C_V$): $C_V = (\frac{\partial U}{\partial T})_V$ For ideal gas: $\Delta U = nC_V\Delta T$ Heat Capacity at Constant Pressure ($C_P$): $C_P = (\frac{\partial H}{\partial T})_P$ For ideal gas: $\Delta H = nC_P\Delta T$ Relation between $C_P$ and $C_V$ for ideal gas: $C_P - C_V = R$ 10. Important Relations and Constants Gas Constant ($R$): $8.314 \text{ J mol}^{-1} \text{ K}^{-1}$ $0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1}$ Standard Temperature and Pressure (STP): $0^\circ C$ ($273.15 \text{ K}$) and $1 \text{ atm}$ Standard Ambient Temperature and Pressure (SATP): $25^\circ C$ ($298.15 \text{ K}$) and $1 \text{ bar}$