Chapter 17 - Spontaneity, Entropy, and Free Energy

17.1 Spontaneous Processes and Entropy

Thermodynamics can tell us the direction in which a process will occur but can say nothing about the speed of the process.
- Thermodynamics considers only the initial and final states and does not require knowledge of the pathway between reactants and products
- It lets us predict whether a process will occur but gives no information about the amount of time required for the process
The driving force for a spontaneous process is an increase in the entropy of the universe
Entropy is a thermodynamic function that describes the number of arrangements that are available to a system existing in a given state.
- Entropy can be viewed as a measure of molecular randomness or disorder.
Nature spontaneously proceeds toward the states that have the highest probabilities of existing
Solids are more ordered than liquids or gases and thus have lower entropy
The tendency to mix is due to the increased volume available to the particles of each component of the mixture
- For example, when two liquids are mixed, the molecules of each liquid have more available volume and thus more available positions

The total energy of the universe is constant, but the entropy is increasing
Using entropy, thermodynamics can predict the direction in which a process will occur spontaneously
For a spontaneous process, ▵Suniv must be positive
- For a process at constant temperature and pressure: ▵Ssys is dominated by “positional” entropy
- For a chemical reaction, ▵Ssys is dominated by changes in the number of gaseous molecules
▵Ssurr is positive for an exothermic process (▵H is negative)
Because ▵Ssurr depends inversely on T, exothermicity becomes a more important driving force at low temperatures
Thermodynamics cannot predict the rate at which a system will spontaneously change; the principles of kinetics are necessary to do this

The central idea is that the entropy changes in the surroundings are primarily determined by heat flow
In an endothermic process, heat flows from the surroundings into the system. In an exothermic process, heat flows into the surroundings from the system.
The significance of exothermicity as a driving force depends on the temperature at which the process occurs
In a process occurring at a constant temperature, the tendency for the system to lower its energy results from the positive value of ▵Ssurr
The transfer of a given quantity of energy as heat produces a much greater percent change in the randomness of the surroundings at a low temperature than it does at a high temperature
When no subscript is present, the quantity (for example, ▵H) refers to the system
The minus sign changes the point of view from the system to the surroundings
Exothermicity is most important as a driving force at low temperatures

Free energy is a state function
A process occurring at constant temperature and pressure is spontaneous in the direction in which its free energy decreases
For a reaction, the standard free energy change is the change in free energy that occurs when reactants in their standard states are converted to products in their standard states
N any real process, w < wmax
When energy is used to do work in a real process, the energy of the universe remains constant but the usefulness of the energy decreases
Concentrated energy is spread out in the surroundings as thermal energy

****Fewer molecules mean fewer possible configurations
When a reaction involves gaseous molecules, the change in positional entropy is dominated by the relative numbers of molecules of gaseous reactants and products.
If the number of molecules of the gaseous products is greater than the number of molecules of the gaseous reactants, positional entropy typically increases, and ▵S will be positive for the reaction.
Every particle must be in its place
The standard entropy values represent the increase in entropy that occurs when a substance is heated from 0 K to 298 K at 1 atm pressure
Since entropy is a state function of the system, the entropy change for a given chemical reaction can be calculated by taking the difference between the standard entropy values of products and those of the reactants
The more complex the molecule, the higher the standard entropy value

****The standard free energy of formation of a substance is defined as the change in free energy that accompanies the formation of 1 mole of that substance from its constituent elements with all reactants and products in their standard states
- The standard free energy change for a reaction is not measured directly
The standard free energy of formation of an element in its standard state is zero
The number of moles of each reactant (nr) and product (np) must be used when calculating ▵G° for a reaction.
To get an accurate comparison of reaction tendencies, we must compare all reactions under the same pressure or concentration conditions

The free energy of a reaction system changes as the reaction proceeds because free energy is dependent on the pressure of a gas or on the concentration of species in the solution
To understand the pressure dependence of free energy, we need to know how pressure affects the thermodynamic functions that comprise free energy, that is, enthalpy and entropy
Q is the reaction quotient (from the law of mass action)
T is the temperature (K)
R is the gas law constant and is equal to 8.3145 J/K x mol
▵G° is the free energy change for the reaction with all reactants and products at a pressure of 1 atm

Equilibrium point occurs at the lowest value of free energy available to the reaction system
- When substances undergo a chemical reaction, the reaction proceeds to the minimum free energy

****The change in free energy is important quantitatively because it can tell us how much work can be done with a given process
In fact, the maximum possible useful work obtainable from a process at constant temperature and pressure is equal to the change in free energy
▵G for a spontaneous process represents the energy that is free to do useful work
Achieving the maximum work available from a spontaneous process can occur only via a hypothetical pathway. Any real pathway wastes energy.
In any real cyclic process in the system, work is changed to heat in the surroundings and the entropy of the universe increases
- This is another way of stating the second law of thermodynamics
When energy is used to do work, it becomes less organized and less concentrated and thus less useful
- Thus the crux of the energy problem is that we are rapidly consuming the concentrated energy found in fossil fuels.
- We must use these energy sources as wisely as possible