Entropy PDF

# Entropy (S) - Definition: A measure of disorder or randomness in a system. - Equation: $ΔS = \sum S_{products} - \sum S_{reactants}$ - Second Law of Thermodynamics: In any spontaneous process, the entropy of the universe increases. - Third Law of Thermodynamics: The entropy of a perfect crystall...

# Entropy (S) - Definition: A measure of disorder or randomness in a system. - Equation: $ΔS = \sum S_{products} - \sum S_{reactants}$ - Second Law of Thermodynamics: In any spontaneous process, the entropy of the universe increases. - Third Law of Thermodynamics: The entropy of a perfect crystalline substance is zero at absolute zero (0 K). # Spontaneous Processes - Criteria for Spontaneity: A process is spontaneous if it leads to an increase in the entropy of the universe. - Free Energy (G): Combines enthalpy (H) and entropy (S) to predict spontaneity. - Equation: $ΔG = ΔH - TΔS$ Where $ΔG$ is the change in Gibbs free energy, $ΔH$ is the change in enthalpy, and T is the temperature in Kelvin. # Gibbs Free Energy (ΔG) - Spontaneity: - $ΔG < 0$: Spontaneous process. - $ΔG > 0$: Non-spontaneous process. - $ΔG = 0$: Equilibrium. - Standard Free Energy Change (ΔG°): $ΔG° = \sum ΔG°_{products} - \sum ΔG°_{reactants}$ Where $ΔG°$ is the standard free energy of formation. - Relationship to Equilibrium Constant (K): $ΔG° = -RTlnK$ Where R is the gas constant (8.314 J/mol⋅K) and T is the temperature in Kelvin. # Equilibrium - At Equilibrium: - $ΔG = 0$ - The forward and reverse reactions occur at the same rate. - Equilibrium Constant (K): - Relationship between ΔG and K: $K = e^{-ΔG/RT}$ # Entropy Changes in Reactions - Entropy Change of the System (ΔSsys): $ΔSsys = \sum S_{products} - \sum S_{reactants}$ - Entropy Change of the Surroundings (ΔSsurr): $ΔSsurr = \frac{ΔH_{sys}}{T}$ Where $ΔH_{sys}$ is the enthalpy change of the system and T is the temperature in Kelvin. # Entropy and Free Energy in Biological Systems - Biological Reactions: Often driven by ATP hydrolysis. - Coupled Reactions: Non-spontaneous reactions can be driven by coupling them with spontaneous ones. - Equation for Coupled Reactions: $ΔG_{total} = ΔG_1 + ΔG_2$