This revision note covers the fundamental principles of chemical thermodynamics, an essential topic for NEET. We will explore key concepts such as energy changes, spontaneity, and equilibrium, providing you with a solid foundation for solving related problems in the exam.
Key Concepts
- System and Surroundings: A system is the part of the universe under observation, while surroundings are everything else. Together, they constitute the universe. Systems can be open (exchange matter and energy), closed (exchange energy but not matter), or isolated (no exchange of matter or energy).
- State Functions vs. Path Functions: State functions are properties that depend only on the initial and final states of the system, not on how the change occurred (e.g., internal energy, enthalpy, entropy, Gibbs free energy, pressure, volume, temperature). Path functions depend on the path taken (e.g., heat, work).
- Extensive vs. Intensive Properties: Extensive properties depend on the amount of matter in the system (e.g., mass, volume, internal energy, enthalpy, entropy). Intensive properties do not depend on the amount of matter (e.g., temperature, pressure, density, molar heat capacity).
- Internal Energy ($U$ or $E$): The total energy contained within a thermodynamic system, including kinetic and potential energies of its particles. It is a state function.
- First Law of Thermodynamics: States that energy cannot be created or destroyed, only transferred or converted from one form to another. Mathematically, it relates the change in internal energy ($\Delta U$) to heat ($q$) absorbed by the system and work ($w$) done on the system: $\Delta U = q + w$.
- Heat ($q$): Energy transferred due to a temperature difference. Endothermic processes absorb heat ($q > 0$), exothermic processes release heat ($q < 0$).
- Work ($w$): Energy transferred due to a force acting over a distance. In chemistry, pressure-volume work is common: $w = -P_{\text{ext}}\Delta V$. Work done by the system on the surroundings is negative, work done on the system by the surroundings is positive.
- Enthalpy ($H$): A thermodynamic potential, defined as $H = U + PV$. At constant pressure, the change in enthalpy ($\Delta H$) equals the heat exchanged: $\Delta H = q_p$. For reactions involving gases, $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in the number of moles of gaseous products minus gaseous reactants.
- Hess's Law of Constant Heat Summation: If a reaction can be expressed as the algebraic sum of two or more other reactions, then the enthalpy change for the overall reaction is the sum of the enthalpy changes for the component reactions.
- Entropy ($S$): A measure of the randomness or disorder of a system. A positive change in entropy ($\Delta S > 0$) indicates an increase in disorder. Entropy generally increases from solid to liquid to gas.
- Second Law of Thermodynamics: States that for any spontaneous process, the total entropy of the universe (system + surroundings) always increases: $\Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0$.
- Third Law of Thermodynamics: States that the entropy of a perfect crystalline substance is zero at absolute zero temperature (0 K).
- Gibbs Free Energy ($G$): A thermodynamic potential that measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Defined as $G = H - TS$. It determines the spontaneity of a process at constant temperature and pressure.
- Spontaneity: A process is spontaneous if it occurs without external intervention. For processes at constant T and P, $\Delta G < 0$ implies spontaneity, $\Delta G > 0$ implies non-spontaneity, and $\Delta G = 0$ implies the system is at equilibrium.
- Standard Conditions: Usually $298.15 \text{ K}$ ($25^\circ \text{C}$) and $1 \text{ atm}$ pressure (or $1 \text{ bar}$ for modern thermochemistry). Standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its elements in their most stable states under standard conditions.
Formulas & Results
- First Law of Thermodynamics: $$\Delta U = q + w$$
- Pressure-Volume Work: $$w = -P_{\text{ext}}\Delta V$$ For a reversible isothermal expansion of an ideal gas: $$w = -2.303 nRT \log \left(\frac{V_2}{V_1}\right) = -2.303 nRT \log \left(\frac{P_1}{P_2}\right)$$
- Enthalpy Change at Constant Pressure: $$\Delta H = q_p$$
- Relationship between $\Delta H$ and $\Delta U$: For reactions involving gases: $$\Delta H = \Delta U + \Delta n_g RT$$ where $\Delta n_g = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$
- Heat Capacity (C): $$C = \frac{q}{\Delta T}$$ At constant volume: $C_v = \left(\frac{\partial U}{\partial T}\right)_V$ (relates to $\Delta U$) At constant pressure: $C_p = \left(\frac{\partial H}{\partial T}\right)_P$ (relates to $\Delta H$)
- Relationship between $C_p$ and $C_v$ for ideal gases: $$C_p - C_v = nR \quad (\text{for n moles})$$ $$C_{p,m} - C_{v,m} = R \quad (\text{for molar heat capacities})$$
- Entropy Change: For a general process: $$\Delta S = \int \frac{dq_{\text{rev}}}{T}$$ For phase transition (e.g., melting, vaporization) at constant T: $$\Delta S_{\text{transition}} = \frac{\Delta H_{\text{transition}}}{T_{\text{transition}}}$$ For a chemical reaction: $$\Delta S^\circ = \sum S^\circ (\text{products}) - \sum S^\circ (\text{reactants})$$
- Gibbs Free Energy Change: $$\Delta G = \Delta H - T\Delta S$$ Under standard conditions: $$\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$$
- Spontaneity Criteria (at constant T and P):
- $\Delta G < 0$: Spontaneous
- $\Delta G > 0$: Non-spontaneous
- $\Delta G = 0$: Equilibrium
- Relationship between $\Delta G^\circ$ and Equilibrium Constant ($K$): $$\Delta G^\circ = -RT \ln K$$ $$\Delta G = \Delta G^\circ + RT \ln Q$$ where $Q$ is the reaction quotient. At equilibrium, $\Delta G = 0$ and $Q = K$.
