Energy, Entropy, and Free Energy
Thermodynamics
- Provides information on whether a reaction is spontaneous based only on the properties of the reactants and products.
- Spontaneous process: Occurs without external intervention.
Entropy (S)
- Measure of molecular randomness or disorder.
- Thermodynamic function that describes the number of combinations available to a system in a given state.
- Nature spontaneously proceeds toward the states with the highest probabilities.
- S{solid} < S{liquid} < S_{gas}
- Entropy change when mixing two pure substances is expected to be positive.
Positional Probability
- Depends on the number of configurations in space that yield a particular state.
- Gas expands into a vacuum to give a uniform distribution.
Second Law of Thermodynamics
- In any spontaneous process, there is always an increase in the entropy of the universe.
- First law of thermodynamics: Energy of the universe is constant.
- \Delta S_{univ} > 0: Process is spontaneous in the direction written
- \Delta S_{univ} < 0: Process is spontaneous in the opposite direction.
- \Delta S_{univ} = 0: Process has no tendency to occur; system is at equilibrium.
Entropy Changes in the Surroundings (ΔSsurr)
- Determined by the flow of energy as heat.
- Exothermic process increases KE associated with the random motions of atoms in the surroundings so \Delta S_{surr} is positive.
- Endothermic process decreases KE associated with the random motions of atoms in the surroundings so \Delta S_{surr} is negative.
- Magnitude of \Delta S_{surr} depends on the magnitude of the heat and the temperature.
- \Delta S_{surr} = -\frac{quantity \space of \space heat (J)}{temperature (K)} = -\frac{\Delta H}{T}
Interplay of \Delta S{Sys} and \Delta S{Surr} in Determining the Sign of \Delta S_{univ}
- \Delta S{univ} = \Delta S{sys} + \Delta S_{surr}
Entropy Changes and Chemical Reactions
- \Delta S = S{product} – S{reactant}
- If the number of product molecules is greater than the number of reactant molecules, \Delta S is positive.
Entropy Values
- Third law of thermodynamics: Entropy of a perfect crystal at 0 K is zero.
- Standard entropy values (S^\circ) represent the increase in entropy when a substance is heated from 0 K to 298 K at 1 atm.
Entropy Change for a Given Chemical Reaction
- \Delta S^\circ = \sum npS^\circ{(products)} - \sum nrS^\circ{(reactants)}
Free Energy (G)
- G = H - TS
- At constant temperature, processes are spontaneous in the direction in which free energy decreases.
- Negative \Delta G means positive \Delta S_{univ}
Various Possible Combinations of \Delta H and \Delta S
- \Delta S positive, \Delta H negative: Spontaneous at all temperatures.
- \Delta S positive, \Delta H positive: Spontaneous at high temperatures.
- \Delta S negative, \Delta H negative: Spontaneous at low temperatures.
- \Delta S negative, \Delta H positive: Process not spontaneous at any temperature.
Standard Free Energy Change (\Delta G^\circ)
- Change in G that will occur if the reactants in their standard states are converted to the products in their standard states.
- Standard state: 1 atm and 25°C.
Methods for Calculating \Delta G^\circ
- \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ
- Treat free energy as a state function and use Hess’s law.
- Use standard free energy of formation.
- Change in free energy that accompanies the formation of 1 mole of a substance from its constituent elements.
- All reactants and products are in their standard states.
- \Delta G_f^\circ of an element in its standard state = 0.
Free Energy and Pressure
Free Energy Change at non-standard conditions
- \Delta G = \Delta G^\circ + RT\ln(Q)
Free Energy and Equilibrium
- System under constant P and T proceeds spontaneously in the direction that lowers its free energy.
- Equilibrium is the point where the free energy value is at its lowest.
- \Delta G^\circ = -RT\ln(K)
- \Delta G = \Delta G^\circ + RT\ln(Q)
Qualitative Relationship between the ΔG and the K for a Given Reaction
- \Delta G^\circ = 0, K = 1
- \Delta G^\circ < 0, K > 1
- \Delta G^\circ > 0, K < 1