Thermodynamic Equations to Know for General Chemistry II

Thermodynamic equations are essential for understanding energy changes in chemical reactions. They help explain how energy is transferred, the heat involved, and the spontaneity of processes, connecting key concepts like enthalpy, entropy, and Gibbs free energy in General Chemistry II.

1. First Law of Thermodynamics

   • Energy cannot be created or destroyed, only transformed from one form to another.
   • The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
   • Mathematically expressed as ΔU = Q - W, where ΔU is the change in internal energy, Q is heat, and W is work.

2. Enthalpy Change Equation

   • Enthalpy (H) is a measure of the total heat content of a system.
   • The change in enthalpy (ΔH) is defined as ΔH = H_products - H_reactants.
   • It is used to quantify the heat absorbed or released during a chemical reaction at constant pressure.

3. Hess's Law

   • The total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps, regardless of the pathway taken.
   • It allows for the calculation of enthalpy changes for reactions that are difficult to measure directly.
   • Useful for determining standard enthalpy changes using known enthalpy values of formation.

4. Born-Haber Cycle

   • A thermodynamic cycle that relates the lattice energy of an ionic solid to its formation enthalpy.
   • It involves breaking down the formation of an ionic compound into several steps, including sublimation, ionization, and electron affinity.
   • Helps in calculating the lattice energy using Hess's Law.

5. Gibbs Free Energy Equation

   • Gibbs free energy (G) determines the spontaneity of a process at constant temperature and pressure.
   • The equation is ΔG = ΔH - TΔS, where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.
   • A negative ΔG indicates a spontaneous process, while a positive ΔG indicates non-spontaneity.

6. Second Law of Thermodynamics

   • States that the total entropy of an isolated system can never decrease over time; it can only increase or remain constant.
   • Introduces the concept of irreversibility in natural processes and the direction of spontaneous change.
   • Entropy is a measure of disorder or randomness in a system.

7. Entropy Change Equation

   • The change in entropy (ΔS) can be calculated using ΔS = Q_rev / T, where Q_rev is the reversible heat transfer and T is the temperature in Kelvin.
   • Entropy changes can also be calculated for phase changes and chemical reactions.
   • A positive ΔS indicates an increase in disorder, while a negative ΔS indicates a decrease.

8. Third Law of Thermodynamics

   • States that as the temperature of a perfect crystal approaches absolute zero, the entropy approaches a constant minimum.
   • At absolute zero (0 K), the entropy of a perfect crystal is zero.
   • Provides a reference point for the calculation of absolute entropies of substances.

9. Heat Capacity Equations

   • Heat capacity (C) is the amount of heat required to change the temperature of a substance by one degree Celsius.
   • Specific heat capacity (c) is defined as C = q / (mΔT), where q is the heat added, m is the mass, and ΔT is the change in temperature.
   • Heat capacity can be constant at constant pressure (Cp) or constant volume (Cv), with Cp > Cv for gases.

10. Van 't Hoff Equation

    • Relates the change in the equilibrium constant (K) of a reaction to the change in temperature.
    • The equation is ln(K2/K1) = -ΔH/R (1/T2 - 1/T1), where ΔH is the change in enthalpy, R is the gas constant, and T is the temperature.
    • Useful for predicting how temperature changes affect the position of equilibrium in chemical reactions.