- Temperature dependence of Spontaneity (based on $\Delta G = \Delta H - T\Delta S$):
$\Delta H$ $\Delta S$ $\Delta G = \Delta H - T\Delta S$ Spontaneity - + Always - Spontaneous at all T + - Always + Non-spontaneous at all T - - - at low T, + at high T Spontaneous at low T + + + at low T, - at high T Spontaneous at high T
Worked Examples
Example 1: Calculate the work done when 2 moles of an ideal gas expand isothermally and reversibly from 10 L to 20 L at $27^\circ \text{C}$. ($R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$)
Solution: Given: $n = 2 \text{ mol}$, $V_1 = 10 \text{ L}$, $V_2 = 20 \text{ L}$, $T = 27^\circ \text{C} = 27 + 273 = 300 \text{ K}$, $R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$. For a reversible isothermal expansion of an ideal gas, the work done is: $$w = -2.303 nRT \log \left(\frac{V_2}{V_1}\right)$$ $$w = -2.303 \times 2 \text{ mol} \times 8.314 \text{ J K}^{-1} \text{mol}^{-1} \times 300 \text{ K} \times \log \left(\frac{20 \text{ L}}{10 \text{ L}}\right)$$ $$w = -2.303 \times 2 \times 8.314 \times 300 \times \log(2)$$ $$w = -2.303 \times 2 \times 8.314 \times 300 \times 0.3010$$ $$w = -3459.7 \text{ J}$$ $$w = -3.46 \text{ kJ}$$ The work done by the system is $-3.46 \text{ kJ}$.
Example 2: For a reaction, $\Delta H = -120 \text{ kJ}$ and $\Delta S = -100 \text{ J K}^{-1}$ at $298 \text{ K}$. Is the reaction spontaneous at this temperature?
Solution: Given: $\Delta H = -120 \text{ kJ} = -120000 \text{ J}$, $\Delta S = -100 \text{ J K}^{-1}$, $T = 298 \text{ K}$. We can determine spontaneity using the Gibbs free energy change formula: $$\Delta G = \Delta H - T\Delta S$$ $$\Delta G = -120000 \text{ J} - (298 \text{ K} \times -100 \text{ J K}^{-1})$$ $$\Delta G = -120000 \text{ J} - (-29800 \text{ J})$$ $$\Delta G = -120000 \text{ J} + 29800 \text{ J}$$ $$\Delta G = -90200 \text{ J}$$ $$\Delta G = -90.2 \text{ kJ}$$ Since $\Delta G$ is negative ($-90.2 \text{ kJ} < 0$), the reaction is spontaneous at $298 \text{ K}$.
Example 3: Calculate $\Delta U$ for a system that absorbs $15 \text{ kJ}$ of heat from the surroundings and does $5 \text{ kJ}$ of work on the surroundings.
Solution: Given: Heat absorbed by the system, $q = +15 \text{ kJ}$ (positive because absorbed). Work done by the system on the surroundings, $w = -5 \text{ kJ}$ (negative because done by the system). Using the First Law of Thermodynamics: $$\Delta U = q + w$$ $$\Delta U = 15 \text{ kJ} + (-5 \text{ kJ})$$ $$\Delta U = 15 \text{ kJ} - 5 \text{ kJ}$$ $$\Delta U = 10 \text{ kJ}$$ The change in internal energy is $+10 \text{ kJ}$.
Common Mistakes
- Sign Conventions for Heat and Work: Confusing the signs for heat absorbed/released and work done on/by the system. Remember: $q > 0$ for heat absorbed, $q < 0$ for heat released; $w > 0$ for work done on the system, $w < 0$ for work done by the system.
- Units: Not converting units consistently (e.g., J to kJ, L atm to J). Always check that all quantities are in compatible units before calculation. Using $R$ in appropriate units (e.g., $8.314 \text{ J K}^{-1} \text{mol}^{-1}$ or $0.0821 \text{ L atm K}^{-1} \text{mol}^{-1}$).
- Standard Conditions: Not recognizing when standard conditions apply or assuming they apply when they don't.
- $\Delta n_g$ Calculation: Errors in calculating $\Delta n_g$ for the $\Delta H = \Delta U + \Delta n_g RT$ equation, especially forgetting to include only gaseous reactants and products.
- Spontaneity Criteria: Incorrectly using $\Delta H$ or $\Delta S$ alone to predict spontaneity instead of $\Delta G$, which accounts for both at constant T and P.
- Reversible vs. Irreversible Processes: Applying formulas for reversible processes (e.g., work calculation) to irreversible processes mistakenly.
- Extensive vs. Intensive Properties: Mixing up extensive and intensive properties, especially when dealing with molar quantities.
Quick Revision Checklist
- Define system, surroundings, extensive, intensive, state function, path function.
- State and apply the First Law of Thermodynamics ($\Delta U = q + w$) with correct sign conventions.
- Calculate pressure-volume work ($w = -P_{\text{ext}}\Delta V$) and work for reversible isothermal expansion.
- Understand enthalpy, its relation to heat at constant pressure ($\Delta H = q_p$), and the relationship $\Delta H = \Delta U + \Delta n_g RT$.
- Apply Hess's Law to calculate enthalpy changes.
- Define entropy and predict its change based on physical state, number of particles, and temperature.
- State the Second Law of Thermodynamics and its implications for spontaneity.
- Define Gibbs free energy ($G = H - TS$) and its role in determining spontaneity ($\Delta G < 0$).
- Analyze the effect of $\Delta H, \Delta S,$ and $T$ on spontaneity.
- Connect $\Delta G^\circ$ to the equilibrium constant $K$ ($\Delta G^\circ = -RT \ln K$).
- Know standard state definitions.
