Thermodynamics: Key Chemistry Formulae

1. Internal Energy and Work

1.1 First Law of Thermodynamics

• Formula: $\Delta U=q+w$
• • Explanation: The first law of thermodynamics states that the change in internal energy of a system is equal to the sum of the heat added to the system and the work done on the system.
  • Units: $\Delta U$ (Joules), $q$ (Joules), $w$ (Joules)
  • Conditions: Applicable to any thermodynamic process.

1.2 Work Done by/on the System

• Formula: $w=-p_{\text{ext}}\Delta V$
• • Explanation: This equation calculates the work done on or by a gas during expansion or compression. The negative sign indicates work done by the system.
  • Units: $w$ (Joules), $p_{\text{ext}}$ (Pascals), $\Delta V$ (cubic meters)
  • Conditions: Valid for processes with constant external pressure.

Common Mistake:

Students often forget to account for the sign convention when calculating work done by or on the system. Always remember that work done by the system is negative, and work done on the system is positive.

2. Enthalpy and Heat

2.1 Relationship between $\Delta U$ and $\Delta H$

• Formula: $\Delta H=\Delta U+\Delta (pV)$
• • Explanation: The change in enthalpy of a system is equal to the change in internal energy plus the product of pressure and change in volume.
  • Units: $\Delta H$ (Joules), $\Delta U$ (Joules), $p$ (Pascals), $V$ (cubic meters)
  • Conditions: Applicable for processes at constant pressure.

2.2 Enthalpy Change at Constant Pressure

• Formula: $\Delta H=q_p$
• • Explanation: At constant pressure, the change in enthalpy is equal to the heat absorbed or released by the system.
  • Units: $\Delta H$ (Joules), $q_p$ (Joules)
  • Conditions: Applicable to isobaric processes.

Real-life Application:

Enthalpy changes are crucial in designing industrial processes such as chemical reactors, where maintaining specific temperature conditions is essential for product yield.

3. Thermodynamic Processes

3.1 Isothermal Process

• Formula: $w_{\text{rev}}=-nRT\ln \left(\frac{V_f}{V_i}\right)$
• • Explanation: For an isothermal process, the work done by the gas is calculated using the logarithmic relation between initial and final volumes.
  • Units: $w_{\text{rev}}$ (Joules), $n$ (moles), $R$ (Joules/mol·K), $T$ (Kelvin), $V$ (cubic meters)
  • Conditions: Applicable only to isothermal, reversible processes.

3.2 Adiabatic Process

• Formula: $\Delta U=w_{\text{ad}}$
• • Explanation: In an adiabatic process, there is no heat exchange with the surroundings, so the change in internal energy equals the work done on or by the system.
  • Units: $\Delta U$ (Joules), $w_{\text{ad}}$ (Joules)
  • Conditions: No heat exchange (adiabatic condition).

Mnemonic:

"Isothermal equals no thermal" — in isothermal processes, the temperature remains constant, whereas in adiabatic processes, there's no heat exchange.

4. Enthalpy Changes for Reactions

4.1 Hess's Law

• Formula: $\Delta H_{\text{reaction}}=\sum \Delta H_f\text{(products)}-\sum \Delta H_f\text{(reactants)}$
• • Explanation: The total enthalpy change of a reaction is the difference between the sum of enthalpies of formation of the products and the reactants.
  • Units: $\Delta H_{\text{reaction}}$ (kJ/mol)
  • Conditions: Applies to reactions at constant pressure.

4.2 Bond Enthalpy

• Formula: $\Delta H_{\text{reaction}}=\sum \text{(Bond energies of reactants)}-\sum \text{(Bond energies of products)}$
• • Explanation: The enthalpy change in a reaction can also be calculated using the bond energies of the reactants and products.
  • Units: kJ/mol
  • Conditions: Valid for reactions involving gaseous molecules.

NEET Problem-Solving Strategy:

When using bond enthalpies to calculate reaction enthalpies, ensure all species are in the gaseous state. This method provides an approximate value and may differ slightly from standard enthalpy changes due to deviations in bond energies.

5. Thermochemical Equations

5.1 Standard Enthalpy of Formation

• Formula: $\Delta H_f^{\circ }=\Delta H_{\text{reaction}}$ (for one mole of product formed from its elements in their standard states)
• • Explanation: The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its elements in their most stable forms under standard conditions.
  • Units: $\Delta H_f^{\circ }$ (kJ/mol)
  • Conditions: Standard conditions (298 K, 1 atm).

Common Misconception:

Students often confuse bond enthalpy with bond dissociation energy. Remember, bond enthalpy is the average energy required to break a bond in a molecule, while bond dissociation energy refers to a specific bond in a specific molecule.

Quick Recap:

• The first law of thermodynamics relates internal energy to heat and work.
• Work done by a system during expansion/compression is given by $w=-p_{\text{ext}}\Delta V$.
• Enthalpy changes are crucial for understanding heat flow in chemical reactions, especially under constant pressure.
• Isothermal and adiabatic processes involve different relationships between heat, work, and internal energy.
• Hess's Law and bond enthalpies are useful for calculating reaction enthalpies.

Concept Connection:

The concepts of enthalpy, internal energy, and thermodynamic processes also relate to Biology in areas like cellular respiration, where energy transformations are critical for biological functions.

This summary covers the critical formulae from the thermodynamics chapter, with explanations, conditions, and applications relevant for NEET preparation.