Entropy
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Topic Summary & Highlights
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Core Concept
Entropy (S) is a thermodynamic quantity that measures the degree of randomness or disorder in a system.
Key Idea: The greater the number of possible arrangements (microstates) for a system, the higher its entropy.
State Function: Entropy depends only on the state of the system, not the path taken to reach that state.
Practice Tips
Entropy measures disorder and energy dispersal in a system.
Spontaneous processes increase the total entropy of the universe.
Factors like phase changes, temperature, and molecular complexity affect entropy.
The relationship between entropy, enthalpy, and temperature determines spontaneity through Gibbs free energy.
Factors Affecting Entropy
Phase Changes:
Solid → Liquid → Gas … Entropy increases.
Example: Melting and boiling increase entropy because molecules have more freedom of motion.
Temperature:
Entropy increases as temperature increases because molecules move more rapidly and occupy more possible energy levels.
Molecular Complexity:
Larger, more complex molecules have higher entropy because they can vibrate, rotate, and arrange themselves in more ways.
Mixing:
Mixing substances (e.g., dissolving salt in water) increases entropy because the components are more dispersed.
Entropy in Chemical Reactions
Standard Molar Entropy ($S^\circ$)
Definition: The entropy of 1 mole of a substance at a standard state (298 K, 1 atm).
Units: $\text{J/K}\cdot\text{mol}$ (Joules per Kelvin per mole).
Change in Entropy ($\Delta S^\circ$)
The change in entropy for a chemical reaction can be calculated using the standard molar entropies of the products and reactants:
$$\Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}}$$
Spontaneity and Entropy (Second Law of Thermodynamics)
A process is spontaneous (thermodynamically favored) if the change in entropy of the universe ($\Delta S_{\text{universe}}$) is greater than zero.
Condition for Spontaneity: $\Delta S_{\text{universe}} > 0$
Second Law of Thermodynamics
The total entropy of the universe ($\Delta S_{\text{universe}}$) always increases in a spontaneous process.
This is mathematically expressed as:
$$\Delta S_{\text{universe}} = \Delta S_{\text{system}} + \Delta S_{\text{surroundings}} > 0$$
Where:
$\Delta S_{\text{system}}$ is the change in entropy of the reacting system.
$\Delta S_{\text{surroundings}}$ is the change in entropy of the surroundings.
